Free Statistics

of Irreproducible Research!

Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationMon, 20 Jul 2015 13:52:53 +0100
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2015/Jul/20/t1437396825z7hiwsm4s1k1yxq.htm/, Retrieved Fri, 17 May 2024 03:46:40 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=279607, Retrieved Fri, 17 May 2024 03:46:40 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact144
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [(Partial) Autocorrelation Function] [STAP 20 Omzet vorken] [2015-07-20 11:10:10] [110a48b2e0105bb86f6db58fdf2bbafc]
- RMP     [Exponential Smoothing] [STAP 32 Omzet vorken] [2015-07-20 12:52:53] [70d22f55a70f3427b60459805adf1606] [Current]
Feedback Forum

Post a new message
Dataseries X:
209.704
208.923
208.131
206.492
222.706
221.848
209.704
201.630
202.411
202.411
203.280
204.842
207.273
207.273
205.711
201.630
222.706
225.918
221.067
209.704
214.566
207.273
210.562
212.135
213.774
209.704
210.562
204.842
222.706
228.349
223.498
214.566
224.279
213.774
223.498
222.706
225.137
216.205
225.918
225.137
239.712
236.423
223.498
216.986
225.918
213.774
222.706
224.279
227.568
220.286
224.279
226.710
235.642
228.349
218.636
208.131
217.855
191.125
204.061
211.343
218.636
208.131
208.131
208.131
213.774
205.711
195.129
186.274
192.698
167.618
182.985
191.917
193.556
184.624
185.405
182.985
191.125
185.405
174.130
165.979
179.762
149.831
169.268
178.123
178.123
167.618
157.905
157.124
165.979
157.905
142.549
131.967
143.330
116.611
140.899
153.824
157.905
148.973
137.687
145.761
148.973
146.542
122.243
110.968
119.031
94.743
119.823
128.755
136.037
123.893
112.530
119.031
122.243
115.819
91.531
80.949
90.662
63.943
93.093
110.968




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time1 seconds
R Server'Gertrude Mary Cox' @ cox.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 & 1 seconds \tabularnewline
R Server & 'Gertrude Mary Cox' @ cox.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=279607&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]1 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Gertrude Mary Cox' @ cox.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=279607&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=279607&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 time1 seconds
R Server'Gertrude Mary Cox' @ cox.wessa.net







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.379244790290799
beta0.0506954647934245
gamma1

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.379244790290799 \tabularnewline
beta & 0.0506954647934245 \tabularnewline
gamma & 1 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=279607&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]0.379244790290799[/C][/ROW]
[ROW][C]beta[/C][C]0.0506954647934245[/C][/ROW]
[ROW][C]gamma[/C][C]1[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=279607&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=279607&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
alpha0.379244790290799
beta0.0506954647934245
gamma1







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
13207.273207.288777052553-0.0157770525534602
14207.273206.8299027815750.443097218425038
15205.711204.9675755487380.743424451262086
16201.63200.8605780146490.769421985351045
17222.706222.059002683560.646997316439666
18225.918225.294208403140.623791596859775
19221.067213.2192904395187.84770956048249
20209.704208.5878887447651.11611125523456
21214.566210.5624811982984.00351880170243
22207.273213.039144462174-5.76614446217437
23210.562212.504887988126-1.94288798812605
24212.135213.727772814231-1.59277281423135
25213.774215.457559407833-1.68355940783329
26209.704214.728578432258-5.02457843225804
27210.562210.911162313747-0.3491623137472
28204.842206.259859534994-1.41785953499394
29222.706226.888664965202-4.18266496520212
30228.349228.1342385610240.214761438975898
31223.498220.0627084438343.43529155616574
32214.566209.3135033853455.25249661465503
33224.279214.4819392941659.79706070583455
34213.774212.8979110552090.876088944790581
35223.498217.420557918126.07744208188035
36222.706222.1966933283720.509306671628337
37225.137225.0179551612920.119044838708191
38216.205223.029377023733-6.82437702373321
39225.918221.7269985409274.19100145907277
40225.137218.1383504801996.99864951980143
41239.712242.260944864292-2.54894486429168
42236.423247.891831082428-11.4688310824285
43223.498237.307132658466-13.8091326584658
44216.986220.708405919398-3.72240591939837
45225.918225.1583748656520.759625134347687
46213.774214.233808115771-0.459808115771068
47222.706221.0964254611951.60957453880525
48224.279220.2990139880053.97998601199549
49227.568223.815465660743.75253433926005
50220.286218.5490075840121.7369924159876
51224.279227.281642436786-3.00264243678578
52226.71222.3819542669694.32804573303068
53235.642239.141738568628-3.49973856862795
54228.349238.383800421265-10.034800421265
55218.636226.433059979-7.79705997899987
56208.131218.142862268434-10.0118622684339
57217.855222.533923294128-4.6789232941276
58191.125208.635820164756-17.510820164756
59204.061209.080383965529-5.01938396552856
60211.343206.3248208566885.01817914331207
61218.636209.0705557039199.56544429608113
62208.131204.5387421962873.59225780371281
63208.131209.977374038734-1.84637403873373
64208.131209.301604060578-1.17060406057766
65213.774217.474967240869-3.70096724086869
66205.711211.964580905593-6.25358090559251
67195.129202.592079216557-7.46307921655739
68186.274192.806507496189-6.53250749618917
69192.698200.104467409179-7.40646740917879
70167.618178.070425012803-10.452425012803
71182.985186.930733516513-3.94573351651286
72191.917189.6186516709452.29834832905502
73193.556192.9621761564840.593823843516191
74184.624181.8304212224012.79357877759935
75185.405182.6306380530632.77436194693666
76182.985183.284762212761-0.299762212760925
77191.125188.5567869251012.56821307489858
78185.405183.7743973383711.63060266162859
79174.13176.873985086713-2.74398508671334
80165.979169.616104800007-3.63710480000731
81179.762176.1157558871523.64624411284842
82149.831157.743574243941-7.9125742439409
83169.268170.137211494148-0.86921149414772
84178.123177.1792257476990.94377425230104
85178.123178.713942535505-0.590942535505178
86167.618169.117807551052-1.49980755105224
87157.905168.053277087641-10.1482770876408
88157.124161.652995241578-4.52899524157834
89165.979165.5611702883650.417829711635221
90157.905159.566277660805-1.66127766080501
91142.549149.466998056761-6.91799805676089
92131.967140.354209254904-8.38720925490369
93143.33146.451553321435-3.12155332143521
94116.611122.493770384993-5.88277038499318
95140.899135.0629684137665.83603158623447
96153.824143.18364846263510.6403515373649
97157.905146.6238272084611.2811727915403
98148.973141.9802828963516.99271710364931
99137.687139.130749581577-1.44374958157701
100145.761139.2171731693316.54382683066854
101148.973149.622092208008-0.649092208007971
102146.542142.728791264223.81320873578039
103122.243132.645025010742-10.4020250107423
104110.968121.973308597339-11.005308597339
105119.031128.958486979794-9.92748697979377
10694.743103.575684108377-8.83268410837729
107119.823118.8261656310550.996834368945343
108128.755126.1103412889252.64465871107477
109136.037126.1511506774179.88584932258301
110123.893119.7073528782514.18564712174945
111112.53111.9455660051080.584433994892322
112119.031116.0676015132962.96339848670412
113122.243119.2895697803242.95343021967608
114115.819116.658069219592-0.839069219591849
11591.53199.4223214903654-7.89132149036541
11680.94990.0585969382313-9.10959693823133
11790.66295.0094114319616-4.34741143196162
11863.94376.2800396211328-12.3370396211328
11993.09389.40512823175533.6878717682447
120110.96895.932143899224615.0358561007754

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 207.273 & 207.288777052553 & -0.0157770525534602 \tabularnewline
14 & 207.273 & 206.829902781575 & 0.443097218425038 \tabularnewline
15 & 205.711 & 204.967575548738 & 0.743424451262086 \tabularnewline
16 & 201.63 & 200.860578014649 & 0.769421985351045 \tabularnewline
17 & 222.706 & 222.05900268356 & 0.646997316439666 \tabularnewline
18 & 225.918 & 225.29420840314 & 0.623791596859775 \tabularnewline
19 & 221.067 & 213.219290439518 & 7.84770956048249 \tabularnewline
20 & 209.704 & 208.587888744765 & 1.11611125523456 \tabularnewline
21 & 214.566 & 210.562481198298 & 4.00351880170243 \tabularnewline
22 & 207.273 & 213.039144462174 & -5.76614446217437 \tabularnewline
23 & 210.562 & 212.504887988126 & -1.94288798812605 \tabularnewline
24 & 212.135 & 213.727772814231 & -1.59277281423135 \tabularnewline
25 & 213.774 & 215.457559407833 & -1.68355940783329 \tabularnewline
26 & 209.704 & 214.728578432258 & -5.02457843225804 \tabularnewline
27 & 210.562 & 210.911162313747 & -0.3491623137472 \tabularnewline
28 & 204.842 & 206.259859534994 & -1.41785953499394 \tabularnewline
29 & 222.706 & 226.888664965202 & -4.18266496520212 \tabularnewline
30 & 228.349 & 228.134238561024 & 0.214761438975898 \tabularnewline
31 & 223.498 & 220.062708443834 & 3.43529155616574 \tabularnewline
32 & 214.566 & 209.313503385345 & 5.25249661465503 \tabularnewline
33 & 224.279 & 214.481939294165 & 9.79706070583455 \tabularnewline
34 & 213.774 & 212.897911055209 & 0.876088944790581 \tabularnewline
35 & 223.498 & 217.42055791812 & 6.07744208188035 \tabularnewline
36 & 222.706 & 222.196693328372 & 0.509306671628337 \tabularnewline
37 & 225.137 & 225.017955161292 & 0.119044838708191 \tabularnewline
38 & 216.205 & 223.029377023733 & -6.82437702373321 \tabularnewline
39 & 225.918 & 221.726998540927 & 4.19100145907277 \tabularnewline
40 & 225.137 & 218.138350480199 & 6.99864951980143 \tabularnewline
41 & 239.712 & 242.260944864292 & -2.54894486429168 \tabularnewline
42 & 236.423 & 247.891831082428 & -11.4688310824285 \tabularnewline
43 & 223.498 & 237.307132658466 & -13.8091326584658 \tabularnewline
44 & 216.986 & 220.708405919398 & -3.72240591939837 \tabularnewline
45 & 225.918 & 225.158374865652 & 0.759625134347687 \tabularnewline
46 & 213.774 & 214.233808115771 & -0.459808115771068 \tabularnewline
47 & 222.706 & 221.096425461195 & 1.60957453880525 \tabularnewline
48 & 224.279 & 220.299013988005 & 3.97998601199549 \tabularnewline
49 & 227.568 & 223.81546566074 & 3.75253433926005 \tabularnewline
50 & 220.286 & 218.549007584012 & 1.7369924159876 \tabularnewline
51 & 224.279 & 227.281642436786 & -3.00264243678578 \tabularnewline
52 & 226.71 & 222.381954266969 & 4.32804573303068 \tabularnewline
53 & 235.642 & 239.141738568628 & -3.49973856862795 \tabularnewline
54 & 228.349 & 238.383800421265 & -10.034800421265 \tabularnewline
55 & 218.636 & 226.433059979 & -7.79705997899987 \tabularnewline
56 & 208.131 & 218.142862268434 & -10.0118622684339 \tabularnewline
57 & 217.855 & 222.533923294128 & -4.6789232941276 \tabularnewline
58 & 191.125 & 208.635820164756 & -17.510820164756 \tabularnewline
59 & 204.061 & 209.080383965529 & -5.01938396552856 \tabularnewline
60 & 211.343 & 206.324820856688 & 5.01817914331207 \tabularnewline
61 & 218.636 & 209.070555703919 & 9.56544429608113 \tabularnewline
62 & 208.131 & 204.538742196287 & 3.59225780371281 \tabularnewline
63 & 208.131 & 209.977374038734 & -1.84637403873373 \tabularnewline
64 & 208.131 & 209.301604060578 & -1.17060406057766 \tabularnewline
65 & 213.774 & 217.474967240869 & -3.70096724086869 \tabularnewline
66 & 205.711 & 211.964580905593 & -6.25358090559251 \tabularnewline
67 & 195.129 & 202.592079216557 & -7.46307921655739 \tabularnewline
68 & 186.274 & 192.806507496189 & -6.53250749618917 \tabularnewline
69 & 192.698 & 200.104467409179 & -7.40646740917879 \tabularnewline
70 & 167.618 & 178.070425012803 & -10.452425012803 \tabularnewline
71 & 182.985 & 186.930733516513 & -3.94573351651286 \tabularnewline
72 & 191.917 & 189.618651670945 & 2.29834832905502 \tabularnewline
73 & 193.556 & 192.962176156484 & 0.593823843516191 \tabularnewline
74 & 184.624 & 181.830421222401 & 2.79357877759935 \tabularnewline
75 & 185.405 & 182.630638053063 & 2.77436194693666 \tabularnewline
76 & 182.985 & 183.284762212761 & -0.299762212760925 \tabularnewline
77 & 191.125 & 188.556786925101 & 2.56821307489858 \tabularnewline
78 & 185.405 & 183.774397338371 & 1.63060266162859 \tabularnewline
79 & 174.13 & 176.873985086713 & -2.74398508671334 \tabularnewline
80 & 165.979 & 169.616104800007 & -3.63710480000731 \tabularnewline
81 & 179.762 & 176.115755887152 & 3.64624411284842 \tabularnewline
82 & 149.831 & 157.743574243941 & -7.9125742439409 \tabularnewline
83 & 169.268 & 170.137211494148 & -0.86921149414772 \tabularnewline
84 & 178.123 & 177.179225747699 & 0.94377425230104 \tabularnewline
85 & 178.123 & 178.713942535505 & -0.590942535505178 \tabularnewline
86 & 167.618 & 169.117807551052 & -1.49980755105224 \tabularnewline
87 & 157.905 & 168.053277087641 & -10.1482770876408 \tabularnewline
88 & 157.124 & 161.652995241578 & -4.52899524157834 \tabularnewline
89 & 165.979 & 165.561170288365 & 0.417829711635221 \tabularnewline
90 & 157.905 & 159.566277660805 & -1.66127766080501 \tabularnewline
91 & 142.549 & 149.466998056761 & -6.91799805676089 \tabularnewline
92 & 131.967 & 140.354209254904 & -8.38720925490369 \tabularnewline
93 & 143.33 & 146.451553321435 & -3.12155332143521 \tabularnewline
94 & 116.611 & 122.493770384993 & -5.88277038499318 \tabularnewline
95 & 140.899 & 135.062968413766 & 5.83603158623447 \tabularnewline
96 & 153.824 & 143.183648462635 & 10.6403515373649 \tabularnewline
97 & 157.905 & 146.62382720846 & 11.2811727915403 \tabularnewline
98 & 148.973 & 141.980282896351 & 6.99271710364931 \tabularnewline
99 & 137.687 & 139.130749581577 & -1.44374958157701 \tabularnewline
100 & 145.761 & 139.217173169331 & 6.54382683066854 \tabularnewline
101 & 148.973 & 149.622092208008 & -0.649092208007971 \tabularnewline
102 & 146.542 & 142.72879126422 & 3.81320873578039 \tabularnewline
103 & 122.243 & 132.645025010742 & -10.4020250107423 \tabularnewline
104 & 110.968 & 121.973308597339 & -11.005308597339 \tabularnewline
105 & 119.031 & 128.958486979794 & -9.92748697979377 \tabularnewline
106 & 94.743 & 103.575684108377 & -8.83268410837729 \tabularnewline
107 & 119.823 & 118.826165631055 & 0.996834368945343 \tabularnewline
108 & 128.755 & 126.110341288925 & 2.64465871107477 \tabularnewline
109 & 136.037 & 126.151150677417 & 9.88584932258301 \tabularnewline
110 & 123.893 & 119.707352878251 & 4.18564712174945 \tabularnewline
111 & 112.53 & 111.945566005108 & 0.584433994892322 \tabularnewline
112 & 119.031 & 116.067601513296 & 2.96339848670412 \tabularnewline
113 & 122.243 & 119.289569780324 & 2.95343021967608 \tabularnewline
114 & 115.819 & 116.658069219592 & -0.839069219591849 \tabularnewline
115 & 91.531 & 99.4223214903654 & -7.89132149036541 \tabularnewline
116 & 80.949 & 90.0585969382313 & -9.10959693823133 \tabularnewline
117 & 90.662 & 95.0094114319616 & -4.34741143196162 \tabularnewline
118 & 63.943 & 76.2800396211328 & -12.3370396211328 \tabularnewline
119 & 93.093 & 89.4051282317553 & 3.6878717682447 \tabularnewline
120 & 110.968 & 95.9321438992246 & 15.0358561007754 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=279607&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]207.273[/C][C]207.288777052553[/C][C]-0.0157770525534602[/C][/ROW]
[ROW][C]14[/C][C]207.273[/C][C]206.829902781575[/C][C]0.443097218425038[/C][/ROW]
[ROW][C]15[/C][C]205.711[/C][C]204.967575548738[/C][C]0.743424451262086[/C][/ROW]
[ROW][C]16[/C][C]201.63[/C][C]200.860578014649[/C][C]0.769421985351045[/C][/ROW]
[ROW][C]17[/C][C]222.706[/C][C]222.05900268356[/C][C]0.646997316439666[/C][/ROW]
[ROW][C]18[/C][C]225.918[/C][C]225.29420840314[/C][C]0.623791596859775[/C][/ROW]
[ROW][C]19[/C][C]221.067[/C][C]213.219290439518[/C][C]7.84770956048249[/C][/ROW]
[ROW][C]20[/C][C]209.704[/C][C]208.587888744765[/C][C]1.11611125523456[/C][/ROW]
[ROW][C]21[/C][C]214.566[/C][C]210.562481198298[/C][C]4.00351880170243[/C][/ROW]
[ROW][C]22[/C][C]207.273[/C][C]213.039144462174[/C][C]-5.76614446217437[/C][/ROW]
[ROW][C]23[/C][C]210.562[/C][C]212.504887988126[/C][C]-1.94288798812605[/C][/ROW]
[ROW][C]24[/C][C]212.135[/C][C]213.727772814231[/C][C]-1.59277281423135[/C][/ROW]
[ROW][C]25[/C][C]213.774[/C][C]215.457559407833[/C][C]-1.68355940783329[/C][/ROW]
[ROW][C]26[/C][C]209.704[/C][C]214.728578432258[/C][C]-5.02457843225804[/C][/ROW]
[ROW][C]27[/C][C]210.562[/C][C]210.911162313747[/C][C]-0.3491623137472[/C][/ROW]
[ROW][C]28[/C][C]204.842[/C][C]206.259859534994[/C][C]-1.41785953499394[/C][/ROW]
[ROW][C]29[/C][C]222.706[/C][C]226.888664965202[/C][C]-4.18266496520212[/C][/ROW]
[ROW][C]30[/C][C]228.349[/C][C]228.134238561024[/C][C]0.214761438975898[/C][/ROW]
[ROW][C]31[/C][C]223.498[/C][C]220.062708443834[/C][C]3.43529155616574[/C][/ROW]
[ROW][C]32[/C][C]214.566[/C][C]209.313503385345[/C][C]5.25249661465503[/C][/ROW]
[ROW][C]33[/C][C]224.279[/C][C]214.481939294165[/C][C]9.79706070583455[/C][/ROW]
[ROW][C]34[/C][C]213.774[/C][C]212.897911055209[/C][C]0.876088944790581[/C][/ROW]
[ROW][C]35[/C][C]223.498[/C][C]217.42055791812[/C][C]6.07744208188035[/C][/ROW]
[ROW][C]36[/C][C]222.706[/C][C]222.196693328372[/C][C]0.509306671628337[/C][/ROW]
[ROW][C]37[/C][C]225.137[/C][C]225.017955161292[/C][C]0.119044838708191[/C][/ROW]
[ROW][C]38[/C][C]216.205[/C][C]223.029377023733[/C][C]-6.82437702373321[/C][/ROW]
[ROW][C]39[/C][C]225.918[/C][C]221.726998540927[/C][C]4.19100145907277[/C][/ROW]
[ROW][C]40[/C][C]225.137[/C][C]218.138350480199[/C][C]6.99864951980143[/C][/ROW]
[ROW][C]41[/C][C]239.712[/C][C]242.260944864292[/C][C]-2.54894486429168[/C][/ROW]
[ROW][C]42[/C][C]236.423[/C][C]247.891831082428[/C][C]-11.4688310824285[/C][/ROW]
[ROW][C]43[/C][C]223.498[/C][C]237.307132658466[/C][C]-13.8091326584658[/C][/ROW]
[ROW][C]44[/C][C]216.986[/C][C]220.708405919398[/C][C]-3.72240591939837[/C][/ROW]
[ROW][C]45[/C][C]225.918[/C][C]225.158374865652[/C][C]0.759625134347687[/C][/ROW]
[ROW][C]46[/C][C]213.774[/C][C]214.233808115771[/C][C]-0.459808115771068[/C][/ROW]
[ROW][C]47[/C][C]222.706[/C][C]221.096425461195[/C][C]1.60957453880525[/C][/ROW]
[ROW][C]48[/C][C]224.279[/C][C]220.299013988005[/C][C]3.97998601199549[/C][/ROW]
[ROW][C]49[/C][C]227.568[/C][C]223.81546566074[/C][C]3.75253433926005[/C][/ROW]
[ROW][C]50[/C][C]220.286[/C][C]218.549007584012[/C][C]1.7369924159876[/C][/ROW]
[ROW][C]51[/C][C]224.279[/C][C]227.281642436786[/C][C]-3.00264243678578[/C][/ROW]
[ROW][C]52[/C][C]226.71[/C][C]222.381954266969[/C][C]4.32804573303068[/C][/ROW]
[ROW][C]53[/C][C]235.642[/C][C]239.141738568628[/C][C]-3.49973856862795[/C][/ROW]
[ROW][C]54[/C][C]228.349[/C][C]238.383800421265[/C][C]-10.034800421265[/C][/ROW]
[ROW][C]55[/C][C]218.636[/C][C]226.433059979[/C][C]-7.79705997899987[/C][/ROW]
[ROW][C]56[/C][C]208.131[/C][C]218.142862268434[/C][C]-10.0118622684339[/C][/ROW]
[ROW][C]57[/C][C]217.855[/C][C]222.533923294128[/C][C]-4.6789232941276[/C][/ROW]
[ROW][C]58[/C][C]191.125[/C][C]208.635820164756[/C][C]-17.510820164756[/C][/ROW]
[ROW][C]59[/C][C]204.061[/C][C]209.080383965529[/C][C]-5.01938396552856[/C][/ROW]
[ROW][C]60[/C][C]211.343[/C][C]206.324820856688[/C][C]5.01817914331207[/C][/ROW]
[ROW][C]61[/C][C]218.636[/C][C]209.070555703919[/C][C]9.56544429608113[/C][/ROW]
[ROW][C]62[/C][C]208.131[/C][C]204.538742196287[/C][C]3.59225780371281[/C][/ROW]
[ROW][C]63[/C][C]208.131[/C][C]209.977374038734[/C][C]-1.84637403873373[/C][/ROW]
[ROW][C]64[/C][C]208.131[/C][C]209.301604060578[/C][C]-1.17060406057766[/C][/ROW]
[ROW][C]65[/C][C]213.774[/C][C]217.474967240869[/C][C]-3.70096724086869[/C][/ROW]
[ROW][C]66[/C][C]205.711[/C][C]211.964580905593[/C][C]-6.25358090559251[/C][/ROW]
[ROW][C]67[/C][C]195.129[/C][C]202.592079216557[/C][C]-7.46307921655739[/C][/ROW]
[ROW][C]68[/C][C]186.274[/C][C]192.806507496189[/C][C]-6.53250749618917[/C][/ROW]
[ROW][C]69[/C][C]192.698[/C][C]200.104467409179[/C][C]-7.40646740917879[/C][/ROW]
[ROW][C]70[/C][C]167.618[/C][C]178.070425012803[/C][C]-10.452425012803[/C][/ROW]
[ROW][C]71[/C][C]182.985[/C][C]186.930733516513[/C][C]-3.94573351651286[/C][/ROW]
[ROW][C]72[/C][C]191.917[/C][C]189.618651670945[/C][C]2.29834832905502[/C][/ROW]
[ROW][C]73[/C][C]193.556[/C][C]192.962176156484[/C][C]0.593823843516191[/C][/ROW]
[ROW][C]74[/C][C]184.624[/C][C]181.830421222401[/C][C]2.79357877759935[/C][/ROW]
[ROW][C]75[/C][C]185.405[/C][C]182.630638053063[/C][C]2.77436194693666[/C][/ROW]
[ROW][C]76[/C][C]182.985[/C][C]183.284762212761[/C][C]-0.299762212760925[/C][/ROW]
[ROW][C]77[/C][C]191.125[/C][C]188.556786925101[/C][C]2.56821307489858[/C][/ROW]
[ROW][C]78[/C][C]185.405[/C][C]183.774397338371[/C][C]1.63060266162859[/C][/ROW]
[ROW][C]79[/C][C]174.13[/C][C]176.873985086713[/C][C]-2.74398508671334[/C][/ROW]
[ROW][C]80[/C][C]165.979[/C][C]169.616104800007[/C][C]-3.63710480000731[/C][/ROW]
[ROW][C]81[/C][C]179.762[/C][C]176.115755887152[/C][C]3.64624411284842[/C][/ROW]
[ROW][C]82[/C][C]149.831[/C][C]157.743574243941[/C][C]-7.9125742439409[/C][/ROW]
[ROW][C]83[/C][C]169.268[/C][C]170.137211494148[/C][C]-0.86921149414772[/C][/ROW]
[ROW][C]84[/C][C]178.123[/C][C]177.179225747699[/C][C]0.94377425230104[/C][/ROW]
[ROW][C]85[/C][C]178.123[/C][C]178.713942535505[/C][C]-0.590942535505178[/C][/ROW]
[ROW][C]86[/C][C]167.618[/C][C]169.117807551052[/C][C]-1.49980755105224[/C][/ROW]
[ROW][C]87[/C][C]157.905[/C][C]168.053277087641[/C][C]-10.1482770876408[/C][/ROW]
[ROW][C]88[/C][C]157.124[/C][C]161.652995241578[/C][C]-4.52899524157834[/C][/ROW]
[ROW][C]89[/C][C]165.979[/C][C]165.561170288365[/C][C]0.417829711635221[/C][/ROW]
[ROW][C]90[/C][C]157.905[/C][C]159.566277660805[/C][C]-1.66127766080501[/C][/ROW]
[ROW][C]91[/C][C]142.549[/C][C]149.466998056761[/C][C]-6.91799805676089[/C][/ROW]
[ROW][C]92[/C][C]131.967[/C][C]140.354209254904[/C][C]-8.38720925490369[/C][/ROW]
[ROW][C]93[/C][C]143.33[/C][C]146.451553321435[/C][C]-3.12155332143521[/C][/ROW]
[ROW][C]94[/C][C]116.611[/C][C]122.493770384993[/C][C]-5.88277038499318[/C][/ROW]
[ROW][C]95[/C][C]140.899[/C][C]135.062968413766[/C][C]5.83603158623447[/C][/ROW]
[ROW][C]96[/C][C]153.824[/C][C]143.183648462635[/C][C]10.6403515373649[/C][/ROW]
[ROW][C]97[/C][C]157.905[/C][C]146.62382720846[/C][C]11.2811727915403[/C][/ROW]
[ROW][C]98[/C][C]148.973[/C][C]141.980282896351[/C][C]6.99271710364931[/C][/ROW]
[ROW][C]99[/C][C]137.687[/C][C]139.130749581577[/C][C]-1.44374958157701[/C][/ROW]
[ROW][C]100[/C][C]145.761[/C][C]139.217173169331[/C][C]6.54382683066854[/C][/ROW]
[ROW][C]101[/C][C]148.973[/C][C]149.622092208008[/C][C]-0.649092208007971[/C][/ROW]
[ROW][C]102[/C][C]146.542[/C][C]142.72879126422[/C][C]3.81320873578039[/C][/ROW]
[ROW][C]103[/C][C]122.243[/C][C]132.645025010742[/C][C]-10.4020250107423[/C][/ROW]
[ROW][C]104[/C][C]110.968[/C][C]121.973308597339[/C][C]-11.005308597339[/C][/ROW]
[ROW][C]105[/C][C]119.031[/C][C]128.958486979794[/C][C]-9.92748697979377[/C][/ROW]
[ROW][C]106[/C][C]94.743[/C][C]103.575684108377[/C][C]-8.83268410837729[/C][/ROW]
[ROW][C]107[/C][C]119.823[/C][C]118.826165631055[/C][C]0.996834368945343[/C][/ROW]
[ROW][C]108[/C][C]128.755[/C][C]126.110341288925[/C][C]2.64465871107477[/C][/ROW]
[ROW][C]109[/C][C]136.037[/C][C]126.151150677417[/C][C]9.88584932258301[/C][/ROW]
[ROW][C]110[/C][C]123.893[/C][C]119.707352878251[/C][C]4.18564712174945[/C][/ROW]
[ROW][C]111[/C][C]112.53[/C][C]111.945566005108[/C][C]0.584433994892322[/C][/ROW]
[ROW][C]112[/C][C]119.031[/C][C]116.067601513296[/C][C]2.96339848670412[/C][/ROW]
[ROW][C]113[/C][C]122.243[/C][C]119.289569780324[/C][C]2.95343021967608[/C][/ROW]
[ROW][C]114[/C][C]115.819[/C][C]116.658069219592[/C][C]-0.839069219591849[/C][/ROW]
[ROW][C]115[/C][C]91.531[/C][C]99.4223214903654[/C][C]-7.89132149036541[/C][/ROW]
[ROW][C]116[/C][C]80.949[/C][C]90.0585969382313[/C][C]-9.10959693823133[/C][/ROW]
[ROW][C]117[/C][C]90.662[/C][C]95.0094114319616[/C][C]-4.34741143196162[/C][/ROW]
[ROW][C]118[/C][C]63.943[/C][C]76.2800396211328[/C][C]-12.3370396211328[/C][/ROW]
[ROW][C]119[/C][C]93.093[/C][C]89.4051282317553[/C][C]3.6878717682447[/C][/ROW]
[ROW][C]120[/C][C]110.968[/C][C]95.9321438992246[/C][C]15.0358561007754[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=279607&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=279607&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
13207.273207.288777052553-0.0157770525534602
14207.273206.8299027815750.443097218425038
15205.711204.9675755487380.743424451262086
16201.63200.8605780146490.769421985351045
17222.706222.059002683560.646997316439666
18225.918225.294208403140.623791596859775
19221.067213.2192904395187.84770956048249
20209.704208.5878887447651.11611125523456
21214.566210.5624811982984.00351880170243
22207.273213.039144462174-5.76614446217437
23210.562212.504887988126-1.94288798812605
24212.135213.727772814231-1.59277281423135
25213.774215.457559407833-1.68355940783329
26209.704214.728578432258-5.02457843225804
27210.562210.911162313747-0.3491623137472
28204.842206.259859534994-1.41785953499394
29222.706226.888664965202-4.18266496520212
30228.349228.1342385610240.214761438975898
31223.498220.0627084438343.43529155616574
32214.566209.3135033853455.25249661465503
33224.279214.4819392941659.79706070583455
34213.774212.8979110552090.876088944790581
35223.498217.420557918126.07744208188035
36222.706222.1966933283720.509306671628337
37225.137225.0179551612920.119044838708191
38216.205223.029377023733-6.82437702373321
39225.918221.7269985409274.19100145907277
40225.137218.1383504801996.99864951980143
41239.712242.260944864292-2.54894486429168
42236.423247.891831082428-11.4688310824285
43223.498237.307132658466-13.8091326584658
44216.986220.708405919398-3.72240591939837
45225.918225.1583748656520.759625134347687
46213.774214.233808115771-0.459808115771068
47222.706221.0964254611951.60957453880525
48224.279220.2990139880053.97998601199549
49227.568223.815465660743.75253433926005
50220.286218.5490075840121.7369924159876
51224.279227.281642436786-3.00264243678578
52226.71222.3819542669694.32804573303068
53235.642239.141738568628-3.49973856862795
54228.349238.383800421265-10.034800421265
55218.636226.433059979-7.79705997899987
56208.131218.142862268434-10.0118622684339
57217.855222.533923294128-4.6789232941276
58191.125208.635820164756-17.510820164756
59204.061209.080383965529-5.01938396552856
60211.343206.3248208566885.01817914331207
61218.636209.0705557039199.56544429608113
62208.131204.5387421962873.59225780371281
63208.131209.977374038734-1.84637403873373
64208.131209.301604060578-1.17060406057766
65213.774217.474967240869-3.70096724086869
66205.711211.964580905593-6.25358090559251
67195.129202.592079216557-7.46307921655739
68186.274192.806507496189-6.53250749618917
69192.698200.104467409179-7.40646740917879
70167.618178.070425012803-10.452425012803
71182.985186.930733516513-3.94573351651286
72191.917189.6186516709452.29834832905502
73193.556192.9621761564840.593823843516191
74184.624181.8304212224012.79357877759935
75185.405182.6306380530632.77436194693666
76182.985183.284762212761-0.299762212760925
77191.125188.5567869251012.56821307489858
78185.405183.7743973383711.63060266162859
79174.13176.873985086713-2.74398508671334
80165.979169.616104800007-3.63710480000731
81179.762176.1157558871523.64624411284842
82149.831157.743574243941-7.9125742439409
83169.268170.137211494148-0.86921149414772
84178.123177.1792257476990.94377425230104
85178.123178.713942535505-0.590942535505178
86167.618169.117807551052-1.49980755105224
87157.905168.053277087641-10.1482770876408
88157.124161.652995241578-4.52899524157834
89165.979165.5611702883650.417829711635221
90157.905159.566277660805-1.66127766080501
91142.549149.466998056761-6.91799805676089
92131.967140.354209254904-8.38720925490369
93143.33146.451553321435-3.12155332143521
94116.611122.493770384993-5.88277038499318
95140.899135.0629684137665.83603158623447
96153.824143.18364846263510.6403515373649
97157.905146.6238272084611.2811727915403
98148.973141.9802828963516.99271710364931
99137.687139.130749581577-1.44374958157701
100145.761139.2171731693316.54382683066854
101148.973149.622092208008-0.649092208007971
102146.542142.728791264223.81320873578039
103122.243132.645025010742-10.4020250107423
104110.968121.973308597339-11.005308597339
105119.031128.958486979794-9.92748697979377
10694.743103.575684108377-8.83268410837729
107119.823118.8261656310550.996834368945343
108128.755126.1103412889252.64465871107477
109136.037126.1511506774179.88584932258301
110123.893119.7073528782514.18564712174945
111112.53111.9455660051080.584433994892322
112119.031116.0676015132962.96339848670412
113122.243119.2895697803242.95343021967608
114115.819116.658069219592-0.839069219591849
11591.53199.4223214903654-7.89132149036541
11680.94990.0585969382313-9.10959693823133
11790.66295.0094114319616-4.34741143196162
11863.94376.2800396211328-12.3370396211328
11993.09389.40512823175533.6878717682447
120110.96895.932143899224615.0358561007754







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
121103.70865126935292.1137197452126115.303582793491
12292.494111118290380.1556379577012104.832584278879
12383.097326925264770.094243268507996.1004105820214
12486.236305532369472.038937837669100.43367322707
12586.824865062183271.4777324478408102.171997676526
12681.541443738375865.515424203708997.5674632730427
12765.660336180694950.160142499474881.1605298619149
12859.768960580275743.836187632125475.7017335284259
12967.581373799811249.176118709009185.9866288906133
13050.419975778209933.753443637835767.0865079185841
13172.086890597211449.33679503975394.8369861546698
13280.784217604352355.8030584204381105.765376788267

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
121 & 103.708651269352 & 92.1137197452126 & 115.303582793491 \tabularnewline
122 & 92.4941111182903 & 80.1556379577012 & 104.832584278879 \tabularnewline
123 & 83.0973269252647 & 70.0942432685079 & 96.1004105820214 \tabularnewline
124 & 86.2363055323694 & 72.038937837669 & 100.43367322707 \tabularnewline
125 & 86.8248650621832 & 71.4777324478408 & 102.171997676526 \tabularnewline
126 & 81.5414437383758 & 65.5154242037089 & 97.5674632730427 \tabularnewline
127 & 65.6603361806949 & 50.1601424994748 & 81.1605298619149 \tabularnewline
128 & 59.7689605802757 & 43.8361876321254 & 75.7017335284259 \tabularnewline
129 & 67.5813737998112 & 49.1761187090091 & 85.9866288906133 \tabularnewline
130 & 50.4199757782099 & 33.7534436378357 & 67.0865079185841 \tabularnewline
131 & 72.0868905972114 & 49.336795039753 & 94.8369861546698 \tabularnewline
132 & 80.7842176043523 & 55.8030584204381 & 105.765376788267 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=279607&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]103.708651269352[/C][C]92.1137197452126[/C][C]115.303582793491[/C][/ROW]
[ROW][C]122[/C][C]92.4941111182903[/C][C]80.1556379577012[/C][C]104.832584278879[/C][/ROW]
[ROW][C]123[/C][C]83.0973269252647[/C][C]70.0942432685079[/C][C]96.1004105820214[/C][/ROW]
[ROW][C]124[/C][C]86.2363055323694[/C][C]72.038937837669[/C][C]100.43367322707[/C][/ROW]
[ROW][C]125[/C][C]86.8248650621832[/C][C]71.4777324478408[/C][C]102.171997676526[/C][/ROW]
[ROW][C]126[/C][C]81.5414437383758[/C][C]65.5154242037089[/C][C]97.5674632730427[/C][/ROW]
[ROW][C]127[/C][C]65.6603361806949[/C][C]50.1601424994748[/C][C]81.1605298619149[/C][/ROW]
[ROW][C]128[/C][C]59.7689605802757[/C][C]43.8361876321254[/C][C]75.7017335284259[/C][/ROW]
[ROW][C]129[/C][C]67.5813737998112[/C][C]49.1761187090091[/C][C]85.9866288906133[/C][/ROW]
[ROW][C]130[/C][C]50.4199757782099[/C][C]33.7534436378357[/C][C]67.0865079185841[/C][/ROW]
[ROW][C]131[/C][C]72.0868905972114[/C][C]49.336795039753[/C][C]94.8369861546698[/C][/ROW]
[ROW][C]132[/C][C]80.7842176043523[/C][C]55.8030584204381[/C][C]105.765376788267[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=279607&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=279607&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
121103.70865126935292.1137197452126115.303582793491
12292.494111118290380.1556379577012104.832584278879
12383.097326925264770.094243268507996.1004105820214
12486.236305532369472.038937837669100.43367322707
12586.824865062183271.4777324478408102.171997676526
12681.541443738375865.515424203708997.5674632730427
12765.660336180694950.160142499474881.1605298619149
12859.768960580275743.836187632125475.7017335284259
12967.581373799811249.176118709009185.9866288906133
13050.419975778209933.753443637835767.0865079185841
13172.086890597211449.33679503975394.8369861546698
13280.784217604352355.8030584204381105.765376788267



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