Free Statistics

of Irreproducible Research!

Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationTue, 19 Jan 2010 15:24:14 -0700
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/Jan/19/t1263939934h1xfnpvnwc5amfv.htm/, Retrieved Thu, 02 May 2024 05:31:00 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=72298, Retrieved Thu, 02 May 2024 05:31:00 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywordsKDGP2W62
Estimated Impact213
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [] [2010-01-19 22:24:14] [60daa7a9bda4a19b1f42562f4658ecc7] [Current]
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Dataseries X:
161.88
162.05
162.16
162.61
162.53
162.53
162.53
162.53
162.83
161.61
161.79
161.79
161.79
161.79
161.85
161.77
161.86
161.89
161.89
161.89
162.18
162.43
162.58
162.57
162.57
162.57
162.44
162.79
163.15
163.23
163.23
163.23
163.38
163.71
163.73
163.73
163.73
163.73
163.93
164.27
164.57
164.73
164.73
164.76
165.75
165.86
165.99
166.13
166.13
166.13
166.15
166.45
166.48
166.51
166.51
166.51
166.58
166.82
167.35
167.5
167.5
167.6
167.72
167.29
166.98
166.98
166.98
166.98
167.63
167.83
167.85
167.87
167.87
167.96
167.7
169.25
168.79
168.77
168.77
169
168.92
169.23
169.28
169.29
169.29
170.29
170.59
171.98
172.31
172.28
172.28
172.45
172.27
172.65
172.08
172.2
172.2
172.2
172.36
172.53
173.18
173.17
173.17
173.17
173.4
174.47
174.56
174.59
174.59
175.22
175.3
175.25
175.54
175.58
175.58
175.68
176.05
176.4
176.58
176.49




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=72298&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=72298&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=72298&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
alpha0.752503278433036
beta0.0380281280298083
gamma1

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.752503278433036 \tabularnewline
beta & 0.0380281280298083 \tabularnewline
gamma & 1 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=72298&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]0.752503278433036[/C][/ROW]
[ROW][C]beta[/C][C]0.0380281280298083[/C][/ROW]
[ROW][C]gamma[/C][C]1[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=72298&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=72298&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
alpha0.752503278433036
beta0.0380281280298083
gamma1







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
13161.79162.070066773504-0.280066773504331
14161.79161.872791520583-0.0827915205832994
15161.85161.882014022659-0.0320140226591263
16161.77161.7276973024710.0423026975287542
17161.86161.7405147041700.119485295829747
18161.89161.7564981567930.133501843207085
19161.89162.237682768199-0.347682768198950
20161.89161.945991657381-0.0559916573813553
21162.18162.181363456848-0.00136345684839512
22162.43160.96197080591.46802919409987
23162.58162.3053104927330.274689507267198
24162.57162.570185414485-0.000185414485059709
25162.57162.5576451423230.0123548576772805
26162.57162.673035602884-0.103035602884120
27162.44162.722804819364-0.282804819364173
28162.79162.4341968330750.355803166924517
29163.15162.7470345125090.402965487491315
30163.23163.0329266465950.197073353405301
31163.23163.497796453228-0.267796453228129
32163.23163.395637739183-0.165637739182699
33163.38163.616108228195-0.236108228195491
34163.71162.6311091313581.07889086864171
35163.73163.4225074970870.307492502913021
36163.73163.6812090434740.0487909565259201
37163.73163.747201754240-0.0172017542402898
38163.73163.849520633067-0.119520633066571
39163.93163.8796494044720.050350595528073
40164.27164.0465859012960.223414098703728
41164.57164.3144749666890.255525033311045
42164.73164.4772429226060.252757077393738
43164.73164.909337497808-0.179337497807893
44164.76164.941936088549-0.181936088548639
45165.75165.1751421069440.574857893055906
46165.86165.1915037886180.668496211382006
47165.99165.5370644380650.452935561935249
48166.13165.8992507947970.230749205203182
49166.13166.149107891066-0.0191078910658575
50166.13166.287887448449-0.157887448448946
51166.15166.393308361539-0.243308361538595
52166.45166.435815473790.0141845262098172
53166.48166.601935870345-0.121935870344544
54166.51166.516906587067-0.00690658706668046
55166.51166.676159190015-0.166159190015321
56166.51166.747906249489-0.237906249488674
57166.58167.154571800821-0.574571800820991
58166.82166.3245398648920.495460135108402
59167.35166.4769689134720.873031086527845
60167.5167.1027388784870.397261121513253
61167.5167.4232736225850.0767263774152411
62167.6167.609779414124-0.00977941412364203
63167.72167.819707133685-0.0997071336846886
64167.29168.052309041777-0.762309041776575
65166.98167.596511520489-0.616511520489212
66166.98167.149714278442-0.169714278442115
67166.98167.124312579372-0.144312579372269
68166.98167.172640808570-0.192640808569678
69167.63167.5092391469990.120760853001485
70167.83167.4663685649850.363631435014867
71167.85167.6083630649420.241636935058409
72167.87167.6185066034000.251493396600239
73167.87167.7230992756310.146900724369345
74167.96167.9160896403780.0439103596216057
75167.7168.120786723988-0.420786723988186
76169.25167.9152197298431.33478027015667
77168.79169.10102045958-0.311020459580106
78168.77169.030876376209-0.260876376208614
79168.77168.976742297021-0.206742297021179
80169168.9979249338410.00207506615905118
81168.92169.595979589385-0.675979589385435
82169.23169.0282352281130.201764771886957
83169.28169.0281656139550.251834386045488
84169.29169.0586483422010.231351657798712
85169.29169.1318476971860.158152302814159
86170.29169.3177868631280.97221313687183
87170.59170.1425601368610.447439863138641
88171.98171.0862153077580.893784692242264
89172.31171.5815972128470.728402787153328
90172.28172.384539543148-0.104539543148036
91172.28172.544427747400-0.264427747399623
92172.45172.655213059747-0.20521305974691
93172.27173.004864152603-0.734864152603336
94172.65172.683760494379-0.0337604943787824
95172.08172.585822229125-0.505822229124533
96172.2172.0863879588190.113612041180943
97172.2172.0947934911640.105206508835892
98172.2172.482775274142-0.28277527414167
99172.36172.2377799887840.122220011215518
100172.53173.04236245027-0.512362450269876
101173.18172.3936312389840.786368761015837
102173.17172.9906501274690.179349872531247
103173.17173.289325572315-0.119325572315148
104173.17173.492839805206-0.322839805206229
105173.4173.58840705326-0.188407053259908
106174.47173.8331901619290.636809838071315
107174.56174.1233689255410.436631074459001
108174.59174.5137557120870.0762442879128287
109174.59174.5182061243980.071793875602026
110175.22174.8103090048810.409690995118751
111175.3175.2317361118720.0682638881279729
112175.25175.88221956009-0.632219560089851
113175.54175.5048575568050.0351424431949567
114175.58175.404974041620.175025958379905
115175.58175.644983847259-0.064983847259299
116175.68175.859085673376-0.179085673375710
117176.05176.120278124767-0.070278124767043
118176.4176.685750608855-0.285750608854613
119176.58176.2333142599170.346685740083132
120176.49176.4654066734710.0245933265290148

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 161.79 & 162.070066773504 & -0.280066773504331 \tabularnewline
14 & 161.79 & 161.872791520583 & -0.0827915205832994 \tabularnewline
15 & 161.85 & 161.882014022659 & -0.0320140226591263 \tabularnewline
16 & 161.77 & 161.727697302471 & 0.0423026975287542 \tabularnewline
17 & 161.86 & 161.740514704170 & 0.119485295829747 \tabularnewline
18 & 161.89 & 161.756498156793 & 0.133501843207085 \tabularnewline
19 & 161.89 & 162.237682768199 & -0.347682768198950 \tabularnewline
20 & 161.89 & 161.945991657381 & -0.0559916573813553 \tabularnewline
21 & 162.18 & 162.181363456848 & -0.00136345684839512 \tabularnewline
22 & 162.43 & 160.9619708059 & 1.46802919409987 \tabularnewline
23 & 162.58 & 162.305310492733 & 0.274689507267198 \tabularnewline
24 & 162.57 & 162.570185414485 & -0.000185414485059709 \tabularnewline
25 & 162.57 & 162.557645142323 & 0.0123548576772805 \tabularnewline
26 & 162.57 & 162.673035602884 & -0.103035602884120 \tabularnewline
27 & 162.44 & 162.722804819364 & -0.282804819364173 \tabularnewline
28 & 162.79 & 162.434196833075 & 0.355803166924517 \tabularnewline
29 & 163.15 & 162.747034512509 & 0.402965487491315 \tabularnewline
30 & 163.23 & 163.032926646595 & 0.197073353405301 \tabularnewline
31 & 163.23 & 163.497796453228 & -0.267796453228129 \tabularnewline
32 & 163.23 & 163.395637739183 & -0.165637739182699 \tabularnewline
33 & 163.38 & 163.616108228195 & -0.236108228195491 \tabularnewline
34 & 163.71 & 162.631109131358 & 1.07889086864171 \tabularnewline
35 & 163.73 & 163.422507497087 & 0.307492502913021 \tabularnewline
36 & 163.73 & 163.681209043474 & 0.0487909565259201 \tabularnewline
37 & 163.73 & 163.747201754240 & -0.0172017542402898 \tabularnewline
38 & 163.73 & 163.849520633067 & -0.119520633066571 \tabularnewline
39 & 163.93 & 163.879649404472 & 0.050350595528073 \tabularnewline
40 & 164.27 & 164.046585901296 & 0.223414098703728 \tabularnewline
41 & 164.57 & 164.314474966689 & 0.255525033311045 \tabularnewline
42 & 164.73 & 164.477242922606 & 0.252757077393738 \tabularnewline
43 & 164.73 & 164.909337497808 & -0.179337497807893 \tabularnewline
44 & 164.76 & 164.941936088549 & -0.181936088548639 \tabularnewline
45 & 165.75 & 165.175142106944 & 0.574857893055906 \tabularnewline
46 & 165.86 & 165.191503788618 & 0.668496211382006 \tabularnewline
47 & 165.99 & 165.537064438065 & 0.452935561935249 \tabularnewline
48 & 166.13 & 165.899250794797 & 0.230749205203182 \tabularnewline
49 & 166.13 & 166.149107891066 & -0.0191078910658575 \tabularnewline
50 & 166.13 & 166.287887448449 & -0.157887448448946 \tabularnewline
51 & 166.15 & 166.393308361539 & -0.243308361538595 \tabularnewline
52 & 166.45 & 166.43581547379 & 0.0141845262098172 \tabularnewline
53 & 166.48 & 166.601935870345 & -0.121935870344544 \tabularnewline
54 & 166.51 & 166.516906587067 & -0.00690658706668046 \tabularnewline
55 & 166.51 & 166.676159190015 & -0.166159190015321 \tabularnewline
56 & 166.51 & 166.747906249489 & -0.237906249488674 \tabularnewline
57 & 166.58 & 167.154571800821 & -0.574571800820991 \tabularnewline
58 & 166.82 & 166.324539864892 & 0.495460135108402 \tabularnewline
59 & 167.35 & 166.476968913472 & 0.873031086527845 \tabularnewline
60 & 167.5 & 167.102738878487 & 0.397261121513253 \tabularnewline
61 & 167.5 & 167.423273622585 & 0.0767263774152411 \tabularnewline
62 & 167.6 & 167.609779414124 & -0.00977941412364203 \tabularnewline
63 & 167.72 & 167.819707133685 & -0.0997071336846886 \tabularnewline
64 & 167.29 & 168.052309041777 & -0.762309041776575 \tabularnewline
65 & 166.98 & 167.596511520489 & -0.616511520489212 \tabularnewline
66 & 166.98 & 167.149714278442 & -0.169714278442115 \tabularnewline
67 & 166.98 & 167.124312579372 & -0.144312579372269 \tabularnewline
68 & 166.98 & 167.172640808570 & -0.192640808569678 \tabularnewline
69 & 167.63 & 167.509239146999 & 0.120760853001485 \tabularnewline
70 & 167.83 & 167.466368564985 & 0.363631435014867 \tabularnewline
71 & 167.85 & 167.608363064942 & 0.241636935058409 \tabularnewline
72 & 167.87 & 167.618506603400 & 0.251493396600239 \tabularnewline
73 & 167.87 & 167.723099275631 & 0.146900724369345 \tabularnewline
74 & 167.96 & 167.916089640378 & 0.0439103596216057 \tabularnewline
75 & 167.7 & 168.120786723988 & -0.420786723988186 \tabularnewline
76 & 169.25 & 167.915219729843 & 1.33478027015667 \tabularnewline
77 & 168.79 & 169.10102045958 & -0.311020459580106 \tabularnewline
78 & 168.77 & 169.030876376209 & -0.260876376208614 \tabularnewline
79 & 168.77 & 168.976742297021 & -0.206742297021179 \tabularnewline
80 & 169 & 168.997924933841 & 0.00207506615905118 \tabularnewline
81 & 168.92 & 169.595979589385 & -0.675979589385435 \tabularnewline
82 & 169.23 & 169.028235228113 & 0.201764771886957 \tabularnewline
83 & 169.28 & 169.028165613955 & 0.251834386045488 \tabularnewline
84 & 169.29 & 169.058648342201 & 0.231351657798712 \tabularnewline
85 & 169.29 & 169.131847697186 & 0.158152302814159 \tabularnewline
86 & 170.29 & 169.317786863128 & 0.97221313687183 \tabularnewline
87 & 170.59 & 170.142560136861 & 0.447439863138641 \tabularnewline
88 & 171.98 & 171.086215307758 & 0.893784692242264 \tabularnewline
89 & 172.31 & 171.581597212847 & 0.728402787153328 \tabularnewline
90 & 172.28 & 172.384539543148 & -0.104539543148036 \tabularnewline
91 & 172.28 & 172.544427747400 & -0.264427747399623 \tabularnewline
92 & 172.45 & 172.655213059747 & -0.20521305974691 \tabularnewline
93 & 172.27 & 173.004864152603 & -0.734864152603336 \tabularnewline
94 & 172.65 & 172.683760494379 & -0.0337604943787824 \tabularnewline
95 & 172.08 & 172.585822229125 & -0.505822229124533 \tabularnewline
96 & 172.2 & 172.086387958819 & 0.113612041180943 \tabularnewline
97 & 172.2 & 172.094793491164 & 0.105206508835892 \tabularnewline
98 & 172.2 & 172.482775274142 & -0.28277527414167 \tabularnewline
99 & 172.36 & 172.237779988784 & 0.122220011215518 \tabularnewline
100 & 172.53 & 173.04236245027 & -0.512362450269876 \tabularnewline
101 & 173.18 & 172.393631238984 & 0.786368761015837 \tabularnewline
102 & 173.17 & 172.990650127469 & 0.179349872531247 \tabularnewline
103 & 173.17 & 173.289325572315 & -0.119325572315148 \tabularnewline
104 & 173.17 & 173.492839805206 & -0.322839805206229 \tabularnewline
105 & 173.4 & 173.58840705326 & -0.188407053259908 \tabularnewline
106 & 174.47 & 173.833190161929 & 0.636809838071315 \tabularnewline
107 & 174.56 & 174.123368925541 & 0.436631074459001 \tabularnewline
108 & 174.59 & 174.513755712087 & 0.0762442879128287 \tabularnewline
109 & 174.59 & 174.518206124398 & 0.071793875602026 \tabularnewline
110 & 175.22 & 174.810309004881 & 0.409690995118751 \tabularnewline
111 & 175.3 & 175.231736111872 & 0.0682638881279729 \tabularnewline
112 & 175.25 & 175.88221956009 & -0.632219560089851 \tabularnewline
113 & 175.54 & 175.504857556805 & 0.0351424431949567 \tabularnewline
114 & 175.58 & 175.40497404162 & 0.175025958379905 \tabularnewline
115 & 175.58 & 175.644983847259 & -0.064983847259299 \tabularnewline
116 & 175.68 & 175.859085673376 & -0.179085673375710 \tabularnewline
117 & 176.05 & 176.120278124767 & -0.070278124767043 \tabularnewline
118 & 176.4 & 176.685750608855 & -0.285750608854613 \tabularnewline
119 & 176.58 & 176.233314259917 & 0.346685740083132 \tabularnewline
120 & 176.49 & 176.465406673471 & 0.0245933265290148 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=72298&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]161.79[/C][C]162.070066773504[/C][C]-0.280066773504331[/C][/ROW]
[ROW][C]14[/C][C]161.79[/C][C]161.872791520583[/C][C]-0.0827915205832994[/C][/ROW]
[ROW][C]15[/C][C]161.85[/C][C]161.882014022659[/C][C]-0.0320140226591263[/C][/ROW]
[ROW][C]16[/C][C]161.77[/C][C]161.727697302471[/C][C]0.0423026975287542[/C][/ROW]
[ROW][C]17[/C][C]161.86[/C][C]161.740514704170[/C][C]0.119485295829747[/C][/ROW]
[ROW][C]18[/C][C]161.89[/C][C]161.756498156793[/C][C]0.133501843207085[/C][/ROW]
[ROW][C]19[/C][C]161.89[/C][C]162.237682768199[/C][C]-0.347682768198950[/C][/ROW]
[ROW][C]20[/C][C]161.89[/C][C]161.945991657381[/C][C]-0.0559916573813553[/C][/ROW]
[ROW][C]21[/C][C]162.18[/C][C]162.181363456848[/C][C]-0.00136345684839512[/C][/ROW]
[ROW][C]22[/C][C]162.43[/C][C]160.9619708059[/C][C]1.46802919409987[/C][/ROW]
[ROW][C]23[/C][C]162.58[/C][C]162.305310492733[/C][C]0.274689507267198[/C][/ROW]
[ROW][C]24[/C][C]162.57[/C][C]162.570185414485[/C][C]-0.000185414485059709[/C][/ROW]
[ROW][C]25[/C][C]162.57[/C][C]162.557645142323[/C][C]0.0123548576772805[/C][/ROW]
[ROW][C]26[/C][C]162.57[/C][C]162.673035602884[/C][C]-0.103035602884120[/C][/ROW]
[ROW][C]27[/C][C]162.44[/C][C]162.722804819364[/C][C]-0.282804819364173[/C][/ROW]
[ROW][C]28[/C][C]162.79[/C][C]162.434196833075[/C][C]0.355803166924517[/C][/ROW]
[ROW][C]29[/C][C]163.15[/C][C]162.747034512509[/C][C]0.402965487491315[/C][/ROW]
[ROW][C]30[/C][C]163.23[/C][C]163.032926646595[/C][C]0.197073353405301[/C][/ROW]
[ROW][C]31[/C][C]163.23[/C][C]163.497796453228[/C][C]-0.267796453228129[/C][/ROW]
[ROW][C]32[/C][C]163.23[/C][C]163.395637739183[/C][C]-0.165637739182699[/C][/ROW]
[ROW][C]33[/C][C]163.38[/C][C]163.616108228195[/C][C]-0.236108228195491[/C][/ROW]
[ROW][C]34[/C][C]163.71[/C][C]162.631109131358[/C][C]1.07889086864171[/C][/ROW]
[ROW][C]35[/C][C]163.73[/C][C]163.422507497087[/C][C]0.307492502913021[/C][/ROW]
[ROW][C]36[/C][C]163.73[/C][C]163.681209043474[/C][C]0.0487909565259201[/C][/ROW]
[ROW][C]37[/C][C]163.73[/C][C]163.747201754240[/C][C]-0.0172017542402898[/C][/ROW]
[ROW][C]38[/C][C]163.73[/C][C]163.849520633067[/C][C]-0.119520633066571[/C][/ROW]
[ROW][C]39[/C][C]163.93[/C][C]163.879649404472[/C][C]0.050350595528073[/C][/ROW]
[ROW][C]40[/C][C]164.27[/C][C]164.046585901296[/C][C]0.223414098703728[/C][/ROW]
[ROW][C]41[/C][C]164.57[/C][C]164.314474966689[/C][C]0.255525033311045[/C][/ROW]
[ROW][C]42[/C][C]164.73[/C][C]164.477242922606[/C][C]0.252757077393738[/C][/ROW]
[ROW][C]43[/C][C]164.73[/C][C]164.909337497808[/C][C]-0.179337497807893[/C][/ROW]
[ROW][C]44[/C][C]164.76[/C][C]164.941936088549[/C][C]-0.181936088548639[/C][/ROW]
[ROW][C]45[/C][C]165.75[/C][C]165.175142106944[/C][C]0.574857893055906[/C][/ROW]
[ROW][C]46[/C][C]165.86[/C][C]165.191503788618[/C][C]0.668496211382006[/C][/ROW]
[ROW][C]47[/C][C]165.99[/C][C]165.537064438065[/C][C]0.452935561935249[/C][/ROW]
[ROW][C]48[/C][C]166.13[/C][C]165.899250794797[/C][C]0.230749205203182[/C][/ROW]
[ROW][C]49[/C][C]166.13[/C][C]166.149107891066[/C][C]-0.0191078910658575[/C][/ROW]
[ROW][C]50[/C][C]166.13[/C][C]166.287887448449[/C][C]-0.157887448448946[/C][/ROW]
[ROW][C]51[/C][C]166.15[/C][C]166.393308361539[/C][C]-0.243308361538595[/C][/ROW]
[ROW][C]52[/C][C]166.45[/C][C]166.43581547379[/C][C]0.0141845262098172[/C][/ROW]
[ROW][C]53[/C][C]166.48[/C][C]166.601935870345[/C][C]-0.121935870344544[/C][/ROW]
[ROW][C]54[/C][C]166.51[/C][C]166.516906587067[/C][C]-0.00690658706668046[/C][/ROW]
[ROW][C]55[/C][C]166.51[/C][C]166.676159190015[/C][C]-0.166159190015321[/C][/ROW]
[ROW][C]56[/C][C]166.51[/C][C]166.747906249489[/C][C]-0.237906249488674[/C][/ROW]
[ROW][C]57[/C][C]166.58[/C][C]167.154571800821[/C][C]-0.574571800820991[/C][/ROW]
[ROW][C]58[/C][C]166.82[/C][C]166.324539864892[/C][C]0.495460135108402[/C][/ROW]
[ROW][C]59[/C][C]167.35[/C][C]166.476968913472[/C][C]0.873031086527845[/C][/ROW]
[ROW][C]60[/C][C]167.5[/C][C]167.102738878487[/C][C]0.397261121513253[/C][/ROW]
[ROW][C]61[/C][C]167.5[/C][C]167.423273622585[/C][C]0.0767263774152411[/C][/ROW]
[ROW][C]62[/C][C]167.6[/C][C]167.609779414124[/C][C]-0.00977941412364203[/C][/ROW]
[ROW][C]63[/C][C]167.72[/C][C]167.819707133685[/C][C]-0.0997071336846886[/C][/ROW]
[ROW][C]64[/C][C]167.29[/C][C]168.052309041777[/C][C]-0.762309041776575[/C][/ROW]
[ROW][C]65[/C][C]166.98[/C][C]167.596511520489[/C][C]-0.616511520489212[/C][/ROW]
[ROW][C]66[/C][C]166.98[/C][C]167.149714278442[/C][C]-0.169714278442115[/C][/ROW]
[ROW][C]67[/C][C]166.98[/C][C]167.124312579372[/C][C]-0.144312579372269[/C][/ROW]
[ROW][C]68[/C][C]166.98[/C][C]167.172640808570[/C][C]-0.192640808569678[/C][/ROW]
[ROW][C]69[/C][C]167.63[/C][C]167.509239146999[/C][C]0.120760853001485[/C][/ROW]
[ROW][C]70[/C][C]167.83[/C][C]167.466368564985[/C][C]0.363631435014867[/C][/ROW]
[ROW][C]71[/C][C]167.85[/C][C]167.608363064942[/C][C]0.241636935058409[/C][/ROW]
[ROW][C]72[/C][C]167.87[/C][C]167.618506603400[/C][C]0.251493396600239[/C][/ROW]
[ROW][C]73[/C][C]167.87[/C][C]167.723099275631[/C][C]0.146900724369345[/C][/ROW]
[ROW][C]74[/C][C]167.96[/C][C]167.916089640378[/C][C]0.0439103596216057[/C][/ROW]
[ROW][C]75[/C][C]167.7[/C][C]168.120786723988[/C][C]-0.420786723988186[/C][/ROW]
[ROW][C]76[/C][C]169.25[/C][C]167.915219729843[/C][C]1.33478027015667[/C][/ROW]
[ROW][C]77[/C][C]168.79[/C][C]169.10102045958[/C][C]-0.311020459580106[/C][/ROW]
[ROW][C]78[/C][C]168.77[/C][C]169.030876376209[/C][C]-0.260876376208614[/C][/ROW]
[ROW][C]79[/C][C]168.77[/C][C]168.976742297021[/C][C]-0.206742297021179[/C][/ROW]
[ROW][C]80[/C][C]169[/C][C]168.997924933841[/C][C]0.00207506615905118[/C][/ROW]
[ROW][C]81[/C][C]168.92[/C][C]169.595979589385[/C][C]-0.675979589385435[/C][/ROW]
[ROW][C]82[/C][C]169.23[/C][C]169.028235228113[/C][C]0.201764771886957[/C][/ROW]
[ROW][C]83[/C][C]169.28[/C][C]169.028165613955[/C][C]0.251834386045488[/C][/ROW]
[ROW][C]84[/C][C]169.29[/C][C]169.058648342201[/C][C]0.231351657798712[/C][/ROW]
[ROW][C]85[/C][C]169.29[/C][C]169.131847697186[/C][C]0.158152302814159[/C][/ROW]
[ROW][C]86[/C][C]170.29[/C][C]169.317786863128[/C][C]0.97221313687183[/C][/ROW]
[ROW][C]87[/C][C]170.59[/C][C]170.142560136861[/C][C]0.447439863138641[/C][/ROW]
[ROW][C]88[/C][C]171.98[/C][C]171.086215307758[/C][C]0.893784692242264[/C][/ROW]
[ROW][C]89[/C][C]172.31[/C][C]171.581597212847[/C][C]0.728402787153328[/C][/ROW]
[ROW][C]90[/C][C]172.28[/C][C]172.384539543148[/C][C]-0.104539543148036[/C][/ROW]
[ROW][C]91[/C][C]172.28[/C][C]172.544427747400[/C][C]-0.264427747399623[/C][/ROW]
[ROW][C]92[/C][C]172.45[/C][C]172.655213059747[/C][C]-0.20521305974691[/C][/ROW]
[ROW][C]93[/C][C]172.27[/C][C]173.004864152603[/C][C]-0.734864152603336[/C][/ROW]
[ROW][C]94[/C][C]172.65[/C][C]172.683760494379[/C][C]-0.0337604943787824[/C][/ROW]
[ROW][C]95[/C][C]172.08[/C][C]172.585822229125[/C][C]-0.505822229124533[/C][/ROW]
[ROW][C]96[/C][C]172.2[/C][C]172.086387958819[/C][C]0.113612041180943[/C][/ROW]
[ROW][C]97[/C][C]172.2[/C][C]172.094793491164[/C][C]0.105206508835892[/C][/ROW]
[ROW][C]98[/C][C]172.2[/C][C]172.482775274142[/C][C]-0.28277527414167[/C][/ROW]
[ROW][C]99[/C][C]172.36[/C][C]172.237779988784[/C][C]0.122220011215518[/C][/ROW]
[ROW][C]100[/C][C]172.53[/C][C]173.04236245027[/C][C]-0.512362450269876[/C][/ROW]
[ROW][C]101[/C][C]173.18[/C][C]172.393631238984[/C][C]0.786368761015837[/C][/ROW]
[ROW][C]102[/C][C]173.17[/C][C]172.990650127469[/C][C]0.179349872531247[/C][/ROW]
[ROW][C]103[/C][C]173.17[/C][C]173.289325572315[/C][C]-0.119325572315148[/C][/ROW]
[ROW][C]104[/C][C]173.17[/C][C]173.492839805206[/C][C]-0.322839805206229[/C][/ROW]
[ROW][C]105[/C][C]173.4[/C][C]173.58840705326[/C][C]-0.188407053259908[/C][/ROW]
[ROW][C]106[/C][C]174.47[/C][C]173.833190161929[/C][C]0.636809838071315[/C][/ROW]
[ROW][C]107[/C][C]174.56[/C][C]174.123368925541[/C][C]0.436631074459001[/C][/ROW]
[ROW][C]108[/C][C]174.59[/C][C]174.513755712087[/C][C]0.0762442879128287[/C][/ROW]
[ROW][C]109[/C][C]174.59[/C][C]174.518206124398[/C][C]0.071793875602026[/C][/ROW]
[ROW][C]110[/C][C]175.22[/C][C]174.810309004881[/C][C]0.409690995118751[/C][/ROW]
[ROW][C]111[/C][C]175.3[/C][C]175.231736111872[/C][C]0.0682638881279729[/C][/ROW]
[ROW][C]112[/C][C]175.25[/C][C]175.88221956009[/C][C]-0.632219560089851[/C][/ROW]
[ROW][C]113[/C][C]175.54[/C][C]175.504857556805[/C][C]0.0351424431949567[/C][/ROW]
[ROW][C]114[/C][C]175.58[/C][C]175.40497404162[/C][C]0.175025958379905[/C][/ROW]
[ROW][C]115[/C][C]175.58[/C][C]175.644983847259[/C][C]-0.064983847259299[/C][/ROW]
[ROW][C]116[/C][C]175.68[/C][C]175.859085673376[/C][C]-0.179085673375710[/C][/ROW]
[ROW][C]117[/C][C]176.05[/C][C]176.120278124767[/C][C]-0.070278124767043[/C][/ROW]
[ROW][C]118[/C][C]176.4[/C][C]176.685750608855[/C][C]-0.285750608854613[/C][/ROW]
[ROW][C]119[/C][C]176.58[/C][C]176.233314259917[/C][C]0.346685740083132[/C][/ROW]
[ROW][C]120[/C][C]176.49[/C][C]176.465406673471[/C][C]0.0245933265290148[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=72298&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=72298&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
13161.79162.070066773504-0.280066773504331
14161.79161.872791520583-0.0827915205832994
15161.85161.882014022659-0.0320140226591263
16161.77161.7276973024710.0423026975287542
17161.86161.7405147041700.119485295829747
18161.89161.7564981567930.133501843207085
19161.89162.237682768199-0.347682768198950
20161.89161.945991657381-0.0559916573813553
21162.18162.181363456848-0.00136345684839512
22162.43160.96197080591.46802919409987
23162.58162.3053104927330.274689507267198
24162.57162.570185414485-0.000185414485059709
25162.57162.5576451423230.0123548576772805
26162.57162.673035602884-0.103035602884120
27162.44162.722804819364-0.282804819364173
28162.79162.4341968330750.355803166924517
29163.15162.7470345125090.402965487491315
30163.23163.0329266465950.197073353405301
31163.23163.497796453228-0.267796453228129
32163.23163.395637739183-0.165637739182699
33163.38163.616108228195-0.236108228195491
34163.71162.6311091313581.07889086864171
35163.73163.4225074970870.307492502913021
36163.73163.6812090434740.0487909565259201
37163.73163.747201754240-0.0172017542402898
38163.73163.849520633067-0.119520633066571
39163.93163.8796494044720.050350595528073
40164.27164.0465859012960.223414098703728
41164.57164.3144749666890.255525033311045
42164.73164.4772429226060.252757077393738
43164.73164.909337497808-0.179337497807893
44164.76164.941936088549-0.181936088548639
45165.75165.1751421069440.574857893055906
46165.86165.1915037886180.668496211382006
47165.99165.5370644380650.452935561935249
48166.13165.8992507947970.230749205203182
49166.13166.149107891066-0.0191078910658575
50166.13166.287887448449-0.157887448448946
51166.15166.393308361539-0.243308361538595
52166.45166.435815473790.0141845262098172
53166.48166.601935870345-0.121935870344544
54166.51166.516906587067-0.00690658706668046
55166.51166.676159190015-0.166159190015321
56166.51166.747906249489-0.237906249488674
57166.58167.154571800821-0.574571800820991
58166.82166.3245398648920.495460135108402
59167.35166.4769689134720.873031086527845
60167.5167.1027388784870.397261121513253
61167.5167.4232736225850.0767263774152411
62167.6167.609779414124-0.00977941412364203
63167.72167.819707133685-0.0997071336846886
64167.29168.052309041777-0.762309041776575
65166.98167.596511520489-0.616511520489212
66166.98167.149714278442-0.169714278442115
67166.98167.124312579372-0.144312579372269
68166.98167.172640808570-0.192640808569678
69167.63167.5092391469990.120760853001485
70167.83167.4663685649850.363631435014867
71167.85167.6083630649420.241636935058409
72167.87167.6185066034000.251493396600239
73167.87167.7230992756310.146900724369345
74167.96167.9160896403780.0439103596216057
75167.7168.120786723988-0.420786723988186
76169.25167.9152197298431.33478027015667
77168.79169.10102045958-0.311020459580106
78168.77169.030876376209-0.260876376208614
79168.77168.976742297021-0.206742297021179
80169168.9979249338410.00207506615905118
81168.92169.595979589385-0.675979589385435
82169.23169.0282352281130.201764771886957
83169.28169.0281656139550.251834386045488
84169.29169.0586483422010.231351657798712
85169.29169.1318476971860.158152302814159
86170.29169.3177868631280.97221313687183
87170.59170.1425601368610.447439863138641
88171.98171.0862153077580.893784692242264
89172.31171.5815972128470.728402787153328
90172.28172.384539543148-0.104539543148036
91172.28172.544427747400-0.264427747399623
92172.45172.655213059747-0.20521305974691
93172.27173.004864152603-0.734864152603336
94172.65172.683760494379-0.0337604943787824
95172.08172.585822229125-0.505822229124533
96172.2172.0863879588190.113612041180943
97172.2172.0947934911640.105206508835892
98172.2172.482775274142-0.28277527414167
99172.36172.2377799887840.122220011215518
100172.53173.04236245027-0.512362450269876
101173.18172.3936312389840.786368761015837
102173.17172.9906501274690.179349872531247
103173.17173.289325572315-0.119325572315148
104173.17173.492839805206-0.322839805206229
105173.4173.58840705326-0.188407053259908
106174.47173.8331901619290.636809838071315
107174.56174.1233689255410.436631074459001
108174.59174.5137557120870.0762442879128287
109174.59174.5182061243980.071793875602026
110175.22174.8103090048810.409690995118751
111175.3175.2317361118720.0682638881279729
112175.25175.88221956009-0.632219560089851
113175.54175.5048575568050.0351424431949567
114175.58175.404974041620.175025958379905
115175.58175.644983847259-0.064983847259299
116175.68175.859085673376-0.179085673375710
117176.05176.120278124767-0.070278124767043
118176.4176.685750608855-0.285750608854613
119176.58176.2333142599170.346685740083132
120176.49176.4654066734710.0245933265290148







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
121176.426994380779175.644288517035177.209700244523
122176.743752364600175.750564381066177.736940348134
123176.755711529035175.577532508447177.933890549623
124177.162833325453175.814248094876178.511418556030
125177.425854805415175.916167856869178.935541753961
126177.33260783522175.668117873330178.997097797111
127177.374960436864175.560076989025179.189843884704
128177.605034633421175.642897195861179.567172070981
129178.028355560677175.921207162871180.135503958484
130178.595831337892176.345258428167180.846404247617
131178.525573811711176.132667872911180.918479750512
132178.417771022660175.883241686965180.952300358355

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
121 & 176.426994380779 & 175.644288517035 & 177.209700244523 \tabularnewline
122 & 176.743752364600 & 175.750564381066 & 177.736940348134 \tabularnewline
123 & 176.755711529035 & 175.577532508447 & 177.933890549623 \tabularnewline
124 & 177.162833325453 & 175.814248094876 & 178.511418556030 \tabularnewline
125 & 177.425854805415 & 175.916167856869 & 178.935541753961 \tabularnewline
126 & 177.33260783522 & 175.668117873330 & 178.997097797111 \tabularnewline
127 & 177.374960436864 & 175.560076989025 & 179.189843884704 \tabularnewline
128 & 177.605034633421 & 175.642897195861 & 179.567172070981 \tabularnewline
129 & 178.028355560677 & 175.921207162871 & 180.135503958484 \tabularnewline
130 & 178.595831337892 & 176.345258428167 & 180.846404247617 \tabularnewline
131 & 178.525573811711 & 176.132667872911 & 180.918479750512 \tabularnewline
132 & 178.417771022660 & 175.883241686965 & 180.952300358355 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=72298&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]176.426994380779[/C][C]175.644288517035[/C][C]177.209700244523[/C][/ROW]
[ROW][C]122[/C][C]176.743752364600[/C][C]175.750564381066[/C][C]177.736940348134[/C][/ROW]
[ROW][C]123[/C][C]176.755711529035[/C][C]175.577532508447[/C][C]177.933890549623[/C][/ROW]
[ROW][C]124[/C][C]177.162833325453[/C][C]175.814248094876[/C][C]178.511418556030[/C][/ROW]
[ROW][C]125[/C][C]177.425854805415[/C][C]175.916167856869[/C][C]178.935541753961[/C][/ROW]
[ROW][C]126[/C][C]177.33260783522[/C][C]175.668117873330[/C][C]178.997097797111[/C][/ROW]
[ROW][C]127[/C][C]177.374960436864[/C][C]175.560076989025[/C][C]179.189843884704[/C][/ROW]
[ROW][C]128[/C][C]177.605034633421[/C][C]175.642897195861[/C][C]179.567172070981[/C][/ROW]
[ROW][C]129[/C][C]178.028355560677[/C][C]175.921207162871[/C][C]180.135503958484[/C][/ROW]
[ROW][C]130[/C][C]178.595831337892[/C][C]176.345258428167[/C][C]180.846404247617[/C][/ROW]
[ROW][C]131[/C][C]178.525573811711[/C][C]176.132667872911[/C][C]180.918479750512[/C][/ROW]
[ROW][C]132[/C][C]178.417771022660[/C][C]175.883241686965[/C][C]180.952300358355[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=72298&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=72298&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
121176.426994380779175.644288517035177.209700244523
122176.743752364600175.750564381066177.736940348134
123176.755711529035175.577532508447177.933890549623
124177.162833325453175.814248094876178.511418556030
125177.425854805415175.916167856869178.935541753961
126177.33260783522175.668117873330178.997097797111
127177.374960436864175.560076989025179.189843884704
128177.605034633421175.642897195861179.567172070981
129178.028355560677175.921207162871180.135503958484
130178.595831337892176.345258428167180.846404247617
131178.525573811711176.132667872911180.918479750512
132178.417771022660175.883241686965180.952300358355



Parameters (Session):
par1 = 12 ; par2 = Single ; 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')