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Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationFri, 05 Jun 2009 02:29:38 -0600
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2009/Jun/05/t124419069619ayydqkrf0g03b.htm/, Retrieved Fri, 10 May 2024 06:29:49 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=41756, Retrieved Fri, 10 May 2024 06:29:49 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact165
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [Classical Decomposition] [decomposition - s...] [2009-06-02 15:41:09] [74be16979710d4c4e7c6647856088456]
- RMPD    [Exponential Smoothing] [exponential smoot...] [2009-06-05 08:29:38] [d41d8cd98f00b204e9800998ecf8427e] [Current]
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Dataseries X:
106.07
106.07
106.07
106.07
106.07
106.2
107.5
108.31
108.53
108.61
108.62
108.62
108.62
108.62
110.1
110.74
110.77
110.77
110.78
110.78
110.78
110.84
110.84
110.84
110.84
110.84
111.01
112.66
114.04
114.16
114.2
114.2
114.23
114.23
114.23
114.23
114.23
114.23
115.97
116.96
117.08
117.08
117.08
117.63
119.12
119.47
119.5
119.52
119.49
119.49
119.5
119.5
119.56
122.35
122.92
122.92
123.04
123.04
123.04
123.06
123.33
128.21
129.57
129.79
131.66
135.01
136.01
136.31
136.37
136.4
136.4
136.4
137.34
142.18
143.79
144.08
144.08
144.09
144.09
144.11
144.11
144.15
144.15
144.16
144.2
144.38
144.38
144.28
144.46
144.53
144.53
145.34
147.98
150.42
150.53
150.64




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time1 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 & 1 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ 72.249.127.135 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=41756&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]'Gwilym Jenkins' @ 72.249.127.135[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=41756&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=41756&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'Gwilym Jenkins' @ 72.249.127.135







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha1
beta0.0252584287655884
gamma0.160169143914703

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 1 \tabularnewline
beta & 0.0252584287655884 \tabularnewline
gamma & 0.160169143914703 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=41756&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]1[/C][/ROW]
[ROW][C]beta[/C][C]0.0252584287655884[/C][/ROW]
[ROW][C]gamma[/C][C]0.160169143914703[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=41756&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=41756&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
alpha1
beta0.0252584287655884
gamma0.160169143914703







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
13108.62106.5011591880342.11884081196575
14108.62108.716653787850-0.0966537878498599
15110.1110.237129131701-0.137129131701201
16110.74110.883665465296-0.143665465296408
17110.77110.911286701375-0.141286701375165
18110.77110.908134687960-0.138134687959607
19110.78110.7658956227840.0141043772162561
20110.78111.697501877191-0.917501877190944
21110.78111.022660554717-0.242660554716934
22110.84110.7881979970480.0518020029519022
23110.84110.7515897675830.0884102324170897
24110.84110.7479895378070.092010462192789
25110.84110.8094802441790.0305197558211461
26110.84110.897751125257-0.0577511252572123
27111.01112.419209089240-1.40920908924043
28112.66111.7236146818440.93638531815597
29114.04112.7885163037001.25148369630018
30114.16114.170543482161-0.0105434821607844
31114.2114.1515271703680.0484728296323169
32114.2115.114001517882-0.914001517882028
33114.23114.439248608984-0.209248608984282
34114.23114.235629984567-0.00562998456663877
35114.23114.1375711133360.0924288866641518
36114.23114.1340723884520.0959276115478076
37114.23114.1956620358620.0343379641382313
38114.23114.284029358883-0.0540293588829286
39115.97115.8055813288370.164418671162991
40116.96116.7197342861300.240265713869704
41117.08117.107053020549-0.027053020548891
42117.08117.196786370423-0.116786370423114
43117.08117.0550865302050.0249134697949813
44117.63117.976965805307-0.34696580530715
45119.12117.8665353275631.25346467243699
46119.47119.1598625423690.310137457631356
47119.5119.4197794605830.0802205394169135
48119.52119.4459723720300.0740276279698548
49119.49119.527008860265-0.0370088602645495
50119.49119.583574074604-0.093574074603879
51119.5121.104127207173-1.60412720717285
52119.5120.243609474380-0.743609474379525
53119.56119.616077067442-0.0560770674415068
54122.35119.6450773154952.70492268450519
55122.92122.3646494124380.555350587562174
56122.92123.869926695694-0.94992669569369
57123.04123.194266373251-0.154266373251303
58123.04123.082036513718-0.0420365137183012
59123.04122.9830580707640.056941929235677
60123.06122.9786630010940.0813369989056554
61123.33123.0598841125540.270115887446124
62128.21123.4242068154554.78579318454462
63129.57129.948005098361-0.378005098360745
64129.79130.468457283511-0.678457283510738
65131.66130.0625705185451.59742948145532
66135.01131.9433357439773.06666425602324
67136.01135.2320448646350.777955135364493
68136.31137.172944789005-0.8629447890049
69136.37136.799481492857-0.429481492856524
70136.4136.620300131830-0.220300131829788
71136.4136.546819029976-0.1468190299762
72136.4136.537277278633-0.137277278632808
73137.34136.5929765369360.747023463064039
74142.18137.6393451758644.540654824136
75143.79144.116951648955-0.326951648955259
76144.08144.888693364020-0.808693364020257
77144.08144.549517040292-0.469517040292004
78144.09144.508074444242-0.418074444242222
79144.09144.368764540674-0.27876454067362
80144.11145.282973386381-1.17297338638062
81144.11144.62167925499-0.511679254990128
82144.15144.380421707644-0.230421707643842
83144.15144.316684950689-0.166684950688591
84144.16144.306641417402-0.146641417402009
85144.2144.372104152273-0.172104152273107
86144.38144.495257071803-0.115257071802631
87144.38146.195262525931-1.81526252593147
88144.28145.319411846729-1.03941184672937
89144.46144.584407936641-0.124407936640665
90144.53144.731682254302-0.201682254301829
91144.53144.657838077448-0.127838077448274
92145.34145.575859088475-0.235859088475479
93147.98145.7282349918242.25176500817614
94150.42148.1967777045462.22322229545358
95150.53150.595016139859-0.0650161398594946
96150.64150.697540600989-0.0575406009889434

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 108.62 & 106.501159188034 & 2.11884081196575 \tabularnewline
14 & 108.62 & 108.716653787850 & -0.0966537878498599 \tabularnewline
15 & 110.1 & 110.237129131701 & -0.137129131701201 \tabularnewline
16 & 110.74 & 110.883665465296 & -0.143665465296408 \tabularnewline
17 & 110.77 & 110.911286701375 & -0.141286701375165 \tabularnewline
18 & 110.77 & 110.908134687960 & -0.138134687959607 \tabularnewline
19 & 110.78 & 110.765895622784 & 0.0141043772162561 \tabularnewline
20 & 110.78 & 111.697501877191 & -0.917501877190944 \tabularnewline
21 & 110.78 & 111.022660554717 & -0.242660554716934 \tabularnewline
22 & 110.84 & 110.788197997048 & 0.0518020029519022 \tabularnewline
23 & 110.84 & 110.751589767583 & 0.0884102324170897 \tabularnewline
24 & 110.84 & 110.747989537807 & 0.092010462192789 \tabularnewline
25 & 110.84 & 110.809480244179 & 0.0305197558211461 \tabularnewline
26 & 110.84 & 110.897751125257 & -0.0577511252572123 \tabularnewline
27 & 111.01 & 112.419209089240 & -1.40920908924043 \tabularnewline
28 & 112.66 & 111.723614681844 & 0.93638531815597 \tabularnewline
29 & 114.04 & 112.788516303700 & 1.25148369630018 \tabularnewline
30 & 114.16 & 114.170543482161 & -0.0105434821607844 \tabularnewline
31 & 114.2 & 114.151527170368 & 0.0484728296323169 \tabularnewline
32 & 114.2 & 115.114001517882 & -0.914001517882028 \tabularnewline
33 & 114.23 & 114.439248608984 & -0.209248608984282 \tabularnewline
34 & 114.23 & 114.235629984567 & -0.00562998456663877 \tabularnewline
35 & 114.23 & 114.137571113336 & 0.0924288866641518 \tabularnewline
36 & 114.23 & 114.134072388452 & 0.0959276115478076 \tabularnewline
37 & 114.23 & 114.195662035862 & 0.0343379641382313 \tabularnewline
38 & 114.23 & 114.284029358883 & -0.0540293588829286 \tabularnewline
39 & 115.97 & 115.805581328837 & 0.164418671162991 \tabularnewline
40 & 116.96 & 116.719734286130 & 0.240265713869704 \tabularnewline
41 & 117.08 & 117.107053020549 & -0.027053020548891 \tabularnewline
42 & 117.08 & 117.196786370423 & -0.116786370423114 \tabularnewline
43 & 117.08 & 117.055086530205 & 0.0249134697949813 \tabularnewline
44 & 117.63 & 117.976965805307 & -0.34696580530715 \tabularnewline
45 & 119.12 & 117.866535327563 & 1.25346467243699 \tabularnewline
46 & 119.47 & 119.159862542369 & 0.310137457631356 \tabularnewline
47 & 119.5 & 119.419779460583 & 0.0802205394169135 \tabularnewline
48 & 119.52 & 119.445972372030 & 0.0740276279698548 \tabularnewline
49 & 119.49 & 119.527008860265 & -0.0370088602645495 \tabularnewline
50 & 119.49 & 119.583574074604 & -0.093574074603879 \tabularnewline
51 & 119.5 & 121.104127207173 & -1.60412720717285 \tabularnewline
52 & 119.5 & 120.243609474380 & -0.743609474379525 \tabularnewline
53 & 119.56 & 119.616077067442 & -0.0560770674415068 \tabularnewline
54 & 122.35 & 119.645077315495 & 2.70492268450519 \tabularnewline
55 & 122.92 & 122.364649412438 & 0.555350587562174 \tabularnewline
56 & 122.92 & 123.869926695694 & -0.94992669569369 \tabularnewline
57 & 123.04 & 123.194266373251 & -0.154266373251303 \tabularnewline
58 & 123.04 & 123.082036513718 & -0.0420365137183012 \tabularnewline
59 & 123.04 & 122.983058070764 & 0.056941929235677 \tabularnewline
60 & 123.06 & 122.978663001094 & 0.0813369989056554 \tabularnewline
61 & 123.33 & 123.059884112554 & 0.270115887446124 \tabularnewline
62 & 128.21 & 123.424206815455 & 4.78579318454462 \tabularnewline
63 & 129.57 & 129.948005098361 & -0.378005098360745 \tabularnewline
64 & 129.79 & 130.468457283511 & -0.678457283510738 \tabularnewline
65 & 131.66 & 130.062570518545 & 1.59742948145532 \tabularnewline
66 & 135.01 & 131.943335743977 & 3.06666425602324 \tabularnewline
67 & 136.01 & 135.232044864635 & 0.777955135364493 \tabularnewline
68 & 136.31 & 137.172944789005 & -0.8629447890049 \tabularnewline
69 & 136.37 & 136.799481492857 & -0.429481492856524 \tabularnewline
70 & 136.4 & 136.620300131830 & -0.220300131829788 \tabularnewline
71 & 136.4 & 136.546819029976 & -0.1468190299762 \tabularnewline
72 & 136.4 & 136.537277278633 & -0.137277278632808 \tabularnewline
73 & 137.34 & 136.592976536936 & 0.747023463064039 \tabularnewline
74 & 142.18 & 137.639345175864 & 4.540654824136 \tabularnewline
75 & 143.79 & 144.116951648955 & -0.326951648955259 \tabularnewline
76 & 144.08 & 144.888693364020 & -0.808693364020257 \tabularnewline
77 & 144.08 & 144.549517040292 & -0.469517040292004 \tabularnewline
78 & 144.09 & 144.508074444242 & -0.418074444242222 \tabularnewline
79 & 144.09 & 144.368764540674 & -0.27876454067362 \tabularnewline
80 & 144.11 & 145.282973386381 & -1.17297338638062 \tabularnewline
81 & 144.11 & 144.62167925499 & -0.511679254990128 \tabularnewline
82 & 144.15 & 144.380421707644 & -0.230421707643842 \tabularnewline
83 & 144.15 & 144.316684950689 & -0.166684950688591 \tabularnewline
84 & 144.16 & 144.306641417402 & -0.146641417402009 \tabularnewline
85 & 144.2 & 144.372104152273 & -0.172104152273107 \tabularnewline
86 & 144.38 & 144.495257071803 & -0.115257071802631 \tabularnewline
87 & 144.38 & 146.195262525931 & -1.81526252593147 \tabularnewline
88 & 144.28 & 145.319411846729 & -1.03941184672937 \tabularnewline
89 & 144.46 & 144.584407936641 & -0.124407936640665 \tabularnewline
90 & 144.53 & 144.731682254302 & -0.201682254301829 \tabularnewline
91 & 144.53 & 144.657838077448 & -0.127838077448274 \tabularnewline
92 & 145.34 & 145.575859088475 & -0.235859088475479 \tabularnewline
93 & 147.98 & 145.728234991824 & 2.25176500817614 \tabularnewline
94 & 150.42 & 148.196777704546 & 2.22322229545358 \tabularnewline
95 & 150.53 & 150.595016139859 & -0.0650161398594946 \tabularnewline
96 & 150.64 & 150.697540600989 & -0.0575406009889434 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=41756&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]108.62[/C][C]106.501159188034[/C][C]2.11884081196575[/C][/ROW]
[ROW][C]14[/C][C]108.62[/C][C]108.716653787850[/C][C]-0.0966537878498599[/C][/ROW]
[ROW][C]15[/C][C]110.1[/C][C]110.237129131701[/C][C]-0.137129131701201[/C][/ROW]
[ROW][C]16[/C][C]110.74[/C][C]110.883665465296[/C][C]-0.143665465296408[/C][/ROW]
[ROW][C]17[/C][C]110.77[/C][C]110.911286701375[/C][C]-0.141286701375165[/C][/ROW]
[ROW][C]18[/C][C]110.77[/C][C]110.908134687960[/C][C]-0.138134687959607[/C][/ROW]
[ROW][C]19[/C][C]110.78[/C][C]110.765895622784[/C][C]0.0141043772162561[/C][/ROW]
[ROW][C]20[/C][C]110.78[/C][C]111.697501877191[/C][C]-0.917501877190944[/C][/ROW]
[ROW][C]21[/C][C]110.78[/C][C]111.022660554717[/C][C]-0.242660554716934[/C][/ROW]
[ROW][C]22[/C][C]110.84[/C][C]110.788197997048[/C][C]0.0518020029519022[/C][/ROW]
[ROW][C]23[/C][C]110.84[/C][C]110.751589767583[/C][C]0.0884102324170897[/C][/ROW]
[ROW][C]24[/C][C]110.84[/C][C]110.747989537807[/C][C]0.092010462192789[/C][/ROW]
[ROW][C]25[/C][C]110.84[/C][C]110.809480244179[/C][C]0.0305197558211461[/C][/ROW]
[ROW][C]26[/C][C]110.84[/C][C]110.897751125257[/C][C]-0.0577511252572123[/C][/ROW]
[ROW][C]27[/C][C]111.01[/C][C]112.419209089240[/C][C]-1.40920908924043[/C][/ROW]
[ROW][C]28[/C][C]112.66[/C][C]111.723614681844[/C][C]0.93638531815597[/C][/ROW]
[ROW][C]29[/C][C]114.04[/C][C]112.788516303700[/C][C]1.25148369630018[/C][/ROW]
[ROW][C]30[/C][C]114.16[/C][C]114.170543482161[/C][C]-0.0105434821607844[/C][/ROW]
[ROW][C]31[/C][C]114.2[/C][C]114.151527170368[/C][C]0.0484728296323169[/C][/ROW]
[ROW][C]32[/C][C]114.2[/C][C]115.114001517882[/C][C]-0.914001517882028[/C][/ROW]
[ROW][C]33[/C][C]114.23[/C][C]114.439248608984[/C][C]-0.209248608984282[/C][/ROW]
[ROW][C]34[/C][C]114.23[/C][C]114.235629984567[/C][C]-0.00562998456663877[/C][/ROW]
[ROW][C]35[/C][C]114.23[/C][C]114.137571113336[/C][C]0.0924288866641518[/C][/ROW]
[ROW][C]36[/C][C]114.23[/C][C]114.134072388452[/C][C]0.0959276115478076[/C][/ROW]
[ROW][C]37[/C][C]114.23[/C][C]114.195662035862[/C][C]0.0343379641382313[/C][/ROW]
[ROW][C]38[/C][C]114.23[/C][C]114.284029358883[/C][C]-0.0540293588829286[/C][/ROW]
[ROW][C]39[/C][C]115.97[/C][C]115.805581328837[/C][C]0.164418671162991[/C][/ROW]
[ROW][C]40[/C][C]116.96[/C][C]116.719734286130[/C][C]0.240265713869704[/C][/ROW]
[ROW][C]41[/C][C]117.08[/C][C]117.107053020549[/C][C]-0.027053020548891[/C][/ROW]
[ROW][C]42[/C][C]117.08[/C][C]117.196786370423[/C][C]-0.116786370423114[/C][/ROW]
[ROW][C]43[/C][C]117.08[/C][C]117.055086530205[/C][C]0.0249134697949813[/C][/ROW]
[ROW][C]44[/C][C]117.63[/C][C]117.976965805307[/C][C]-0.34696580530715[/C][/ROW]
[ROW][C]45[/C][C]119.12[/C][C]117.866535327563[/C][C]1.25346467243699[/C][/ROW]
[ROW][C]46[/C][C]119.47[/C][C]119.159862542369[/C][C]0.310137457631356[/C][/ROW]
[ROW][C]47[/C][C]119.5[/C][C]119.419779460583[/C][C]0.0802205394169135[/C][/ROW]
[ROW][C]48[/C][C]119.52[/C][C]119.445972372030[/C][C]0.0740276279698548[/C][/ROW]
[ROW][C]49[/C][C]119.49[/C][C]119.527008860265[/C][C]-0.0370088602645495[/C][/ROW]
[ROW][C]50[/C][C]119.49[/C][C]119.583574074604[/C][C]-0.093574074603879[/C][/ROW]
[ROW][C]51[/C][C]119.5[/C][C]121.104127207173[/C][C]-1.60412720717285[/C][/ROW]
[ROW][C]52[/C][C]119.5[/C][C]120.243609474380[/C][C]-0.743609474379525[/C][/ROW]
[ROW][C]53[/C][C]119.56[/C][C]119.616077067442[/C][C]-0.0560770674415068[/C][/ROW]
[ROW][C]54[/C][C]122.35[/C][C]119.645077315495[/C][C]2.70492268450519[/C][/ROW]
[ROW][C]55[/C][C]122.92[/C][C]122.364649412438[/C][C]0.555350587562174[/C][/ROW]
[ROW][C]56[/C][C]122.92[/C][C]123.869926695694[/C][C]-0.94992669569369[/C][/ROW]
[ROW][C]57[/C][C]123.04[/C][C]123.194266373251[/C][C]-0.154266373251303[/C][/ROW]
[ROW][C]58[/C][C]123.04[/C][C]123.082036513718[/C][C]-0.0420365137183012[/C][/ROW]
[ROW][C]59[/C][C]123.04[/C][C]122.983058070764[/C][C]0.056941929235677[/C][/ROW]
[ROW][C]60[/C][C]123.06[/C][C]122.978663001094[/C][C]0.0813369989056554[/C][/ROW]
[ROW][C]61[/C][C]123.33[/C][C]123.059884112554[/C][C]0.270115887446124[/C][/ROW]
[ROW][C]62[/C][C]128.21[/C][C]123.424206815455[/C][C]4.78579318454462[/C][/ROW]
[ROW][C]63[/C][C]129.57[/C][C]129.948005098361[/C][C]-0.378005098360745[/C][/ROW]
[ROW][C]64[/C][C]129.79[/C][C]130.468457283511[/C][C]-0.678457283510738[/C][/ROW]
[ROW][C]65[/C][C]131.66[/C][C]130.062570518545[/C][C]1.59742948145532[/C][/ROW]
[ROW][C]66[/C][C]135.01[/C][C]131.943335743977[/C][C]3.06666425602324[/C][/ROW]
[ROW][C]67[/C][C]136.01[/C][C]135.232044864635[/C][C]0.777955135364493[/C][/ROW]
[ROW][C]68[/C][C]136.31[/C][C]137.172944789005[/C][C]-0.8629447890049[/C][/ROW]
[ROW][C]69[/C][C]136.37[/C][C]136.799481492857[/C][C]-0.429481492856524[/C][/ROW]
[ROW][C]70[/C][C]136.4[/C][C]136.620300131830[/C][C]-0.220300131829788[/C][/ROW]
[ROW][C]71[/C][C]136.4[/C][C]136.546819029976[/C][C]-0.1468190299762[/C][/ROW]
[ROW][C]72[/C][C]136.4[/C][C]136.537277278633[/C][C]-0.137277278632808[/C][/ROW]
[ROW][C]73[/C][C]137.34[/C][C]136.592976536936[/C][C]0.747023463064039[/C][/ROW]
[ROW][C]74[/C][C]142.18[/C][C]137.639345175864[/C][C]4.540654824136[/C][/ROW]
[ROW][C]75[/C][C]143.79[/C][C]144.116951648955[/C][C]-0.326951648955259[/C][/ROW]
[ROW][C]76[/C][C]144.08[/C][C]144.888693364020[/C][C]-0.808693364020257[/C][/ROW]
[ROW][C]77[/C][C]144.08[/C][C]144.549517040292[/C][C]-0.469517040292004[/C][/ROW]
[ROW][C]78[/C][C]144.09[/C][C]144.508074444242[/C][C]-0.418074444242222[/C][/ROW]
[ROW][C]79[/C][C]144.09[/C][C]144.368764540674[/C][C]-0.27876454067362[/C][/ROW]
[ROW][C]80[/C][C]144.11[/C][C]145.282973386381[/C][C]-1.17297338638062[/C][/ROW]
[ROW][C]81[/C][C]144.11[/C][C]144.62167925499[/C][C]-0.511679254990128[/C][/ROW]
[ROW][C]82[/C][C]144.15[/C][C]144.380421707644[/C][C]-0.230421707643842[/C][/ROW]
[ROW][C]83[/C][C]144.15[/C][C]144.316684950689[/C][C]-0.166684950688591[/C][/ROW]
[ROW][C]84[/C][C]144.16[/C][C]144.306641417402[/C][C]-0.146641417402009[/C][/ROW]
[ROW][C]85[/C][C]144.2[/C][C]144.372104152273[/C][C]-0.172104152273107[/C][/ROW]
[ROW][C]86[/C][C]144.38[/C][C]144.495257071803[/C][C]-0.115257071802631[/C][/ROW]
[ROW][C]87[/C][C]144.38[/C][C]146.195262525931[/C][C]-1.81526252593147[/C][/ROW]
[ROW][C]88[/C][C]144.28[/C][C]145.319411846729[/C][C]-1.03941184672937[/C][/ROW]
[ROW][C]89[/C][C]144.46[/C][C]144.584407936641[/C][C]-0.124407936640665[/C][/ROW]
[ROW][C]90[/C][C]144.53[/C][C]144.731682254302[/C][C]-0.201682254301829[/C][/ROW]
[ROW][C]91[/C][C]144.53[/C][C]144.657838077448[/C][C]-0.127838077448274[/C][/ROW]
[ROW][C]92[/C][C]145.34[/C][C]145.575859088475[/C][C]-0.235859088475479[/C][/ROW]
[ROW][C]93[/C][C]147.98[/C][C]145.728234991824[/C][C]2.25176500817614[/C][/ROW]
[ROW][C]94[/C][C]150.42[/C][C]148.196777704546[/C][C]2.22322229545358[/C][/ROW]
[ROW][C]95[/C][C]150.53[/C][C]150.595016139859[/C][C]-0.0650161398594946[/C][/ROW]
[ROW][C]96[/C][C]150.64[/C][C]150.697540600989[/C][C]-0.0575406009889434[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=41756&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=41756&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
13108.62106.5011591880342.11884081196575
14108.62108.716653787850-0.0966537878498599
15110.1110.237129131701-0.137129131701201
16110.74110.883665465296-0.143665465296408
17110.77110.911286701375-0.141286701375165
18110.77110.908134687960-0.138134687959607
19110.78110.7658956227840.0141043772162561
20110.78111.697501877191-0.917501877190944
21110.78111.022660554717-0.242660554716934
22110.84110.7881979970480.0518020029519022
23110.84110.7515897675830.0884102324170897
24110.84110.7479895378070.092010462192789
25110.84110.8094802441790.0305197558211461
26110.84110.897751125257-0.0577511252572123
27111.01112.419209089240-1.40920908924043
28112.66111.7236146818440.93638531815597
29114.04112.7885163037001.25148369630018
30114.16114.170543482161-0.0105434821607844
31114.2114.1515271703680.0484728296323169
32114.2115.114001517882-0.914001517882028
33114.23114.439248608984-0.209248608984282
34114.23114.235629984567-0.00562998456663877
35114.23114.1375711133360.0924288866641518
36114.23114.1340723884520.0959276115478076
37114.23114.1956620358620.0343379641382313
38114.23114.284029358883-0.0540293588829286
39115.97115.8055813288370.164418671162991
40116.96116.7197342861300.240265713869704
41117.08117.107053020549-0.027053020548891
42117.08117.196786370423-0.116786370423114
43117.08117.0550865302050.0249134697949813
44117.63117.976965805307-0.34696580530715
45119.12117.8665353275631.25346467243699
46119.47119.1598625423690.310137457631356
47119.5119.4197794605830.0802205394169135
48119.52119.4459723720300.0740276279698548
49119.49119.527008860265-0.0370088602645495
50119.49119.583574074604-0.093574074603879
51119.5121.104127207173-1.60412720717285
52119.5120.243609474380-0.743609474379525
53119.56119.616077067442-0.0560770674415068
54122.35119.6450773154952.70492268450519
55122.92122.3646494124380.555350587562174
56122.92123.869926695694-0.94992669569369
57123.04123.194266373251-0.154266373251303
58123.04123.082036513718-0.0420365137183012
59123.04122.9830580707640.056941929235677
60123.06122.9786630010940.0813369989056554
61123.33123.0598841125540.270115887446124
62128.21123.4242068154554.78579318454462
63129.57129.948005098361-0.378005098360745
64129.79130.468457283511-0.678457283510738
65131.66130.0625705185451.59742948145532
66135.01131.9433357439773.06666425602324
67136.01135.2320448646350.777955135364493
68136.31137.172944789005-0.8629447890049
69136.37136.799481492857-0.429481492856524
70136.4136.620300131830-0.220300131829788
71136.4136.546819029976-0.1468190299762
72136.4136.537277278633-0.137277278632808
73137.34136.5929765369360.747023463064039
74142.18137.6393451758644.540654824136
75143.79144.116951648955-0.326951648955259
76144.08144.888693364020-0.808693364020257
77144.08144.549517040292-0.469517040292004
78144.09144.508074444242-0.418074444242222
79144.09144.368764540674-0.27876454067362
80144.11145.282973386381-1.17297338638062
81144.11144.62167925499-0.511679254990128
82144.15144.380421707644-0.230421707643842
83144.15144.316684950689-0.166684950688591
84144.16144.306641417402-0.146641417402009
85144.2144.372104152273-0.172104152273107
86144.38144.495257071803-0.115257071802631
87144.38146.195262525931-1.81526252593147
88144.28145.319411846729-1.03941184672937
89144.46144.584407936641-0.124407936640665
90144.53144.731682254302-0.201682254301829
91144.53144.657838077448-0.127838077448274
92145.34145.575859088475-0.235859088475479
93147.98145.7282349918242.25176500817614
94150.42148.1967777045462.22322229545358
95150.53150.595016139859-0.0650161398594946
96150.64150.697540600989-0.0575406009889434







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
97150.865253882484148.725181116073153.005326648896
98151.178007764969148.113026924141154.242988605796
99153.013678314120149.212568977828156.814787650412
100154.019348863271149.575394633073158.463303093468
101154.416269412422149.386275132633159.446263692211
102154.783606628240149.205917518094160.361295738385
103155.012193844057148.914334127451161.110053560664
104156.162031059875149.564568043247162.759494076503
105156.660201609026149.578935121621163.741468096431
106156.930038824844149.377344774892164.482732874795
107157.101959373995149.087664697949165.116254050040
108157.268046589812148.800025914841165.736067264783

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
97 & 150.865253882484 & 148.725181116073 & 153.005326648896 \tabularnewline
98 & 151.178007764969 & 148.113026924141 & 154.242988605796 \tabularnewline
99 & 153.013678314120 & 149.212568977828 & 156.814787650412 \tabularnewline
100 & 154.019348863271 & 149.575394633073 & 158.463303093468 \tabularnewline
101 & 154.416269412422 & 149.386275132633 & 159.446263692211 \tabularnewline
102 & 154.783606628240 & 149.205917518094 & 160.361295738385 \tabularnewline
103 & 155.012193844057 & 148.914334127451 & 161.110053560664 \tabularnewline
104 & 156.162031059875 & 149.564568043247 & 162.759494076503 \tabularnewline
105 & 156.660201609026 & 149.578935121621 & 163.741468096431 \tabularnewline
106 & 156.930038824844 & 149.377344774892 & 164.482732874795 \tabularnewline
107 & 157.101959373995 & 149.087664697949 & 165.116254050040 \tabularnewline
108 & 157.268046589812 & 148.800025914841 & 165.736067264783 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=41756&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]97[/C][C]150.865253882484[/C][C]148.725181116073[/C][C]153.005326648896[/C][/ROW]
[ROW][C]98[/C][C]151.178007764969[/C][C]148.113026924141[/C][C]154.242988605796[/C][/ROW]
[ROW][C]99[/C][C]153.013678314120[/C][C]149.212568977828[/C][C]156.814787650412[/C][/ROW]
[ROW][C]100[/C][C]154.019348863271[/C][C]149.575394633073[/C][C]158.463303093468[/C][/ROW]
[ROW][C]101[/C][C]154.416269412422[/C][C]149.386275132633[/C][C]159.446263692211[/C][/ROW]
[ROW][C]102[/C][C]154.783606628240[/C][C]149.205917518094[/C][C]160.361295738385[/C][/ROW]
[ROW][C]103[/C][C]155.012193844057[/C][C]148.914334127451[/C][C]161.110053560664[/C][/ROW]
[ROW][C]104[/C][C]156.162031059875[/C][C]149.564568043247[/C][C]162.759494076503[/C][/ROW]
[ROW][C]105[/C][C]156.660201609026[/C][C]149.578935121621[/C][C]163.741468096431[/C][/ROW]
[ROW][C]106[/C][C]156.930038824844[/C][C]149.377344774892[/C][C]164.482732874795[/C][/ROW]
[ROW][C]107[/C][C]157.101959373995[/C][C]149.087664697949[/C][C]165.116254050040[/C][/ROW]
[ROW][C]108[/C][C]157.268046589812[/C][C]148.800025914841[/C][C]165.736067264783[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=41756&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=41756&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
97150.865253882484148.725181116073153.005326648896
98151.178007764969148.113026924141154.242988605796
99153.013678314120149.212568977828156.814787650412
100154.019348863271149.575394633073158.463303093468
101154.416269412422149.386275132633159.446263692211
102154.783606628240149.205917518094160.361295738385
103155.012193844057148.914334127451161.110053560664
104156.162031059875149.564568043247162.759494076503
105156.660201609026149.578935121621163.741468096431
106156.930038824844149.377344774892164.482732874795
107157.101959373995149.087664697949165.116254050040
108157.268046589812148.800025914841165.736067264783



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=0, beta=0)
if (par2 == 'Double') fit <- HoltWinters(x, gamma=0)
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')