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Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationMon, 26 May 2008 03:23:08 -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/2008/May/26/t1211793852zg9xmwv9l593qcr.htm/, Retrieved Mon, 13 May 2024 22:08:18 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=13253, Retrieved Mon, 13 May 2024 22:08:18 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact204
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [exponential smoot...] [2008-05-26 09:23:08] [1e17f2ab0c3b2b3de21c4ac88dec2f8d] [Current]
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Dataseries X:
104,7
104,7
104,7
104,7
106
107
107
107
107
107
107
107
107
107
107
107
107,6
109,9
109,9
109,9
109,9
109,9
109,9
109,9
109,9
109,9
109,9
109,9
110,6
114,3
114,3
114,3
114,3
114,3
114,3
114,3
114,3
114,3
114,3
114,3
114,3
119,01
119,01
119,01
119,01
119,01
119,01
119,01
119,01
119,01
119,01
119,01
121,27
123,54
123,54
123,54
123,54
123,54
123,54
123,54
123,54
123,54
123,54
123,54
123,54
125,24
125,24
125,24
125,24
125,24
125,24
125,24
125,24
125,24
125,24
125,24
125,24
128,35
128,35
128,35
128,35
128,35
128,35
128,35




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time3 seconds
R Server'Sir Ronald Aylmer Fisher' @ 193.190.124.24

\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 & 3 seconds \tabularnewline
R Server & 'Sir Ronald Aylmer Fisher' @ 193.190.124.24 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=13253&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]3 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Sir Ronald Aylmer Fisher' @ 193.190.124.24[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=13253&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=13253&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 time3 seconds
R Server'Sir Ronald Aylmer Fisher' @ 193.190.124.24







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha1
beta0.0267675815717632
gamma0

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 1 \tabularnewline
beta & 0.0267675815717632 \tabularnewline
gamma & 0 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=13253&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]0.0267675815717632[/C][/ROW]
[ROW][C]gamma[/C][C]0[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=13253&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=13253&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
beta0.0267675815717632
gamma0







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
3104.7104.70
4104.7104.70
5106104.71.30000000000000
6107106.0347978560430.965202143956702
7107107.060633983165-0.060633983164891
8107107.059010958075-0.0590109580745093
9107107.057431377441-0.0574313774406221
10107107.055894078360-0.0558940783601969
11107107.054397929058-0.054397929058311
12107107.052941828055-0.0529418280549123
13107107.051524703354-0.0515247033538913
14107107.050145511654-0.0501455116539091
15107107.048803237580-0.048803237580259
16107107.047496892937-0.0474968929373603
17107.6107.0462255159810.553774484018746
18109.9107.6610487196552.23895128034543
19109.9110.020980030686-0.120980030686439
20109.9110.017741687846-0.117741687846475
21109.9110.014590027613-0.114590027612650
22109.9110.011522729701-0.111522729701221
23109.9110.008537535937-0.108537535936833
24109.9110.00563224859-0.105632248590055
25109.9110.002804728759-0.102804728759310
26109.9110.000052894796-0.100052894796278
27109.9109.997374720773-0.097374720773331
28109.9109.994768234992-0.094768234992003
29110.6109.9922315185310.607768481468554
30114.3110.7085000109363.59149998906410
31114.3114.504635779858-0.204635779858151
32114.3114.499158174928-0.1991581749283
33114.3114.493827192235-0.193827192235219
34114.3114.488638907056-0.188638907056244
35114.3114.483589499724-0.183589499724008
36114.3114.478675252814-0.178675252814429
37114.3114.473892548410-0.173892548409853
38114.3114.469237865436-0.169237865435576
39114.3114.464707777068-0.164707777067505
40114.3114.460298948209-0.160298948209345
41114.3114.456008133037-0.156008133037275
42119.01114.4518321726104.55816782738967
43119.01119.283843301748-0.273843301747789
44119.01119.276513178830-0.266513178830365
45119.01119.269379265576-0.259379265576072
46119.01119.262436309927-0.252436309926750
47119.01119.255679200409-0.245679200409114
48119.01119.249102962372-0.239102962371675
49119.01119.242702754322-0.232702754322332
50119.01119.236473864364-0.226473864364038
51119.01119.230411706726-0.220411706725798
52119.01119.224511818387-0.214511818386654
53121.27119.218769855792.05123014421011
54123.54121.5336763259972.00632367400253
55123.54123.857380758601-0.317380758600706
56123.54123.848885243256-0.308885243255546
57123.54123.840617132310-0.300617132310393
58123.54123.832570338699-0.292570338699406
59123.54123.824738938293-0.28473893829279
60123.54123.817117165535-0.277117165535387
61123.54123.809699409202-0.269699409201976
62123.54123.802480208266-0.262480208266311
63123.54123.795454247881-0.255454247880564
64123.54123.788616355463-0.248616355462573
65123.54123.781961496888-0.241961496887654
66125.24123.7754847727821.46451522721750
67125.24125.51468630359-0.274686303590116
68125.24125.507333615552-0.267333615552118
69125.24125.500177741191-0.260177741190958
70125.24125.493213412280-0.253213412280473
71125.24125.486435501612-0.246435501612183
72125.24125.479839019221-0.239839019220611
73125.24125.473419108710-0.233419108709526
74125.24125.467171043677-0.227171043676734
75125.24125.461090224234-0.221090224234374
76125.24125.455172173622-0.215172173622463
77125.24125.449412534913-0.209412534913056
78128.35125.4438070678032.90619293219738
79128.35128.631598824178-0.281598824178502
80128.35128.624061104682-0.274061104681778
81128.35128.616725151707-0.266725151706567
82128.35128.609585564451-0.259585564451015
83128.35128.602637086680-0.252637086679727
84128.35128.595874602854-0.245874602853974

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
3 & 104.7 & 104.7 & 0 \tabularnewline
4 & 104.7 & 104.7 & 0 \tabularnewline
5 & 106 & 104.7 & 1.30000000000000 \tabularnewline
6 & 107 & 106.034797856043 & 0.965202143956702 \tabularnewline
7 & 107 & 107.060633983165 & -0.060633983164891 \tabularnewline
8 & 107 & 107.059010958075 & -0.0590109580745093 \tabularnewline
9 & 107 & 107.057431377441 & -0.0574313774406221 \tabularnewline
10 & 107 & 107.055894078360 & -0.0558940783601969 \tabularnewline
11 & 107 & 107.054397929058 & -0.054397929058311 \tabularnewline
12 & 107 & 107.052941828055 & -0.0529418280549123 \tabularnewline
13 & 107 & 107.051524703354 & -0.0515247033538913 \tabularnewline
14 & 107 & 107.050145511654 & -0.0501455116539091 \tabularnewline
15 & 107 & 107.048803237580 & -0.048803237580259 \tabularnewline
16 & 107 & 107.047496892937 & -0.0474968929373603 \tabularnewline
17 & 107.6 & 107.046225515981 & 0.553774484018746 \tabularnewline
18 & 109.9 & 107.661048719655 & 2.23895128034543 \tabularnewline
19 & 109.9 & 110.020980030686 & -0.120980030686439 \tabularnewline
20 & 109.9 & 110.017741687846 & -0.117741687846475 \tabularnewline
21 & 109.9 & 110.014590027613 & -0.114590027612650 \tabularnewline
22 & 109.9 & 110.011522729701 & -0.111522729701221 \tabularnewline
23 & 109.9 & 110.008537535937 & -0.108537535936833 \tabularnewline
24 & 109.9 & 110.00563224859 & -0.105632248590055 \tabularnewline
25 & 109.9 & 110.002804728759 & -0.102804728759310 \tabularnewline
26 & 109.9 & 110.000052894796 & -0.100052894796278 \tabularnewline
27 & 109.9 & 109.997374720773 & -0.097374720773331 \tabularnewline
28 & 109.9 & 109.994768234992 & -0.094768234992003 \tabularnewline
29 & 110.6 & 109.992231518531 & 0.607768481468554 \tabularnewline
30 & 114.3 & 110.708500010936 & 3.59149998906410 \tabularnewline
31 & 114.3 & 114.504635779858 & -0.204635779858151 \tabularnewline
32 & 114.3 & 114.499158174928 & -0.1991581749283 \tabularnewline
33 & 114.3 & 114.493827192235 & -0.193827192235219 \tabularnewline
34 & 114.3 & 114.488638907056 & -0.188638907056244 \tabularnewline
35 & 114.3 & 114.483589499724 & -0.183589499724008 \tabularnewline
36 & 114.3 & 114.478675252814 & -0.178675252814429 \tabularnewline
37 & 114.3 & 114.473892548410 & -0.173892548409853 \tabularnewline
38 & 114.3 & 114.469237865436 & -0.169237865435576 \tabularnewline
39 & 114.3 & 114.464707777068 & -0.164707777067505 \tabularnewline
40 & 114.3 & 114.460298948209 & -0.160298948209345 \tabularnewline
41 & 114.3 & 114.456008133037 & -0.156008133037275 \tabularnewline
42 & 119.01 & 114.451832172610 & 4.55816782738967 \tabularnewline
43 & 119.01 & 119.283843301748 & -0.273843301747789 \tabularnewline
44 & 119.01 & 119.276513178830 & -0.266513178830365 \tabularnewline
45 & 119.01 & 119.269379265576 & -0.259379265576072 \tabularnewline
46 & 119.01 & 119.262436309927 & -0.252436309926750 \tabularnewline
47 & 119.01 & 119.255679200409 & -0.245679200409114 \tabularnewline
48 & 119.01 & 119.249102962372 & -0.239102962371675 \tabularnewline
49 & 119.01 & 119.242702754322 & -0.232702754322332 \tabularnewline
50 & 119.01 & 119.236473864364 & -0.226473864364038 \tabularnewline
51 & 119.01 & 119.230411706726 & -0.220411706725798 \tabularnewline
52 & 119.01 & 119.224511818387 & -0.214511818386654 \tabularnewline
53 & 121.27 & 119.21876985579 & 2.05123014421011 \tabularnewline
54 & 123.54 & 121.533676325997 & 2.00632367400253 \tabularnewline
55 & 123.54 & 123.857380758601 & -0.317380758600706 \tabularnewline
56 & 123.54 & 123.848885243256 & -0.308885243255546 \tabularnewline
57 & 123.54 & 123.840617132310 & -0.300617132310393 \tabularnewline
58 & 123.54 & 123.832570338699 & -0.292570338699406 \tabularnewline
59 & 123.54 & 123.824738938293 & -0.28473893829279 \tabularnewline
60 & 123.54 & 123.817117165535 & -0.277117165535387 \tabularnewline
61 & 123.54 & 123.809699409202 & -0.269699409201976 \tabularnewline
62 & 123.54 & 123.802480208266 & -0.262480208266311 \tabularnewline
63 & 123.54 & 123.795454247881 & -0.255454247880564 \tabularnewline
64 & 123.54 & 123.788616355463 & -0.248616355462573 \tabularnewline
65 & 123.54 & 123.781961496888 & -0.241961496887654 \tabularnewline
66 & 125.24 & 123.775484772782 & 1.46451522721750 \tabularnewline
67 & 125.24 & 125.51468630359 & -0.274686303590116 \tabularnewline
68 & 125.24 & 125.507333615552 & -0.267333615552118 \tabularnewline
69 & 125.24 & 125.500177741191 & -0.260177741190958 \tabularnewline
70 & 125.24 & 125.493213412280 & -0.253213412280473 \tabularnewline
71 & 125.24 & 125.486435501612 & -0.246435501612183 \tabularnewline
72 & 125.24 & 125.479839019221 & -0.239839019220611 \tabularnewline
73 & 125.24 & 125.473419108710 & -0.233419108709526 \tabularnewline
74 & 125.24 & 125.467171043677 & -0.227171043676734 \tabularnewline
75 & 125.24 & 125.461090224234 & -0.221090224234374 \tabularnewline
76 & 125.24 & 125.455172173622 & -0.215172173622463 \tabularnewline
77 & 125.24 & 125.449412534913 & -0.209412534913056 \tabularnewline
78 & 128.35 & 125.443807067803 & 2.90619293219738 \tabularnewline
79 & 128.35 & 128.631598824178 & -0.281598824178502 \tabularnewline
80 & 128.35 & 128.624061104682 & -0.274061104681778 \tabularnewline
81 & 128.35 & 128.616725151707 & -0.266725151706567 \tabularnewline
82 & 128.35 & 128.609585564451 & -0.259585564451015 \tabularnewline
83 & 128.35 & 128.602637086680 & -0.252637086679727 \tabularnewline
84 & 128.35 & 128.595874602854 & -0.245874602853974 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=13253&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]3[/C][C]104.7[/C][C]104.7[/C][C]0[/C][/ROW]
[ROW][C]4[/C][C]104.7[/C][C]104.7[/C][C]0[/C][/ROW]
[ROW][C]5[/C][C]106[/C][C]104.7[/C][C]1.30000000000000[/C][/ROW]
[ROW][C]6[/C][C]107[/C][C]106.034797856043[/C][C]0.965202143956702[/C][/ROW]
[ROW][C]7[/C][C]107[/C][C]107.060633983165[/C][C]-0.060633983164891[/C][/ROW]
[ROW][C]8[/C][C]107[/C][C]107.059010958075[/C][C]-0.0590109580745093[/C][/ROW]
[ROW][C]9[/C][C]107[/C][C]107.057431377441[/C][C]-0.0574313774406221[/C][/ROW]
[ROW][C]10[/C][C]107[/C][C]107.055894078360[/C][C]-0.0558940783601969[/C][/ROW]
[ROW][C]11[/C][C]107[/C][C]107.054397929058[/C][C]-0.054397929058311[/C][/ROW]
[ROW][C]12[/C][C]107[/C][C]107.052941828055[/C][C]-0.0529418280549123[/C][/ROW]
[ROW][C]13[/C][C]107[/C][C]107.051524703354[/C][C]-0.0515247033538913[/C][/ROW]
[ROW][C]14[/C][C]107[/C][C]107.050145511654[/C][C]-0.0501455116539091[/C][/ROW]
[ROW][C]15[/C][C]107[/C][C]107.048803237580[/C][C]-0.048803237580259[/C][/ROW]
[ROW][C]16[/C][C]107[/C][C]107.047496892937[/C][C]-0.0474968929373603[/C][/ROW]
[ROW][C]17[/C][C]107.6[/C][C]107.046225515981[/C][C]0.553774484018746[/C][/ROW]
[ROW][C]18[/C][C]109.9[/C][C]107.661048719655[/C][C]2.23895128034543[/C][/ROW]
[ROW][C]19[/C][C]109.9[/C][C]110.020980030686[/C][C]-0.120980030686439[/C][/ROW]
[ROW][C]20[/C][C]109.9[/C][C]110.017741687846[/C][C]-0.117741687846475[/C][/ROW]
[ROW][C]21[/C][C]109.9[/C][C]110.014590027613[/C][C]-0.114590027612650[/C][/ROW]
[ROW][C]22[/C][C]109.9[/C][C]110.011522729701[/C][C]-0.111522729701221[/C][/ROW]
[ROW][C]23[/C][C]109.9[/C][C]110.008537535937[/C][C]-0.108537535936833[/C][/ROW]
[ROW][C]24[/C][C]109.9[/C][C]110.00563224859[/C][C]-0.105632248590055[/C][/ROW]
[ROW][C]25[/C][C]109.9[/C][C]110.002804728759[/C][C]-0.102804728759310[/C][/ROW]
[ROW][C]26[/C][C]109.9[/C][C]110.000052894796[/C][C]-0.100052894796278[/C][/ROW]
[ROW][C]27[/C][C]109.9[/C][C]109.997374720773[/C][C]-0.097374720773331[/C][/ROW]
[ROW][C]28[/C][C]109.9[/C][C]109.994768234992[/C][C]-0.094768234992003[/C][/ROW]
[ROW][C]29[/C][C]110.6[/C][C]109.992231518531[/C][C]0.607768481468554[/C][/ROW]
[ROW][C]30[/C][C]114.3[/C][C]110.708500010936[/C][C]3.59149998906410[/C][/ROW]
[ROW][C]31[/C][C]114.3[/C][C]114.504635779858[/C][C]-0.204635779858151[/C][/ROW]
[ROW][C]32[/C][C]114.3[/C][C]114.499158174928[/C][C]-0.1991581749283[/C][/ROW]
[ROW][C]33[/C][C]114.3[/C][C]114.493827192235[/C][C]-0.193827192235219[/C][/ROW]
[ROW][C]34[/C][C]114.3[/C][C]114.488638907056[/C][C]-0.188638907056244[/C][/ROW]
[ROW][C]35[/C][C]114.3[/C][C]114.483589499724[/C][C]-0.183589499724008[/C][/ROW]
[ROW][C]36[/C][C]114.3[/C][C]114.478675252814[/C][C]-0.178675252814429[/C][/ROW]
[ROW][C]37[/C][C]114.3[/C][C]114.473892548410[/C][C]-0.173892548409853[/C][/ROW]
[ROW][C]38[/C][C]114.3[/C][C]114.469237865436[/C][C]-0.169237865435576[/C][/ROW]
[ROW][C]39[/C][C]114.3[/C][C]114.464707777068[/C][C]-0.164707777067505[/C][/ROW]
[ROW][C]40[/C][C]114.3[/C][C]114.460298948209[/C][C]-0.160298948209345[/C][/ROW]
[ROW][C]41[/C][C]114.3[/C][C]114.456008133037[/C][C]-0.156008133037275[/C][/ROW]
[ROW][C]42[/C][C]119.01[/C][C]114.451832172610[/C][C]4.55816782738967[/C][/ROW]
[ROW][C]43[/C][C]119.01[/C][C]119.283843301748[/C][C]-0.273843301747789[/C][/ROW]
[ROW][C]44[/C][C]119.01[/C][C]119.276513178830[/C][C]-0.266513178830365[/C][/ROW]
[ROW][C]45[/C][C]119.01[/C][C]119.269379265576[/C][C]-0.259379265576072[/C][/ROW]
[ROW][C]46[/C][C]119.01[/C][C]119.262436309927[/C][C]-0.252436309926750[/C][/ROW]
[ROW][C]47[/C][C]119.01[/C][C]119.255679200409[/C][C]-0.245679200409114[/C][/ROW]
[ROW][C]48[/C][C]119.01[/C][C]119.249102962372[/C][C]-0.239102962371675[/C][/ROW]
[ROW][C]49[/C][C]119.01[/C][C]119.242702754322[/C][C]-0.232702754322332[/C][/ROW]
[ROW][C]50[/C][C]119.01[/C][C]119.236473864364[/C][C]-0.226473864364038[/C][/ROW]
[ROW][C]51[/C][C]119.01[/C][C]119.230411706726[/C][C]-0.220411706725798[/C][/ROW]
[ROW][C]52[/C][C]119.01[/C][C]119.224511818387[/C][C]-0.214511818386654[/C][/ROW]
[ROW][C]53[/C][C]121.27[/C][C]119.21876985579[/C][C]2.05123014421011[/C][/ROW]
[ROW][C]54[/C][C]123.54[/C][C]121.533676325997[/C][C]2.00632367400253[/C][/ROW]
[ROW][C]55[/C][C]123.54[/C][C]123.857380758601[/C][C]-0.317380758600706[/C][/ROW]
[ROW][C]56[/C][C]123.54[/C][C]123.848885243256[/C][C]-0.308885243255546[/C][/ROW]
[ROW][C]57[/C][C]123.54[/C][C]123.840617132310[/C][C]-0.300617132310393[/C][/ROW]
[ROW][C]58[/C][C]123.54[/C][C]123.832570338699[/C][C]-0.292570338699406[/C][/ROW]
[ROW][C]59[/C][C]123.54[/C][C]123.824738938293[/C][C]-0.28473893829279[/C][/ROW]
[ROW][C]60[/C][C]123.54[/C][C]123.817117165535[/C][C]-0.277117165535387[/C][/ROW]
[ROW][C]61[/C][C]123.54[/C][C]123.809699409202[/C][C]-0.269699409201976[/C][/ROW]
[ROW][C]62[/C][C]123.54[/C][C]123.802480208266[/C][C]-0.262480208266311[/C][/ROW]
[ROW][C]63[/C][C]123.54[/C][C]123.795454247881[/C][C]-0.255454247880564[/C][/ROW]
[ROW][C]64[/C][C]123.54[/C][C]123.788616355463[/C][C]-0.248616355462573[/C][/ROW]
[ROW][C]65[/C][C]123.54[/C][C]123.781961496888[/C][C]-0.241961496887654[/C][/ROW]
[ROW][C]66[/C][C]125.24[/C][C]123.775484772782[/C][C]1.46451522721750[/C][/ROW]
[ROW][C]67[/C][C]125.24[/C][C]125.51468630359[/C][C]-0.274686303590116[/C][/ROW]
[ROW][C]68[/C][C]125.24[/C][C]125.507333615552[/C][C]-0.267333615552118[/C][/ROW]
[ROW][C]69[/C][C]125.24[/C][C]125.500177741191[/C][C]-0.260177741190958[/C][/ROW]
[ROW][C]70[/C][C]125.24[/C][C]125.493213412280[/C][C]-0.253213412280473[/C][/ROW]
[ROW][C]71[/C][C]125.24[/C][C]125.486435501612[/C][C]-0.246435501612183[/C][/ROW]
[ROW][C]72[/C][C]125.24[/C][C]125.479839019221[/C][C]-0.239839019220611[/C][/ROW]
[ROW][C]73[/C][C]125.24[/C][C]125.473419108710[/C][C]-0.233419108709526[/C][/ROW]
[ROW][C]74[/C][C]125.24[/C][C]125.467171043677[/C][C]-0.227171043676734[/C][/ROW]
[ROW][C]75[/C][C]125.24[/C][C]125.461090224234[/C][C]-0.221090224234374[/C][/ROW]
[ROW][C]76[/C][C]125.24[/C][C]125.455172173622[/C][C]-0.215172173622463[/C][/ROW]
[ROW][C]77[/C][C]125.24[/C][C]125.449412534913[/C][C]-0.209412534913056[/C][/ROW]
[ROW][C]78[/C][C]128.35[/C][C]125.443807067803[/C][C]2.90619293219738[/C][/ROW]
[ROW][C]79[/C][C]128.35[/C][C]128.631598824178[/C][C]-0.281598824178502[/C][/ROW]
[ROW][C]80[/C][C]128.35[/C][C]128.624061104682[/C][C]-0.274061104681778[/C][/ROW]
[ROW][C]81[/C][C]128.35[/C][C]128.616725151707[/C][C]-0.266725151706567[/C][/ROW]
[ROW][C]82[/C][C]128.35[/C][C]128.609585564451[/C][C]-0.259585564451015[/C][/ROW]
[ROW][C]83[/C][C]128.35[/C][C]128.602637086680[/C][C]-0.252637086679727[/C][/ROW]
[ROW][C]84[/C][C]128.35[/C][C]128.595874602854[/C][C]-0.245874602853974[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=13253&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=13253&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
3104.7104.70
4104.7104.70
5106104.71.30000000000000
6107106.0347978560430.965202143956702
7107107.060633983165-0.060633983164891
8107107.059010958075-0.0590109580745093
9107107.057431377441-0.0574313774406221
10107107.055894078360-0.0558940783601969
11107107.054397929058-0.054397929058311
12107107.052941828055-0.0529418280549123
13107107.051524703354-0.0515247033538913
14107107.050145511654-0.0501455116539091
15107107.048803237580-0.048803237580259
16107107.047496892937-0.0474968929373603
17107.6107.0462255159810.553774484018746
18109.9107.6610487196552.23895128034543
19109.9110.020980030686-0.120980030686439
20109.9110.017741687846-0.117741687846475
21109.9110.014590027613-0.114590027612650
22109.9110.011522729701-0.111522729701221
23109.9110.008537535937-0.108537535936833
24109.9110.00563224859-0.105632248590055
25109.9110.002804728759-0.102804728759310
26109.9110.000052894796-0.100052894796278
27109.9109.997374720773-0.097374720773331
28109.9109.994768234992-0.094768234992003
29110.6109.9922315185310.607768481468554
30114.3110.7085000109363.59149998906410
31114.3114.504635779858-0.204635779858151
32114.3114.499158174928-0.1991581749283
33114.3114.493827192235-0.193827192235219
34114.3114.488638907056-0.188638907056244
35114.3114.483589499724-0.183589499724008
36114.3114.478675252814-0.178675252814429
37114.3114.473892548410-0.173892548409853
38114.3114.469237865436-0.169237865435576
39114.3114.464707777068-0.164707777067505
40114.3114.460298948209-0.160298948209345
41114.3114.456008133037-0.156008133037275
42119.01114.4518321726104.55816782738967
43119.01119.283843301748-0.273843301747789
44119.01119.276513178830-0.266513178830365
45119.01119.269379265576-0.259379265576072
46119.01119.262436309927-0.252436309926750
47119.01119.255679200409-0.245679200409114
48119.01119.249102962372-0.239102962371675
49119.01119.242702754322-0.232702754322332
50119.01119.236473864364-0.226473864364038
51119.01119.230411706726-0.220411706725798
52119.01119.224511818387-0.214511818386654
53121.27119.218769855792.05123014421011
54123.54121.5336763259972.00632367400253
55123.54123.857380758601-0.317380758600706
56123.54123.848885243256-0.308885243255546
57123.54123.840617132310-0.300617132310393
58123.54123.832570338699-0.292570338699406
59123.54123.824738938293-0.28473893829279
60123.54123.817117165535-0.277117165535387
61123.54123.809699409202-0.269699409201976
62123.54123.802480208266-0.262480208266311
63123.54123.795454247881-0.255454247880564
64123.54123.788616355463-0.248616355462573
65123.54123.781961496888-0.241961496887654
66125.24123.7754847727821.46451522721750
67125.24125.51468630359-0.274686303590116
68125.24125.507333615552-0.267333615552118
69125.24125.500177741191-0.260177741190958
70125.24125.493213412280-0.253213412280473
71125.24125.486435501612-0.246435501612183
72125.24125.479839019221-0.239839019220611
73125.24125.473419108710-0.233419108709526
74125.24125.467171043677-0.227171043676734
75125.24125.461090224234-0.221090224234374
76125.24125.455172173622-0.215172173622463
77125.24125.449412534913-0.209412534913056
78128.35125.4438070678032.90619293219738
79128.35128.631598824178-0.281598824178502
80128.35128.624061104682-0.274061104681778
81128.35128.616725151707-0.266725151706567
82128.35128.609585564451-0.259585564451015
83128.35128.602637086680-0.252637086679727
84128.35128.595874602854-0.245874602853974







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
85128.589293134366126.862852891432130.315733377299
86128.828586268731126.354138023071131.303034514392
87129.067879403097125.996859077791132.138899728403
88129.307172537463125.714167906135132.900177168791
89129.546465671828125.476734149762133.616197193895
90129.785758806194125.269728005185134.301789607203
91130.025051940560125.084463706656134.965640174463
92130.264345074925124.915362033262135.613328116589
93130.503638209291124.758603147685136.248673270897
94130.742931343657124.611446356432136.874416330881
95130.982224478022124.471853393146137.492595562898
96131.221517612388124.33826477553138.104770449246

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
85 & 128.589293134366 & 126.862852891432 & 130.315733377299 \tabularnewline
86 & 128.828586268731 & 126.354138023071 & 131.303034514392 \tabularnewline
87 & 129.067879403097 & 125.996859077791 & 132.138899728403 \tabularnewline
88 & 129.307172537463 & 125.714167906135 & 132.900177168791 \tabularnewline
89 & 129.546465671828 & 125.476734149762 & 133.616197193895 \tabularnewline
90 & 129.785758806194 & 125.269728005185 & 134.301789607203 \tabularnewline
91 & 130.025051940560 & 125.084463706656 & 134.965640174463 \tabularnewline
92 & 130.264345074925 & 124.915362033262 & 135.613328116589 \tabularnewline
93 & 130.503638209291 & 124.758603147685 & 136.248673270897 \tabularnewline
94 & 130.742931343657 & 124.611446356432 & 136.874416330881 \tabularnewline
95 & 130.982224478022 & 124.471853393146 & 137.492595562898 \tabularnewline
96 & 131.221517612388 & 124.33826477553 & 138.104770449246 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=13253&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]85[/C][C]128.589293134366[/C][C]126.862852891432[/C][C]130.315733377299[/C][/ROW]
[ROW][C]86[/C][C]128.828586268731[/C][C]126.354138023071[/C][C]131.303034514392[/C][/ROW]
[ROW][C]87[/C][C]129.067879403097[/C][C]125.996859077791[/C][C]132.138899728403[/C][/ROW]
[ROW][C]88[/C][C]129.307172537463[/C][C]125.714167906135[/C][C]132.900177168791[/C][/ROW]
[ROW][C]89[/C][C]129.546465671828[/C][C]125.476734149762[/C][C]133.616197193895[/C][/ROW]
[ROW][C]90[/C][C]129.785758806194[/C][C]125.269728005185[/C][C]134.301789607203[/C][/ROW]
[ROW][C]91[/C][C]130.025051940560[/C][C]125.084463706656[/C][C]134.965640174463[/C][/ROW]
[ROW][C]92[/C][C]130.264345074925[/C][C]124.915362033262[/C][C]135.613328116589[/C][/ROW]
[ROW][C]93[/C][C]130.503638209291[/C][C]124.758603147685[/C][C]136.248673270897[/C][/ROW]
[ROW][C]94[/C][C]130.742931343657[/C][C]124.611446356432[/C][C]136.874416330881[/C][/ROW]
[ROW][C]95[/C][C]130.982224478022[/C][C]124.471853393146[/C][C]137.492595562898[/C][/ROW]
[ROW][C]96[/C][C]131.221517612388[/C][C]124.33826477553[/C][C]138.104770449246[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=13253&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=13253&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
85128.589293134366126.862852891432130.315733377299
86128.828586268731126.354138023071131.303034514392
87129.067879403097125.996859077791132.138899728403
88129.307172537463125.714167906135132.900177168791
89129.546465671828125.476734149762133.616197193895
90129.785758806194125.269728005185134.301789607203
91130.025051940560125.084463706656134.965640174463
92130.264345074925124.915362033262135.613328116589
93130.503638209291124.758603147685136.248673270897
94130.742931343657124.611446356432136.874416330881
95130.982224478022124.471853393146137.492595562898
96131.221517612388124.33826477553138.104770449246



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