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Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationSat, 05 Dec 2015 11:02:56 +0000
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2015/Dec/05/t1449313434yv1jtlu9ntm3geh.htm/, Retrieved Fri, 17 May 2024 19:57:35 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=285194, Retrieved Fri, 17 May 2024 19:57:35 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact123
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [] [2015-12-05 11:02:56] [5a70237751c59f15349851dd3eb2a645] [Current]
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Dataseries X:
92,51
92,51
92,51
92,51
92,51
92,51
92,51
92,51
92,51
96,67
96,67
96,67
96,67
96,67
96,67
96,67
96,67
96,67
96,67
96,67
96,67
96,19
96,19
96,19
96,19
96,19
96,19
96,19
96,19
96,19
96,19
96,19
96,19
99,13
99,13
99,13
99,13
99,13
99,13
99,13
99,13
99,13
99,13
99,13
99,13
99,58
99,58
99,58
99,58
99,58
99,58
99,58
99,58
99,58
99,58
99,58
99,58
101,27
101,27
101,27
101,25
101,25
101,25
101,25
101,25
101,25
101,25
101,25
101,25
102,55
102,55
102,55





Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time1 seconds
R Server'George Udny Yule' @ yule.wessa.net
R Framework error message
Warning: there are blank lines in the 'Data' field.
Please, use NA for missing data - blank lines are simply
 deleted and are NOT treated as missing values.

\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 & 'George Udny Yule' @ yule.wessa.net \tabularnewline
R Framework error message & 
Warning: there are blank lines in the 'Data' field.
Please, use NA for missing data - blank lines are simply
 deleted and are NOT treated as missing values.
\tabularnewline \hline \end{tabular} %Source: https://freestatistics.org/blog/index.php?pk=285194&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]'George Udny Yule' @ yule.wessa.net[/C][/ROW]
[ROW][C]R Framework error message[/C][C]
Warning: there are blank lines in the 'Data' field.
Please, use NA for missing data - blank lines are simply
 deleted and are NOT treated as missing values.
[/C][/ROW] [/TABLE] Source: https://freestatistics.org/blog/index.php?pk=285194&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=285194&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'George Udny Yule' @ yule.wessa.net
R Framework error message
Warning: there are blank lines in the 'Data' field.
Please, use NA for missing data - blank lines are simply
 deleted and are NOT treated as missing values.







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.694728410449203
beta0.0153981886004326
gamma1

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.694728410449203 \tabularnewline
beta & 0.0153981886004326 \tabularnewline
gamma & 1 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=285194&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]0.694728410449203[/C][/ROW]
[ROW][C]beta[/C][C]0.0153981886004326[/C][/ROW]
[ROW][C]gamma[/C][C]1[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=285194&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=285194&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
alpha0.694728410449203
beta0.0153981886004326
gamma1







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
1396.6794.61979779449842.05020220550159
1496.6796.00733017277360.662669827226438
1596.6796.4365783787150.233421621285032
1696.6796.7629189177007-0.0929189177007146
1796.6797.0549670237403-0.384967023740344
1896.6797.1401857352105-0.470185735210521
1996.6795.76459441509420.905405584905779
2096.6796.35015899495970.319841005040317
2196.6796.5318273676310.138172632369049
2296.19100.932115269419-4.74211526941873
2396.1997.5585198155567-1.36851981555668
2496.1996.5180977442365-0.328097744236544
2596.1996.8253372490706-0.635337249070588
2696.1995.86436051822240.325639481777571
2796.1995.86733712562430.322662874375709
2896.1996.09482992958240.0951700704175664
2996.1996.3676534510384-0.177653451038452
3096.1996.5118670441956-0.321867044195628
3196.1995.60479298247290.585207017527068
3296.1995.73310376508420.45689623491576
3396.1995.89936199538970.290638004610258
3499.1398.79500374098840.334996259011575
3599.1399.9901611825208-0.860161182520841
3699.1399.6205439144481-0.490543914448111
3799.1399.7257362307838-0.5957362307838
3899.1399.06996961169390.0600303883060747
3999.1398.87001029556820.259989704431845
4099.1398.97149290148840.15850709851162
4199.1399.198215315994-0.0682153159940526
4299.1399.3716729805519-0.241672980551925
4399.1398.77516967798230.354830322017719
4499.1398.6837876199260.446212380074044
4599.1398.77499810318980.355001896810151
4699.58101.797810313479-2.21781031347942
4799.58100.826626328682-1.2466263286824
4899.58100.267207026267-0.687207026267487
4999.58100.167481285042-0.587481285041548
5099.5899.6795015926541-0.0995015926541214
5199.5899.38970554217230.190294457827733
5299.5899.3718813929260.208118607073956
5399.5899.52523234223260.0547676577673997
5499.5899.6942168641879-0.114216864187895
5599.5899.33073457298880.249265427011196
5699.5899.15550619973510.424493800264869
5799.5899.16597701198540.414022988014565
58101.27101.40368750557-0.133687505570094
59101.27102.170552721664-0.900552721664354
60101.27102.016021715096-0.746021715096177
61101.25101.897856503614-0.647856503614392
62101.25101.50263254827-0.252632548269574
63101.25101.1756766589290.0743233410712918
64101.25101.0623968528840.187603147115667
65101.25101.1360787503690.113921249631318
66101.25101.278465871933-0.0284658719330935
67101.25101.0659901915780.184009808422033
68101.25100.8767581511480.373241848852359
69101.25100.8261574614520.423842538548286
70102.55102.913425042071-0.363425042070659
71102.55103.273725786133-0.723725786132576
72102.55103.277693365246-0.727693365246182

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 96.67 & 94.6197977944984 & 2.05020220550159 \tabularnewline
14 & 96.67 & 96.0073301727736 & 0.662669827226438 \tabularnewline
15 & 96.67 & 96.436578378715 & 0.233421621285032 \tabularnewline
16 & 96.67 & 96.7629189177007 & -0.0929189177007146 \tabularnewline
17 & 96.67 & 97.0549670237403 & -0.384967023740344 \tabularnewline
18 & 96.67 & 97.1401857352105 & -0.470185735210521 \tabularnewline
19 & 96.67 & 95.7645944150942 & 0.905405584905779 \tabularnewline
20 & 96.67 & 96.3501589949597 & 0.319841005040317 \tabularnewline
21 & 96.67 & 96.531827367631 & 0.138172632369049 \tabularnewline
22 & 96.19 & 100.932115269419 & -4.74211526941873 \tabularnewline
23 & 96.19 & 97.5585198155567 & -1.36851981555668 \tabularnewline
24 & 96.19 & 96.5180977442365 & -0.328097744236544 \tabularnewline
25 & 96.19 & 96.8253372490706 & -0.635337249070588 \tabularnewline
26 & 96.19 & 95.8643605182224 & 0.325639481777571 \tabularnewline
27 & 96.19 & 95.8673371256243 & 0.322662874375709 \tabularnewline
28 & 96.19 & 96.0948299295824 & 0.0951700704175664 \tabularnewline
29 & 96.19 & 96.3676534510384 & -0.177653451038452 \tabularnewline
30 & 96.19 & 96.5118670441956 & -0.321867044195628 \tabularnewline
31 & 96.19 & 95.6047929824729 & 0.585207017527068 \tabularnewline
32 & 96.19 & 95.7331037650842 & 0.45689623491576 \tabularnewline
33 & 96.19 & 95.8993619953897 & 0.290638004610258 \tabularnewline
34 & 99.13 & 98.7950037409884 & 0.334996259011575 \tabularnewline
35 & 99.13 & 99.9901611825208 & -0.860161182520841 \tabularnewline
36 & 99.13 & 99.6205439144481 & -0.490543914448111 \tabularnewline
37 & 99.13 & 99.7257362307838 & -0.5957362307838 \tabularnewline
38 & 99.13 & 99.0699696116939 & 0.0600303883060747 \tabularnewline
39 & 99.13 & 98.8700102955682 & 0.259989704431845 \tabularnewline
40 & 99.13 & 98.9714929014884 & 0.15850709851162 \tabularnewline
41 & 99.13 & 99.198215315994 & -0.0682153159940526 \tabularnewline
42 & 99.13 & 99.3716729805519 & -0.241672980551925 \tabularnewline
43 & 99.13 & 98.7751696779823 & 0.354830322017719 \tabularnewline
44 & 99.13 & 98.683787619926 & 0.446212380074044 \tabularnewline
45 & 99.13 & 98.7749981031898 & 0.355001896810151 \tabularnewline
46 & 99.58 & 101.797810313479 & -2.21781031347942 \tabularnewline
47 & 99.58 & 100.826626328682 & -1.2466263286824 \tabularnewline
48 & 99.58 & 100.267207026267 & -0.687207026267487 \tabularnewline
49 & 99.58 & 100.167481285042 & -0.587481285041548 \tabularnewline
50 & 99.58 & 99.6795015926541 & -0.0995015926541214 \tabularnewline
51 & 99.58 & 99.3897055421723 & 0.190294457827733 \tabularnewline
52 & 99.58 & 99.371881392926 & 0.208118607073956 \tabularnewline
53 & 99.58 & 99.5252323422326 & 0.0547676577673997 \tabularnewline
54 & 99.58 & 99.6942168641879 & -0.114216864187895 \tabularnewline
55 & 99.58 & 99.3307345729888 & 0.249265427011196 \tabularnewline
56 & 99.58 & 99.1555061997351 & 0.424493800264869 \tabularnewline
57 & 99.58 & 99.1659770119854 & 0.414022988014565 \tabularnewline
58 & 101.27 & 101.40368750557 & -0.133687505570094 \tabularnewline
59 & 101.27 & 102.170552721664 & -0.900552721664354 \tabularnewline
60 & 101.27 & 102.016021715096 & -0.746021715096177 \tabularnewline
61 & 101.25 & 101.897856503614 & -0.647856503614392 \tabularnewline
62 & 101.25 & 101.50263254827 & -0.252632548269574 \tabularnewline
63 & 101.25 & 101.175676658929 & 0.0743233410712918 \tabularnewline
64 & 101.25 & 101.062396852884 & 0.187603147115667 \tabularnewline
65 & 101.25 & 101.136078750369 & 0.113921249631318 \tabularnewline
66 & 101.25 & 101.278465871933 & -0.0284658719330935 \tabularnewline
67 & 101.25 & 101.065990191578 & 0.184009808422033 \tabularnewline
68 & 101.25 & 100.876758151148 & 0.373241848852359 \tabularnewline
69 & 101.25 & 100.826157461452 & 0.423842538548286 \tabularnewline
70 & 102.55 & 102.913425042071 & -0.363425042070659 \tabularnewline
71 & 102.55 & 103.273725786133 & -0.723725786132576 \tabularnewline
72 & 102.55 & 103.277693365246 & -0.727693365246182 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=285194&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]96.67[/C][C]94.6197977944984[/C][C]2.05020220550159[/C][/ROW]
[ROW][C]14[/C][C]96.67[/C][C]96.0073301727736[/C][C]0.662669827226438[/C][/ROW]
[ROW][C]15[/C][C]96.67[/C][C]96.436578378715[/C][C]0.233421621285032[/C][/ROW]
[ROW][C]16[/C][C]96.67[/C][C]96.7629189177007[/C][C]-0.0929189177007146[/C][/ROW]
[ROW][C]17[/C][C]96.67[/C][C]97.0549670237403[/C][C]-0.384967023740344[/C][/ROW]
[ROW][C]18[/C][C]96.67[/C][C]97.1401857352105[/C][C]-0.470185735210521[/C][/ROW]
[ROW][C]19[/C][C]96.67[/C][C]95.7645944150942[/C][C]0.905405584905779[/C][/ROW]
[ROW][C]20[/C][C]96.67[/C][C]96.3501589949597[/C][C]0.319841005040317[/C][/ROW]
[ROW][C]21[/C][C]96.67[/C][C]96.531827367631[/C][C]0.138172632369049[/C][/ROW]
[ROW][C]22[/C][C]96.19[/C][C]100.932115269419[/C][C]-4.74211526941873[/C][/ROW]
[ROW][C]23[/C][C]96.19[/C][C]97.5585198155567[/C][C]-1.36851981555668[/C][/ROW]
[ROW][C]24[/C][C]96.19[/C][C]96.5180977442365[/C][C]-0.328097744236544[/C][/ROW]
[ROW][C]25[/C][C]96.19[/C][C]96.8253372490706[/C][C]-0.635337249070588[/C][/ROW]
[ROW][C]26[/C][C]96.19[/C][C]95.8643605182224[/C][C]0.325639481777571[/C][/ROW]
[ROW][C]27[/C][C]96.19[/C][C]95.8673371256243[/C][C]0.322662874375709[/C][/ROW]
[ROW][C]28[/C][C]96.19[/C][C]96.0948299295824[/C][C]0.0951700704175664[/C][/ROW]
[ROW][C]29[/C][C]96.19[/C][C]96.3676534510384[/C][C]-0.177653451038452[/C][/ROW]
[ROW][C]30[/C][C]96.19[/C][C]96.5118670441956[/C][C]-0.321867044195628[/C][/ROW]
[ROW][C]31[/C][C]96.19[/C][C]95.6047929824729[/C][C]0.585207017527068[/C][/ROW]
[ROW][C]32[/C][C]96.19[/C][C]95.7331037650842[/C][C]0.45689623491576[/C][/ROW]
[ROW][C]33[/C][C]96.19[/C][C]95.8993619953897[/C][C]0.290638004610258[/C][/ROW]
[ROW][C]34[/C][C]99.13[/C][C]98.7950037409884[/C][C]0.334996259011575[/C][/ROW]
[ROW][C]35[/C][C]99.13[/C][C]99.9901611825208[/C][C]-0.860161182520841[/C][/ROW]
[ROW][C]36[/C][C]99.13[/C][C]99.6205439144481[/C][C]-0.490543914448111[/C][/ROW]
[ROW][C]37[/C][C]99.13[/C][C]99.7257362307838[/C][C]-0.5957362307838[/C][/ROW]
[ROW][C]38[/C][C]99.13[/C][C]99.0699696116939[/C][C]0.0600303883060747[/C][/ROW]
[ROW][C]39[/C][C]99.13[/C][C]98.8700102955682[/C][C]0.259989704431845[/C][/ROW]
[ROW][C]40[/C][C]99.13[/C][C]98.9714929014884[/C][C]0.15850709851162[/C][/ROW]
[ROW][C]41[/C][C]99.13[/C][C]99.198215315994[/C][C]-0.0682153159940526[/C][/ROW]
[ROW][C]42[/C][C]99.13[/C][C]99.3716729805519[/C][C]-0.241672980551925[/C][/ROW]
[ROW][C]43[/C][C]99.13[/C][C]98.7751696779823[/C][C]0.354830322017719[/C][/ROW]
[ROW][C]44[/C][C]99.13[/C][C]98.683787619926[/C][C]0.446212380074044[/C][/ROW]
[ROW][C]45[/C][C]99.13[/C][C]98.7749981031898[/C][C]0.355001896810151[/C][/ROW]
[ROW][C]46[/C][C]99.58[/C][C]101.797810313479[/C][C]-2.21781031347942[/C][/ROW]
[ROW][C]47[/C][C]99.58[/C][C]100.826626328682[/C][C]-1.2466263286824[/C][/ROW]
[ROW][C]48[/C][C]99.58[/C][C]100.267207026267[/C][C]-0.687207026267487[/C][/ROW]
[ROW][C]49[/C][C]99.58[/C][C]100.167481285042[/C][C]-0.587481285041548[/C][/ROW]
[ROW][C]50[/C][C]99.58[/C][C]99.6795015926541[/C][C]-0.0995015926541214[/C][/ROW]
[ROW][C]51[/C][C]99.58[/C][C]99.3897055421723[/C][C]0.190294457827733[/C][/ROW]
[ROW][C]52[/C][C]99.58[/C][C]99.371881392926[/C][C]0.208118607073956[/C][/ROW]
[ROW][C]53[/C][C]99.58[/C][C]99.5252323422326[/C][C]0.0547676577673997[/C][/ROW]
[ROW][C]54[/C][C]99.58[/C][C]99.6942168641879[/C][C]-0.114216864187895[/C][/ROW]
[ROW][C]55[/C][C]99.58[/C][C]99.3307345729888[/C][C]0.249265427011196[/C][/ROW]
[ROW][C]56[/C][C]99.58[/C][C]99.1555061997351[/C][C]0.424493800264869[/C][/ROW]
[ROW][C]57[/C][C]99.58[/C][C]99.1659770119854[/C][C]0.414022988014565[/C][/ROW]
[ROW][C]58[/C][C]101.27[/C][C]101.40368750557[/C][C]-0.133687505570094[/C][/ROW]
[ROW][C]59[/C][C]101.27[/C][C]102.170552721664[/C][C]-0.900552721664354[/C][/ROW]
[ROW][C]60[/C][C]101.27[/C][C]102.016021715096[/C][C]-0.746021715096177[/C][/ROW]
[ROW][C]61[/C][C]101.25[/C][C]101.897856503614[/C][C]-0.647856503614392[/C][/ROW]
[ROW][C]62[/C][C]101.25[/C][C]101.50263254827[/C][C]-0.252632548269574[/C][/ROW]
[ROW][C]63[/C][C]101.25[/C][C]101.175676658929[/C][C]0.0743233410712918[/C][/ROW]
[ROW][C]64[/C][C]101.25[/C][C]101.062396852884[/C][C]0.187603147115667[/C][/ROW]
[ROW][C]65[/C][C]101.25[/C][C]101.136078750369[/C][C]0.113921249631318[/C][/ROW]
[ROW][C]66[/C][C]101.25[/C][C]101.278465871933[/C][C]-0.0284658719330935[/C][/ROW]
[ROW][C]67[/C][C]101.25[/C][C]101.065990191578[/C][C]0.184009808422033[/C][/ROW]
[ROW][C]68[/C][C]101.25[/C][C]100.876758151148[/C][C]0.373241848852359[/C][/ROW]
[ROW][C]69[/C][C]101.25[/C][C]100.826157461452[/C][C]0.423842538548286[/C][/ROW]
[ROW][C]70[/C][C]102.55[/C][C]102.913425042071[/C][C]-0.363425042070659[/C][/ROW]
[ROW][C]71[/C][C]102.55[/C][C]103.273725786133[/C][C]-0.723725786132576[/C][/ROW]
[ROW][C]72[/C][C]102.55[/C][C]103.277693365246[/C][C]-0.727693365246182[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=285194&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=285194&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
1396.6794.61979779449842.05020220550159
1496.6796.00733017277360.662669827226438
1596.6796.4365783787150.233421621285032
1696.6796.7629189177007-0.0929189177007146
1796.6797.0549670237403-0.384967023740344
1896.6797.1401857352105-0.470185735210521
1996.6795.76459441509420.905405584905779
2096.6796.35015899495970.319841005040317
2196.6796.5318273676310.138172632369049
2296.19100.932115269419-4.74211526941873
2396.1997.5585198155567-1.36851981555668
2496.1996.5180977442365-0.328097744236544
2596.1996.8253372490706-0.635337249070588
2696.1995.86436051822240.325639481777571
2796.1995.86733712562430.322662874375709
2896.1996.09482992958240.0951700704175664
2996.1996.3676534510384-0.177653451038452
3096.1996.5118670441956-0.321867044195628
3196.1995.60479298247290.585207017527068
3296.1995.73310376508420.45689623491576
3396.1995.89936199538970.290638004610258
3499.1398.79500374098840.334996259011575
3599.1399.9901611825208-0.860161182520841
3699.1399.6205439144481-0.490543914448111
3799.1399.7257362307838-0.5957362307838
3899.1399.06996961169390.0600303883060747
3999.1398.87001029556820.259989704431845
4099.1398.97149290148840.15850709851162
4199.1399.198215315994-0.0682153159940526
4299.1399.3716729805519-0.241672980551925
4399.1398.77516967798230.354830322017719
4499.1398.6837876199260.446212380074044
4599.1398.77499810318980.355001896810151
4699.58101.797810313479-2.21781031347942
4799.58100.826626328682-1.2466263286824
4899.58100.267207026267-0.687207026267487
4999.58100.167481285042-0.587481285041548
5099.5899.6795015926541-0.0995015926541214
5199.5899.38970554217230.190294457827733
5299.5899.3718813929260.208118607073956
5399.5899.52523234223260.0547676577673997
5499.5899.6942168641879-0.114216864187895
5599.5899.33073457298880.249265427011196
5699.5899.15550619973510.424493800264869
5799.5899.16597701198540.414022988014565
58101.27101.40368750557-0.133687505570094
59101.27102.170552721664-0.900552721664354
60101.27102.016021715096-0.746021715096177
61101.25101.897856503614-0.647856503614392
62101.25101.50263254827-0.252632548269574
63101.25101.1756766589290.0743233410712918
64101.25101.0623968528840.187603147115667
65101.25101.1360787503690.113921249631318
66101.25101.278465871933-0.0284658719330935
67101.25101.0659901915780.184009808422033
68101.25100.8767581511480.373241848852359
69101.25100.8261574614520.423842538548286
70102.55102.913425042071-0.363425042070659
71102.55103.273725786133-0.723725786132576
72102.55103.277693365246-0.727693365246182







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
73103.189949151777101.500134397723104.87976390583
74103.357067261238101.289293867493105.424840654982
75103.295172995936100.902309168119105.688036823754
76103.15230073386100.46801879521105.836582672509
77103.060077444663100.106316537146106.01383835218
78103.0676052085699.8591412363635106.276069180757
79102.92513602233399.4788396935751106.37143235109
80102.6473253385298.9777075878338106.316943089207
81102.33108791861198.4483629414954106.213812895727
82103.87830177888799.7281420956486108.028461462125
83104.36834439844299.9921466185961108.744542178289
84104.87041145918895.108175541787114.632647376589

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
73 & 103.189949151777 & 101.500134397723 & 104.87976390583 \tabularnewline
74 & 103.357067261238 & 101.289293867493 & 105.424840654982 \tabularnewline
75 & 103.295172995936 & 100.902309168119 & 105.688036823754 \tabularnewline
76 & 103.15230073386 & 100.46801879521 & 105.836582672509 \tabularnewline
77 & 103.060077444663 & 100.106316537146 & 106.01383835218 \tabularnewline
78 & 103.06760520856 & 99.8591412363635 & 106.276069180757 \tabularnewline
79 & 102.925136022333 & 99.4788396935751 & 106.37143235109 \tabularnewline
80 & 102.64732533852 & 98.9777075878338 & 106.316943089207 \tabularnewline
81 & 102.331087918611 & 98.4483629414954 & 106.213812895727 \tabularnewline
82 & 103.878301778887 & 99.7281420956486 & 108.028461462125 \tabularnewline
83 & 104.368344398442 & 99.9921466185961 & 108.744542178289 \tabularnewline
84 & 104.870411459188 & 95.108175541787 & 114.632647376589 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=285194&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]73[/C][C]103.189949151777[/C][C]101.500134397723[/C][C]104.87976390583[/C][/ROW]
[ROW][C]74[/C][C]103.357067261238[/C][C]101.289293867493[/C][C]105.424840654982[/C][/ROW]
[ROW][C]75[/C][C]103.295172995936[/C][C]100.902309168119[/C][C]105.688036823754[/C][/ROW]
[ROW][C]76[/C][C]103.15230073386[/C][C]100.46801879521[/C][C]105.836582672509[/C][/ROW]
[ROW][C]77[/C][C]103.060077444663[/C][C]100.106316537146[/C][C]106.01383835218[/C][/ROW]
[ROW][C]78[/C][C]103.06760520856[/C][C]99.8591412363635[/C][C]106.276069180757[/C][/ROW]
[ROW][C]79[/C][C]102.925136022333[/C][C]99.4788396935751[/C][C]106.37143235109[/C][/ROW]
[ROW][C]80[/C][C]102.64732533852[/C][C]98.9777075878338[/C][C]106.316943089207[/C][/ROW]
[ROW][C]81[/C][C]102.331087918611[/C][C]98.4483629414954[/C][C]106.213812895727[/C][/ROW]
[ROW][C]82[/C][C]103.878301778887[/C][C]99.7281420956486[/C][C]108.028461462125[/C][/ROW]
[ROW][C]83[/C][C]104.368344398442[/C][C]99.9921466185961[/C][C]108.744542178289[/C][/ROW]
[ROW][C]84[/C][C]104.870411459188[/C][C]95.108175541787[/C][C]114.632647376589[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=285194&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=285194&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
73103.189949151777101.500134397723104.87976390583
74103.357067261238101.289293867493105.424840654982
75103.295172995936100.902309168119105.688036823754
76103.15230073386100.46801879521105.836582672509
77103.060077444663100.106316537146106.01383835218
78103.0676052085699.8591412363635106.276069180757
79102.92513602233399.4788396935751106.37143235109
80102.6473253385298.9777075878338106.316943089207
81102.33108791861198.4483629414954106.213812895727
82103.87830177888799.7281420956486108.028461462125
83104.36834439844299.9921466185961108.744542178289
84104.87041145918895.108175541787114.632647376589



Parameters (Session):
par1 = 12 ; par2 = Triple ; par3 = multiplicative ;
Parameters (R input):
par1 = 12 ; par2 = Triple ; par3 = multiplicative ;
R code (references can be found in the software module):
par1 <- as.numeric(par1)
if (par2 == 'Single') K <- 1
if (par2 == 'Double') K <- 2
if (par2 == 'Triple') K <- par1
nx <- length(x)
nxmK <- nx - K
x <- ts(x, frequency = par1)
if (par2 == 'Single') fit <- HoltWinters(x, gamma=F, beta=F)
if (par2 == 'Double') fit <- HoltWinters(x, gamma=F)
if (par2 == 'Triple') fit <- HoltWinters(x, seasonal=par3)
fit
myresid <- x - fit$fitted[,'xhat']
bitmap(file='test1.png')
op <- par(mfrow=c(2,1))
plot(fit,ylab='Observed (black) / Fitted (red)',main='Interpolation Fit of Exponential Smoothing')
plot(myresid,ylab='Residuals',main='Interpolation Prediction Errors')
par(op)
dev.off()
bitmap(file='test2.png')
p <- predict(fit, par1, prediction.interval=TRUE)
np <- length(p[,1])
plot(fit,p,ylab='Observed (black) / Fitted (red)',main='Extrapolation Fit of Exponential Smoothing')
dev.off()
bitmap(file='test3.png')
op <- par(mfrow = c(2,2))
acf(as.numeric(myresid),lag.max = nx/2,main='Residual ACF')
spectrum(myresid,main='Residals Periodogram')
cpgram(myresid,main='Residal Cumulative Periodogram')
qqnorm(myresid,main='Residual Normal QQ Plot')
qqline(myresid)
par(op)
dev.off()
load(file='createtable')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Estimated Parameters of Exponential Smoothing',2,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'Parameter',header=TRUE)
a<-table.element(a,'Value',header=TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'alpha',header=TRUE)
a<-table.element(a,fit$alpha)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'beta',header=TRUE)
a<-table.element(a,fit$beta)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'gamma',header=TRUE)
a<-table.element(a,fit$gamma)
a<-table.row.end(a)
a<-table.end(a)
table.save(a,file='mytable.tab')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Interpolation Forecasts of Exponential Smoothing',4,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'t',header=TRUE)
a<-table.element(a,'Observed',header=TRUE)
a<-table.element(a,'Fitted',header=TRUE)
a<-table.element(a,'Residuals',header=TRUE)
a<-table.row.end(a)
for (i in 1:nxmK) {
a<-table.row.start(a)
a<-table.element(a,i+K,header=TRUE)
a<-table.element(a,x[i+K])
a<-table.element(a,fit$fitted[i,'xhat'])
a<-table.element(a,myresid[i])
a<-table.row.end(a)
}
a<-table.end(a)
table.save(a,file='mytable1.tab')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Extrapolation Forecasts of Exponential Smoothing',4,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'t',header=TRUE)
a<-table.element(a,'Forecast',header=TRUE)
a<-table.element(a,'95% Lower Bound',header=TRUE)
a<-table.element(a,'95% Upper Bound',header=TRUE)
a<-table.row.end(a)
for (i in 1:np) {
a<-table.row.start(a)
a<-table.element(a,nx+i,header=TRUE)
a<-table.element(a,p[i,'fit'])
a<-table.element(a,p[i,'lwr'])
a<-table.element(a,p[i,'upr'])
a<-table.row.end(a)
}
a<-table.end(a)
table.save(a,file='mytable2.tab')