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Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationSun, 16 Jan 2011 21:38:38 +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/2011/Jan/16/t1295213807fyclr29bqj7ussn.htm/, Retrieved Thu, 16 May 2024 11:38:49 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=117476, Retrieved Thu, 16 May 2024 11:38:49 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywordsKDGP2W102
Estimated Impact93
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [] [2011-01-16 21:38:38] [9d49b4c553d27c097eebc753f5e7db7d] [Current]
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Dataseries X:
98,1
98,0
98,3
98,5
98,7
99,3
99,5
99,8
100,3
99,3
99,6
99,3



99,4
99,7
100,0
99,3
100,3
100,8
101,4
101,1
100,6
99,5
99,1
98,8



99,1
98,8
98,5
99,0
99,0
100,6
101,0
101,8
101,8
101,8
101,8
102,4



103,0
103,3
103,6
104,1
104,5
105,6
105,9
106,0
106,3
107,3
107,1
107,3



107,7
108,0
108,9
108,5
109,0
108,9
109,0
108,9
110,3
109,4
108,6
108,0



108,4
108,0
108,0
107,6
107,5
107,9
108,0
107,5
106,8
106,7
107,2
107,8




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time1 seconds
R Server'RServer@AstonUniversity' @ vre.aston.ac.uk
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 & 'RServer@AstonUniversity' @ vre.aston.ac.uk \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=117476&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]'RServer@AstonUniversity' @ vre.aston.ac.uk[/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=117476&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=117476&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'RServer@AstonUniversity' @ vre.aston.ac.uk
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
alpha1
beta0.100572298014721
gammaFALSE

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 1 \tabularnewline
beta & 0.100572298014721 \tabularnewline
gamma & FALSE \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=117476&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]0.100572298014721[/C][/ROW]
[ROW][C]gamma[/C][C]FALSE[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=117476&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=117476&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
beta0.100572298014721
gammaFALSE







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
398.397.90.399999999999991
498.598.2402289192060.25977108079411
598.798.46635469375910.233645306240874
699.398.68985293912810.610147060871867
799.599.3512168311670.148783168833063
899.899.56618029636240.233819703637607
9100.399.88969608127830.410303918721652
1099.3100.430961289269-1.13096128926863
1199.699.31721791344120.282782086558811
1299.399.6456579577238-0.345657957723802
1399.499.31089434258840.0891056574115652
1499.799.41985590332050.28014409667955
1510099.74803063889880.251969361101231
1699.3100.073371776574-0.773371776574024
17100.399.29559199978421.00440800021576
18100.8100.396607620510.403392379489688
19101.4100.9371777191170.46282228088279
20101.1101.583724819478-0.483724819478027
21100.6101.235075502776-0.635075502776346
2299.5100.671204500049-1.17120450004927
2399.199.4534137720341-0.353413772034145
2498.899.0178701368306-0.217870136830612
2599.198.69595843650080.40404156349922
2698.899.0365938250354-0.236593825035357
2798.598.7127990403554-0.212799040355449
289998.39139735185160.60860264814842
299998.95260591875370.0473940812462814
30100.698.9573724504171.64262754958304
31101100.7225752778610.277424722139202
32101.8101.1504765196920.64952348030755
33101.8102.015800588721-0.215800588721493
34101.8101.994097027601-0.194097027600847
35101.8101.974576243497-0.174576243497199
36102.4101.957018709510.442981290490096
37103102.6015703558720.398429644127972
38103.3103.2416413407790.0583586592208434
39103.6103.5475106052460.052489394753934
40104.1103.8527895842980.247210415702142
41104.5104.3776521038980.1223478961018
42105.6104.7899569129660.810043087033563
43105.9105.97142480772-0.0714248077203194
44106106.264241450673-0.264241450672642
45106.3106.337666080748-0.0376660807477549
46107.3106.633877916450.666122083550263
47107.1107.700871345151-0.60087134515075
48107.3107.440440333158-0.140440333157727
49107.7107.6263159261180.0736840738818927
50108108.033726502755-0.0337265027554992
51108.9108.3303345508690.569665449130625
52108.5109.287627114188-0.78762711418804
53109108.8084136453350.191586354664565
54108.9109.327681925292-0.427681925292305
55109109.184668971246-0.18466897124631
56108.9109.266096388436-0.366096388436048
57110.3109.1292772333561.17072276664385
58109.4110.647019512336-1.24701951233567
59108.6109.621603894311-1.02160389431089
60108108.718858842999-0.718858842999239
61108.4108.0465615572110.353438442789397
62108108.482107673609-0.482107673608681
63108108.033620996983-0.0336209969833305
64107.6108.030239656055-0.430239656055178
65107.5107.586969465149-0.086969465148627
66107.9107.4782227461820.421777253818476
67108107.9206418538480.0793581461516055
68107.5108.028623084973-0.528623084973049
69106.8107.475458246534-0.67545824653368
70106.7106.707525858467-0.00752585846677789
71107.2106.6067689655860.593231034413748
72107.8107.1664315739710.6335684260291

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
3 & 98.3 & 97.9 & 0.399999999999991 \tabularnewline
4 & 98.5 & 98.240228919206 & 0.25977108079411 \tabularnewline
5 & 98.7 & 98.4663546937591 & 0.233645306240874 \tabularnewline
6 & 99.3 & 98.6898529391281 & 0.610147060871867 \tabularnewline
7 & 99.5 & 99.351216831167 & 0.148783168833063 \tabularnewline
8 & 99.8 & 99.5661802963624 & 0.233819703637607 \tabularnewline
9 & 100.3 & 99.8896960812783 & 0.410303918721652 \tabularnewline
10 & 99.3 & 100.430961289269 & -1.13096128926863 \tabularnewline
11 & 99.6 & 99.3172179134412 & 0.282782086558811 \tabularnewline
12 & 99.3 & 99.6456579577238 & -0.345657957723802 \tabularnewline
13 & 99.4 & 99.3108943425884 & 0.0891056574115652 \tabularnewline
14 & 99.7 & 99.4198559033205 & 0.28014409667955 \tabularnewline
15 & 100 & 99.7480306388988 & 0.251969361101231 \tabularnewline
16 & 99.3 & 100.073371776574 & -0.773371776574024 \tabularnewline
17 & 100.3 & 99.2955919997842 & 1.00440800021576 \tabularnewline
18 & 100.8 & 100.39660762051 & 0.403392379489688 \tabularnewline
19 & 101.4 & 100.937177719117 & 0.46282228088279 \tabularnewline
20 & 101.1 & 101.583724819478 & -0.483724819478027 \tabularnewline
21 & 100.6 & 101.235075502776 & -0.635075502776346 \tabularnewline
22 & 99.5 & 100.671204500049 & -1.17120450004927 \tabularnewline
23 & 99.1 & 99.4534137720341 & -0.353413772034145 \tabularnewline
24 & 98.8 & 99.0178701368306 & -0.217870136830612 \tabularnewline
25 & 99.1 & 98.6959584365008 & 0.40404156349922 \tabularnewline
26 & 98.8 & 99.0365938250354 & -0.236593825035357 \tabularnewline
27 & 98.5 & 98.7127990403554 & -0.212799040355449 \tabularnewline
28 & 99 & 98.3913973518516 & 0.60860264814842 \tabularnewline
29 & 99 & 98.9526059187537 & 0.0473940812462814 \tabularnewline
30 & 100.6 & 98.957372450417 & 1.64262754958304 \tabularnewline
31 & 101 & 100.722575277861 & 0.277424722139202 \tabularnewline
32 & 101.8 & 101.150476519692 & 0.64952348030755 \tabularnewline
33 & 101.8 & 102.015800588721 & -0.215800588721493 \tabularnewline
34 & 101.8 & 101.994097027601 & -0.194097027600847 \tabularnewline
35 & 101.8 & 101.974576243497 & -0.174576243497199 \tabularnewline
36 & 102.4 & 101.95701870951 & 0.442981290490096 \tabularnewline
37 & 103 & 102.601570355872 & 0.398429644127972 \tabularnewline
38 & 103.3 & 103.241641340779 & 0.0583586592208434 \tabularnewline
39 & 103.6 & 103.547510605246 & 0.052489394753934 \tabularnewline
40 & 104.1 & 103.852789584298 & 0.247210415702142 \tabularnewline
41 & 104.5 & 104.377652103898 & 0.1223478961018 \tabularnewline
42 & 105.6 & 104.789956912966 & 0.810043087033563 \tabularnewline
43 & 105.9 & 105.97142480772 & -0.0714248077203194 \tabularnewline
44 & 106 & 106.264241450673 & -0.264241450672642 \tabularnewline
45 & 106.3 & 106.337666080748 & -0.0376660807477549 \tabularnewline
46 & 107.3 & 106.63387791645 & 0.666122083550263 \tabularnewline
47 & 107.1 & 107.700871345151 & -0.60087134515075 \tabularnewline
48 & 107.3 & 107.440440333158 & -0.140440333157727 \tabularnewline
49 & 107.7 & 107.626315926118 & 0.0736840738818927 \tabularnewline
50 & 108 & 108.033726502755 & -0.0337265027554992 \tabularnewline
51 & 108.9 & 108.330334550869 & 0.569665449130625 \tabularnewline
52 & 108.5 & 109.287627114188 & -0.78762711418804 \tabularnewline
53 & 109 & 108.808413645335 & 0.191586354664565 \tabularnewline
54 & 108.9 & 109.327681925292 & -0.427681925292305 \tabularnewline
55 & 109 & 109.184668971246 & -0.18466897124631 \tabularnewline
56 & 108.9 & 109.266096388436 & -0.366096388436048 \tabularnewline
57 & 110.3 & 109.129277233356 & 1.17072276664385 \tabularnewline
58 & 109.4 & 110.647019512336 & -1.24701951233567 \tabularnewline
59 & 108.6 & 109.621603894311 & -1.02160389431089 \tabularnewline
60 & 108 & 108.718858842999 & -0.718858842999239 \tabularnewline
61 & 108.4 & 108.046561557211 & 0.353438442789397 \tabularnewline
62 & 108 & 108.482107673609 & -0.482107673608681 \tabularnewline
63 & 108 & 108.033620996983 & -0.0336209969833305 \tabularnewline
64 & 107.6 & 108.030239656055 & -0.430239656055178 \tabularnewline
65 & 107.5 & 107.586969465149 & -0.086969465148627 \tabularnewline
66 & 107.9 & 107.478222746182 & 0.421777253818476 \tabularnewline
67 & 108 & 107.920641853848 & 0.0793581461516055 \tabularnewline
68 & 107.5 & 108.028623084973 & -0.528623084973049 \tabularnewline
69 & 106.8 & 107.475458246534 & -0.67545824653368 \tabularnewline
70 & 106.7 & 106.707525858467 & -0.00752585846677789 \tabularnewline
71 & 107.2 & 106.606768965586 & 0.593231034413748 \tabularnewline
72 & 107.8 & 107.166431573971 & 0.6335684260291 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=117476&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]98.3[/C][C]97.9[/C][C]0.399999999999991[/C][/ROW]
[ROW][C]4[/C][C]98.5[/C][C]98.240228919206[/C][C]0.25977108079411[/C][/ROW]
[ROW][C]5[/C][C]98.7[/C][C]98.4663546937591[/C][C]0.233645306240874[/C][/ROW]
[ROW][C]6[/C][C]99.3[/C][C]98.6898529391281[/C][C]0.610147060871867[/C][/ROW]
[ROW][C]7[/C][C]99.5[/C][C]99.351216831167[/C][C]0.148783168833063[/C][/ROW]
[ROW][C]8[/C][C]99.8[/C][C]99.5661802963624[/C][C]0.233819703637607[/C][/ROW]
[ROW][C]9[/C][C]100.3[/C][C]99.8896960812783[/C][C]0.410303918721652[/C][/ROW]
[ROW][C]10[/C][C]99.3[/C][C]100.430961289269[/C][C]-1.13096128926863[/C][/ROW]
[ROW][C]11[/C][C]99.6[/C][C]99.3172179134412[/C][C]0.282782086558811[/C][/ROW]
[ROW][C]12[/C][C]99.3[/C][C]99.6456579577238[/C][C]-0.345657957723802[/C][/ROW]
[ROW][C]13[/C][C]99.4[/C][C]99.3108943425884[/C][C]0.0891056574115652[/C][/ROW]
[ROW][C]14[/C][C]99.7[/C][C]99.4198559033205[/C][C]0.28014409667955[/C][/ROW]
[ROW][C]15[/C][C]100[/C][C]99.7480306388988[/C][C]0.251969361101231[/C][/ROW]
[ROW][C]16[/C][C]99.3[/C][C]100.073371776574[/C][C]-0.773371776574024[/C][/ROW]
[ROW][C]17[/C][C]100.3[/C][C]99.2955919997842[/C][C]1.00440800021576[/C][/ROW]
[ROW][C]18[/C][C]100.8[/C][C]100.39660762051[/C][C]0.403392379489688[/C][/ROW]
[ROW][C]19[/C][C]101.4[/C][C]100.937177719117[/C][C]0.46282228088279[/C][/ROW]
[ROW][C]20[/C][C]101.1[/C][C]101.583724819478[/C][C]-0.483724819478027[/C][/ROW]
[ROW][C]21[/C][C]100.6[/C][C]101.235075502776[/C][C]-0.635075502776346[/C][/ROW]
[ROW][C]22[/C][C]99.5[/C][C]100.671204500049[/C][C]-1.17120450004927[/C][/ROW]
[ROW][C]23[/C][C]99.1[/C][C]99.4534137720341[/C][C]-0.353413772034145[/C][/ROW]
[ROW][C]24[/C][C]98.8[/C][C]99.0178701368306[/C][C]-0.217870136830612[/C][/ROW]
[ROW][C]25[/C][C]99.1[/C][C]98.6959584365008[/C][C]0.40404156349922[/C][/ROW]
[ROW][C]26[/C][C]98.8[/C][C]99.0365938250354[/C][C]-0.236593825035357[/C][/ROW]
[ROW][C]27[/C][C]98.5[/C][C]98.7127990403554[/C][C]-0.212799040355449[/C][/ROW]
[ROW][C]28[/C][C]99[/C][C]98.3913973518516[/C][C]0.60860264814842[/C][/ROW]
[ROW][C]29[/C][C]99[/C][C]98.9526059187537[/C][C]0.0473940812462814[/C][/ROW]
[ROW][C]30[/C][C]100.6[/C][C]98.957372450417[/C][C]1.64262754958304[/C][/ROW]
[ROW][C]31[/C][C]101[/C][C]100.722575277861[/C][C]0.277424722139202[/C][/ROW]
[ROW][C]32[/C][C]101.8[/C][C]101.150476519692[/C][C]0.64952348030755[/C][/ROW]
[ROW][C]33[/C][C]101.8[/C][C]102.015800588721[/C][C]-0.215800588721493[/C][/ROW]
[ROW][C]34[/C][C]101.8[/C][C]101.994097027601[/C][C]-0.194097027600847[/C][/ROW]
[ROW][C]35[/C][C]101.8[/C][C]101.974576243497[/C][C]-0.174576243497199[/C][/ROW]
[ROW][C]36[/C][C]102.4[/C][C]101.95701870951[/C][C]0.442981290490096[/C][/ROW]
[ROW][C]37[/C][C]103[/C][C]102.601570355872[/C][C]0.398429644127972[/C][/ROW]
[ROW][C]38[/C][C]103.3[/C][C]103.241641340779[/C][C]0.0583586592208434[/C][/ROW]
[ROW][C]39[/C][C]103.6[/C][C]103.547510605246[/C][C]0.052489394753934[/C][/ROW]
[ROW][C]40[/C][C]104.1[/C][C]103.852789584298[/C][C]0.247210415702142[/C][/ROW]
[ROW][C]41[/C][C]104.5[/C][C]104.377652103898[/C][C]0.1223478961018[/C][/ROW]
[ROW][C]42[/C][C]105.6[/C][C]104.789956912966[/C][C]0.810043087033563[/C][/ROW]
[ROW][C]43[/C][C]105.9[/C][C]105.97142480772[/C][C]-0.0714248077203194[/C][/ROW]
[ROW][C]44[/C][C]106[/C][C]106.264241450673[/C][C]-0.264241450672642[/C][/ROW]
[ROW][C]45[/C][C]106.3[/C][C]106.337666080748[/C][C]-0.0376660807477549[/C][/ROW]
[ROW][C]46[/C][C]107.3[/C][C]106.63387791645[/C][C]0.666122083550263[/C][/ROW]
[ROW][C]47[/C][C]107.1[/C][C]107.700871345151[/C][C]-0.60087134515075[/C][/ROW]
[ROW][C]48[/C][C]107.3[/C][C]107.440440333158[/C][C]-0.140440333157727[/C][/ROW]
[ROW][C]49[/C][C]107.7[/C][C]107.626315926118[/C][C]0.0736840738818927[/C][/ROW]
[ROW][C]50[/C][C]108[/C][C]108.033726502755[/C][C]-0.0337265027554992[/C][/ROW]
[ROW][C]51[/C][C]108.9[/C][C]108.330334550869[/C][C]0.569665449130625[/C][/ROW]
[ROW][C]52[/C][C]108.5[/C][C]109.287627114188[/C][C]-0.78762711418804[/C][/ROW]
[ROW][C]53[/C][C]109[/C][C]108.808413645335[/C][C]0.191586354664565[/C][/ROW]
[ROW][C]54[/C][C]108.9[/C][C]109.327681925292[/C][C]-0.427681925292305[/C][/ROW]
[ROW][C]55[/C][C]109[/C][C]109.184668971246[/C][C]-0.18466897124631[/C][/ROW]
[ROW][C]56[/C][C]108.9[/C][C]109.266096388436[/C][C]-0.366096388436048[/C][/ROW]
[ROW][C]57[/C][C]110.3[/C][C]109.129277233356[/C][C]1.17072276664385[/C][/ROW]
[ROW][C]58[/C][C]109.4[/C][C]110.647019512336[/C][C]-1.24701951233567[/C][/ROW]
[ROW][C]59[/C][C]108.6[/C][C]109.621603894311[/C][C]-1.02160389431089[/C][/ROW]
[ROW][C]60[/C][C]108[/C][C]108.718858842999[/C][C]-0.718858842999239[/C][/ROW]
[ROW][C]61[/C][C]108.4[/C][C]108.046561557211[/C][C]0.353438442789397[/C][/ROW]
[ROW][C]62[/C][C]108[/C][C]108.482107673609[/C][C]-0.482107673608681[/C][/ROW]
[ROW][C]63[/C][C]108[/C][C]108.033620996983[/C][C]-0.0336209969833305[/C][/ROW]
[ROW][C]64[/C][C]107.6[/C][C]108.030239656055[/C][C]-0.430239656055178[/C][/ROW]
[ROW][C]65[/C][C]107.5[/C][C]107.586969465149[/C][C]-0.086969465148627[/C][/ROW]
[ROW][C]66[/C][C]107.9[/C][C]107.478222746182[/C][C]0.421777253818476[/C][/ROW]
[ROW][C]67[/C][C]108[/C][C]107.920641853848[/C][C]0.0793581461516055[/C][/ROW]
[ROW][C]68[/C][C]107.5[/C][C]108.028623084973[/C][C]-0.528623084973049[/C][/ROW]
[ROW][C]69[/C][C]106.8[/C][C]107.475458246534[/C][C]-0.67545824653368[/C][/ROW]
[ROW][C]70[/C][C]106.7[/C][C]106.707525858467[/C][C]-0.00752585846677789[/C][/ROW]
[ROW][C]71[/C][C]107.2[/C][C]106.606768965586[/C][C]0.593231034413748[/C][/ROW]
[ROW][C]72[/C][C]107.8[/C][C]107.166431573971[/C][C]0.6335684260291[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=117476&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=117476&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
398.397.90.399999999999991
498.598.2402289192060.25977108079411
598.798.46635469375910.233645306240874
699.398.68985293912810.610147060871867
799.599.3512168311670.148783168833063
899.899.56618029636240.233819703637607
9100.399.88969608127830.410303918721652
1099.3100.430961289269-1.13096128926863
1199.699.31721791344120.282782086558811
1299.399.6456579577238-0.345657957723802
1399.499.31089434258840.0891056574115652
1499.799.41985590332050.28014409667955
1510099.74803063889880.251969361101231
1699.3100.073371776574-0.773371776574024
17100.399.29559199978421.00440800021576
18100.8100.396607620510.403392379489688
19101.4100.9371777191170.46282228088279
20101.1101.583724819478-0.483724819478027
21100.6101.235075502776-0.635075502776346
2299.5100.671204500049-1.17120450004927
2399.199.4534137720341-0.353413772034145
2498.899.0178701368306-0.217870136830612
2599.198.69595843650080.40404156349922
2698.899.0365938250354-0.236593825035357
2798.598.7127990403554-0.212799040355449
289998.39139735185160.60860264814842
299998.95260591875370.0473940812462814
30100.698.9573724504171.64262754958304
31101100.7225752778610.277424722139202
32101.8101.1504765196920.64952348030755
33101.8102.015800588721-0.215800588721493
34101.8101.994097027601-0.194097027600847
35101.8101.974576243497-0.174576243497199
36102.4101.957018709510.442981290490096
37103102.6015703558720.398429644127972
38103.3103.2416413407790.0583586592208434
39103.6103.5475106052460.052489394753934
40104.1103.8527895842980.247210415702142
41104.5104.3776521038980.1223478961018
42105.6104.7899569129660.810043087033563
43105.9105.97142480772-0.0714248077203194
44106106.264241450673-0.264241450672642
45106.3106.337666080748-0.0376660807477549
46107.3106.633877916450.666122083550263
47107.1107.700871345151-0.60087134515075
48107.3107.440440333158-0.140440333157727
49107.7107.6263159261180.0736840738818927
50108108.033726502755-0.0337265027554992
51108.9108.3303345508690.569665449130625
52108.5109.287627114188-0.78762711418804
53109108.8084136453350.191586354664565
54108.9109.327681925292-0.427681925292305
55109109.184668971246-0.18466897124631
56108.9109.266096388436-0.366096388436048
57110.3109.1292772333561.17072276664385
58109.4110.647019512336-1.24701951233567
59108.6109.621603894311-1.02160389431089
60108108.718858842999-0.718858842999239
61108.4108.0465615572110.353438442789397
62108108.482107673609-0.482107673608681
63108108.033620996983-0.0336209969833305
64107.6108.030239656055-0.430239656055178
65107.5107.586969465149-0.086969465148627
66107.9107.4782227461820.421777253818476
67108107.9206418538480.0793581461516055
68107.5108.028623084973-0.528623084973049
69106.8107.475458246534-0.67545824653368
70106.7106.707525858467-0.00752585846677789
71107.2106.6067689655860.593231034413748
72107.8107.1664315739710.6335684260291







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
73107.830151006526106.757616873859108.902685139194
74107.860302013052106.265411162607109.455192863497
75107.890453019579105.840254796812109.940651242345
76107.920604026105105.440179077737110.401028974473
77107.950755032631105.04997358348110.851536481782
78107.980906039157104.662373426431111.299438651884
79108.011057045683104.273389904563111.748724186804
80108.04120805221103.880643840552112.201772263868
81108.071359058736103.482639620633112.660078496839
82108.101510065262103.078405358007113.124614772517
83108.131661071788102.667297459258113.596024684319
84108.161812078314102.248886987747114.074737168882

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
73 & 107.830151006526 & 106.757616873859 & 108.902685139194 \tabularnewline
74 & 107.860302013052 & 106.265411162607 & 109.455192863497 \tabularnewline
75 & 107.890453019579 & 105.840254796812 & 109.940651242345 \tabularnewline
76 & 107.920604026105 & 105.440179077737 & 110.401028974473 \tabularnewline
77 & 107.950755032631 & 105.04997358348 & 110.851536481782 \tabularnewline
78 & 107.980906039157 & 104.662373426431 & 111.299438651884 \tabularnewline
79 & 108.011057045683 & 104.273389904563 & 111.748724186804 \tabularnewline
80 & 108.04120805221 & 103.880643840552 & 112.201772263868 \tabularnewline
81 & 108.071359058736 & 103.482639620633 & 112.660078496839 \tabularnewline
82 & 108.101510065262 & 103.078405358007 & 113.124614772517 \tabularnewline
83 & 108.131661071788 & 102.667297459258 & 113.596024684319 \tabularnewline
84 & 108.161812078314 & 102.248886987747 & 114.074737168882 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=117476&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]107.830151006526[/C][C]106.757616873859[/C][C]108.902685139194[/C][/ROW]
[ROW][C]74[/C][C]107.860302013052[/C][C]106.265411162607[/C][C]109.455192863497[/C][/ROW]
[ROW][C]75[/C][C]107.890453019579[/C][C]105.840254796812[/C][C]109.940651242345[/C][/ROW]
[ROW][C]76[/C][C]107.920604026105[/C][C]105.440179077737[/C][C]110.401028974473[/C][/ROW]
[ROW][C]77[/C][C]107.950755032631[/C][C]105.04997358348[/C][C]110.851536481782[/C][/ROW]
[ROW][C]78[/C][C]107.980906039157[/C][C]104.662373426431[/C][C]111.299438651884[/C][/ROW]
[ROW][C]79[/C][C]108.011057045683[/C][C]104.273389904563[/C][C]111.748724186804[/C][/ROW]
[ROW][C]80[/C][C]108.04120805221[/C][C]103.880643840552[/C][C]112.201772263868[/C][/ROW]
[ROW][C]81[/C][C]108.071359058736[/C][C]103.482639620633[/C][C]112.660078496839[/C][/ROW]
[ROW][C]82[/C][C]108.101510065262[/C][C]103.078405358007[/C][C]113.124614772517[/C][/ROW]
[ROW][C]83[/C][C]108.131661071788[/C][C]102.667297459258[/C][C]113.596024684319[/C][/ROW]
[ROW][C]84[/C][C]108.161812078314[/C][C]102.248886987747[/C][C]114.074737168882[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=117476&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=117476&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
73107.830151006526106.757616873859108.902685139194
74107.860302013052106.265411162607109.455192863497
75107.890453019579105.840254796812109.940651242345
76107.920604026105105.440179077737110.401028974473
77107.950755032631105.04997358348110.851536481782
78107.980906039157104.662373426431111.299438651884
79108.011057045683104.273389904563111.748724186804
80108.04120805221103.880643840552112.201772263868
81108.071359058736103.482639620633112.660078496839
82108.101510065262103.078405358007113.124614772517
83108.131661071788102.667297459258113.596024684319
84108.161812078314102.248886987747114.074737168882



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