Free Statistics

of Irreproducible Research!

Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationTue, 19 Jan 2010 13:52:57 -0700
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2010/Jan/19/t1263934821v5g42pbdoy5gvln.htm/, Retrieved Thu, 02 May 2024 11:15:18 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=72296, Retrieved Thu, 02 May 2024 11:15:18 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywordsKDGP2W62
Estimated Impact186
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [] [2010-01-19 20:52:57] [d3c74fcd05a317afdc84de11f936034f] [Current]
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Dataseries X:
8.55
8.56
8.57
8.59
8.61
8.62
8.62
8.63
8.71
8.72
8.74
8.75
8.79
8.82
8.82
8.84
8.86
8.86
8.85
8.86
8.86
8.87
8.88
8.9
8.91
8.96
8.98
8.99
9
9
9
9.01
9.01
8.99
8.99
8.99
9
9
9.02
9.05
9.05
9.05
9.06
9.06
9.08
9.07
9.06
9.08
9.07
9.11
9.15
9.15
9.17
9.2
9.23
9.26
9.27
9.28
9.29
9.29
9.11
9.06
9.11
9.13
9.13
9.19
9.2
9.23
9.24
9.28
9.32
9.32
9.32
9.36
9.37
9.38
9.41
9.44
9.44
9.44
9.47
9.48
9.56
9.58
9.56
9.58
9.7
9.74
9.76
9.78
9.84
9.88
9.96
9.97
9.96
9.96




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'Gwilym Jenkins' @ 72.249.127.135

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input & view raw input (R code)  \tabularnewline
Raw Output & view raw output of R engine  \tabularnewline
Computing time & 2 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ 72.249.127.135 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=72296&T=0

[TABLE]
[ROW][C]Summary of computational transaction[/C][/ROW]
[ROW][C]Raw Input[/C][C]view raw input (R code) [/C][/ROW]
[ROW][C]Raw Output[/C][C]view raw output of R engine [/C][/ROW]
[ROW][C]Computing time[/C][C]2 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Gwilym Jenkins' @ 72.249.127.135[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=72296&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=72296&T=0

As an alternative you can also use a QR Code:  

The GUIDs for individual cells are displayed in the table below:

Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'Gwilym Jenkins' @ 72.249.127.135







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha1
beta0.0405252708246452
gammaFALSE

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 1 \tabularnewline
beta & 0.0405252708246452 \tabularnewline
gamma & FALSE \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=72296&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]0.0405252708246452[/C][/ROW]
[ROW][C]gamma[/C][C]FALSE[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=72296&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=72296&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
beta0.0405252708246452
gammaFALSE







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
38.578.570
48.598.580.00999999999999979
58.618.600405252708250.0095947472917537
68.628.62079408244074-0.00079408244073953
78.628.63076190203477-0.0107619020347709
88.638.63032577304022-0.000325773040222188
98.718.640312570999540.0696874290004601
108.728.72313667293286-0.00313667293285746
118.748.733009558412770.00699044158723439
128.758.75329284795127-0.00329284795127194
138.798.763159404396260.0268405956037370
148.828.80424712680220.0157528731978029
158.828.8348855162548-0.0148855162548056
168.848.834282276677210.00571772332278542
178.868.854513988963370.00548601103662882
188.868.87473631104638-0.0147363110463772
198.858.87413911805027-0.0241391180502664
208.868.86316087375381-0.0031608737538118
218.868.87303277848889-0.0130327784888955
228.878.87250462161104-0.00250462161103648
238.888.88240312114193-0.00240312114193308
248.98.892305734006830.00769426599316603
258.918.91261754622-0.00261754622000332
268.968.922511469450540.0374885305494583
278.988.974030702303880.00596929769612231
288.998.99427260970965-0.00427260970964483
2999.00409946104404-0.00409946104403502
3099.01393332927499-0.0139333292749892
3199.01336867733263-0.0133686773326307
329.019.01282690806316-0.00282690806315955
339.019.0227123468483-0.0127123468483035
348.999.02219717554946-0.0321971755494594
358.999.00089237629053-0.0108923762905277
368.999.00045095979143-0.0104509597914308
3799.0000274318155-2.74318155053521e-05
3899.01002632013375-0.0100263201337540
399.029.009620000794960.0103799992050408
409.059.03004065307390.0199593469260986
419.059.06084951101357-0.0108495110135660
429.059.06040983164143-0.0104098316414252
439.069.059987970394921.20296050827307e-05
449.069.06998845789792-0.00998845789792213
459.089.069583672936490.0104163270635116
469.079.09000579741173-0.0200057974117342
479.069.07919505705356-0.0191950570535617
489.089.068417172167970.0115828278320276
499.079.08888656940278-0.0188865694027793
509.119.078121186062780.0318788139372153
519.159.119413083631160.0305869163688435
529.159.1606526267007-0.0106526267006952
539.179.160220926118660.0097790738813437
549.29.180617225736110.019382774263887
559.239.211402717912490.0185972820875122
569.269.242156377805690.0178436221943112
579.279.2728794954276-0.00287949542760479
589.289.28276280309556-0.00276280309556221
599.299.29265083975188-0.00265083975187963
609.299.30254341375302-0.0125434137530220
619.119.30203508851361-0.192035088513615
629.069.11425281454377-0.0542528145437657
639.119.062054204541380.0479457954586184
649.139.113997220887240.0160027791127568
659.139.13464573784474-0.00464573784473643
669.199.13445746806040.0555425319396008
679.29.196708344209540.00329165579046276
689.239.20684173945190.0231582605480938
699.249.237780234232450.00221976576755445
709.289.247870190841340.0321298091586559
719.329.289172260059040.0308277399409587
729.329.33042156256906-0.0104215625690607
739.329.32999922592353-0.00999922592353464
749.369.329594004584950.0304059954150535
759.379.37082621578383-0.000826215783833462
769.389.38079273316543-0.000792733165432935
779.419.390760607439210.0192393925607863
789.449.421540289033240.0184597109667592
799.449.45228837381951-0.0122883738195139
809.449.45179038414248-0.0117903841424827
819.479.451312575631980.0186874243680180
829.489.48206988856551-0.00206988856551149
839.569.491986005770820.0680139942291831
849.589.574742291306820.0052577086931791
859.569.59495536137553-0.0349553613755287
869.589.573538785889010.00646121411098655
879.79.593800628340720.106199371659283
889.749.718104386638610.0218956133613855
899.769.758991712299960.00100828770004213
909.789.779032573432070.000967426567928698
919.849.799071778655740.0409282213442612
929.889.860730405910090.0192695940899146
939.969.901511311429260.0584886885707387
949.979.98388158137377-0.0138815813737683
959.969.99331902652912-0.0333190265291226
969.969.98196876395542-0.0219687639554156

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
3 & 8.57 & 8.57 & 0 \tabularnewline
4 & 8.59 & 8.58 & 0.00999999999999979 \tabularnewline
5 & 8.61 & 8.60040525270825 & 0.0095947472917537 \tabularnewline
6 & 8.62 & 8.62079408244074 & -0.00079408244073953 \tabularnewline
7 & 8.62 & 8.63076190203477 & -0.0107619020347709 \tabularnewline
8 & 8.63 & 8.63032577304022 & -0.000325773040222188 \tabularnewline
9 & 8.71 & 8.64031257099954 & 0.0696874290004601 \tabularnewline
10 & 8.72 & 8.72313667293286 & -0.00313667293285746 \tabularnewline
11 & 8.74 & 8.73300955841277 & 0.00699044158723439 \tabularnewline
12 & 8.75 & 8.75329284795127 & -0.00329284795127194 \tabularnewline
13 & 8.79 & 8.76315940439626 & 0.0268405956037370 \tabularnewline
14 & 8.82 & 8.8042471268022 & 0.0157528731978029 \tabularnewline
15 & 8.82 & 8.8348855162548 & -0.0148855162548056 \tabularnewline
16 & 8.84 & 8.83428227667721 & 0.00571772332278542 \tabularnewline
17 & 8.86 & 8.85451398896337 & 0.00548601103662882 \tabularnewline
18 & 8.86 & 8.87473631104638 & -0.0147363110463772 \tabularnewline
19 & 8.85 & 8.87413911805027 & -0.0241391180502664 \tabularnewline
20 & 8.86 & 8.86316087375381 & -0.0031608737538118 \tabularnewline
21 & 8.86 & 8.87303277848889 & -0.0130327784888955 \tabularnewline
22 & 8.87 & 8.87250462161104 & -0.00250462161103648 \tabularnewline
23 & 8.88 & 8.88240312114193 & -0.00240312114193308 \tabularnewline
24 & 8.9 & 8.89230573400683 & 0.00769426599316603 \tabularnewline
25 & 8.91 & 8.91261754622 & -0.00261754622000332 \tabularnewline
26 & 8.96 & 8.92251146945054 & 0.0374885305494583 \tabularnewline
27 & 8.98 & 8.97403070230388 & 0.00596929769612231 \tabularnewline
28 & 8.99 & 8.99427260970965 & -0.00427260970964483 \tabularnewline
29 & 9 & 9.00409946104404 & -0.00409946104403502 \tabularnewline
30 & 9 & 9.01393332927499 & -0.0139333292749892 \tabularnewline
31 & 9 & 9.01336867733263 & -0.0133686773326307 \tabularnewline
32 & 9.01 & 9.01282690806316 & -0.00282690806315955 \tabularnewline
33 & 9.01 & 9.0227123468483 & -0.0127123468483035 \tabularnewline
34 & 8.99 & 9.02219717554946 & -0.0321971755494594 \tabularnewline
35 & 8.99 & 9.00089237629053 & -0.0108923762905277 \tabularnewline
36 & 8.99 & 9.00045095979143 & -0.0104509597914308 \tabularnewline
37 & 9 & 9.0000274318155 & -2.74318155053521e-05 \tabularnewline
38 & 9 & 9.01002632013375 & -0.0100263201337540 \tabularnewline
39 & 9.02 & 9.00962000079496 & 0.0103799992050408 \tabularnewline
40 & 9.05 & 9.0300406530739 & 0.0199593469260986 \tabularnewline
41 & 9.05 & 9.06084951101357 & -0.0108495110135660 \tabularnewline
42 & 9.05 & 9.06040983164143 & -0.0104098316414252 \tabularnewline
43 & 9.06 & 9.05998797039492 & 1.20296050827307e-05 \tabularnewline
44 & 9.06 & 9.06998845789792 & -0.00998845789792213 \tabularnewline
45 & 9.08 & 9.06958367293649 & 0.0104163270635116 \tabularnewline
46 & 9.07 & 9.09000579741173 & -0.0200057974117342 \tabularnewline
47 & 9.06 & 9.07919505705356 & -0.0191950570535617 \tabularnewline
48 & 9.08 & 9.06841717216797 & 0.0115828278320276 \tabularnewline
49 & 9.07 & 9.08888656940278 & -0.0188865694027793 \tabularnewline
50 & 9.11 & 9.07812118606278 & 0.0318788139372153 \tabularnewline
51 & 9.15 & 9.11941308363116 & 0.0305869163688435 \tabularnewline
52 & 9.15 & 9.1606526267007 & -0.0106526267006952 \tabularnewline
53 & 9.17 & 9.16022092611866 & 0.0097790738813437 \tabularnewline
54 & 9.2 & 9.18061722573611 & 0.019382774263887 \tabularnewline
55 & 9.23 & 9.21140271791249 & 0.0185972820875122 \tabularnewline
56 & 9.26 & 9.24215637780569 & 0.0178436221943112 \tabularnewline
57 & 9.27 & 9.2728794954276 & -0.00287949542760479 \tabularnewline
58 & 9.28 & 9.28276280309556 & -0.00276280309556221 \tabularnewline
59 & 9.29 & 9.29265083975188 & -0.00265083975187963 \tabularnewline
60 & 9.29 & 9.30254341375302 & -0.0125434137530220 \tabularnewline
61 & 9.11 & 9.30203508851361 & -0.192035088513615 \tabularnewline
62 & 9.06 & 9.11425281454377 & -0.0542528145437657 \tabularnewline
63 & 9.11 & 9.06205420454138 & 0.0479457954586184 \tabularnewline
64 & 9.13 & 9.11399722088724 & 0.0160027791127568 \tabularnewline
65 & 9.13 & 9.13464573784474 & -0.00464573784473643 \tabularnewline
66 & 9.19 & 9.1344574680604 & 0.0555425319396008 \tabularnewline
67 & 9.2 & 9.19670834420954 & 0.00329165579046276 \tabularnewline
68 & 9.23 & 9.2068417394519 & 0.0231582605480938 \tabularnewline
69 & 9.24 & 9.23778023423245 & 0.00221976576755445 \tabularnewline
70 & 9.28 & 9.24787019084134 & 0.0321298091586559 \tabularnewline
71 & 9.32 & 9.28917226005904 & 0.0308277399409587 \tabularnewline
72 & 9.32 & 9.33042156256906 & -0.0104215625690607 \tabularnewline
73 & 9.32 & 9.32999922592353 & -0.00999922592353464 \tabularnewline
74 & 9.36 & 9.32959400458495 & 0.0304059954150535 \tabularnewline
75 & 9.37 & 9.37082621578383 & -0.000826215783833462 \tabularnewline
76 & 9.38 & 9.38079273316543 & -0.000792733165432935 \tabularnewline
77 & 9.41 & 9.39076060743921 & 0.0192393925607863 \tabularnewline
78 & 9.44 & 9.42154028903324 & 0.0184597109667592 \tabularnewline
79 & 9.44 & 9.45228837381951 & -0.0122883738195139 \tabularnewline
80 & 9.44 & 9.45179038414248 & -0.0117903841424827 \tabularnewline
81 & 9.47 & 9.45131257563198 & 0.0186874243680180 \tabularnewline
82 & 9.48 & 9.48206988856551 & -0.00206988856551149 \tabularnewline
83 & 9.56 & 9.49198600577082 & 0.0680139942291831 \tabularnewline
84 & 9.58 & 9.57474229130682 & 0.0052577086931791 \tabularnewline
85 & 9.56 & 9.59495536137553 & -0.0349553613755287 \tabularnewline
86 & 9.58 & 9.57353878588901 & 0.00646121411098655 \tabularnewline
87 & 9.7 & 9.59380062834072 & 0.106199371659283 \tabularnewline
88 & 9.74 & 9.71810438663861 & 0.0218956133613855 \tabularnewline
89 & 9.76 & 9.75899171229996 & 0.00100828770004213 \tabularnewline
90 & 9.78 & 9.77903257343207 & 0.000967426567928698 \tabularnewline
91 & 9.84 & 9.79907177865574 & 0.0409282213442612 \tabularnewline
92 & 9.88 & 9.86073040591009 & 0.0192695940899146 \tabularnewline
93 & 9.96 & 9.90151131142926 & 0.0584886885707387 \tabularnewline
94 & 9.97 & 9.98388158137377 & -0.0138815813737683 \tabularnewline
95 & 9.96 & 9.99331902652912 & -0.0333190265291226 \tabularnewline
96 & 9.96 & 9.98196876395542 & -0.0219687639554156 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=72296&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]8.57[/C][C]8.57[/C][C]0[/C][/ROW]
[ROW][C]4[/C][C]8.59[/C][C]8.58[/C][C]0.00999999999999979[/C][/ROW]
[ROW][C]5[/C][C]8.61[/C][C]8.60040525270825[/C][C]0.0095947472917537[/C][/ROW]
[ROW][C]6[/C][C]8.62[/C][C]8.62079408244074[/C][C]-0.00079408244073953[/C][/ROW]
[ROW][C]7[/C][C]8.62[/C][C]8.63076190203477[/C][C]-0.0107619020347709[/C][/ROW]
[ROW][C]8[/C][C]8.63[/C][C]8.63032577304022[/C][C]-0.000325773040222188[/C][/ROW]
[ROW][C]9[/C][C]8.71[/C][C]8.64031257099954[/C][C]0.0696874290004601[/C][/ROW]
[ROW][C]10[/C][C]8.72[/C][C]8.72313667293286[/C][C]-0.00313667293285746[/C][/ROW]
[ROW][C]11[/C][C]8.74[/C][C]8.73300955841277[/C][C]0.00699044158723439[/C][/ROW]
[ROW][C]12[/C][C]8.75[/C][C]8.75329284795127[/C][C]-0.00329284795127194[/C][/ROW]
[ROW][C]13[/C][C]8.79[/C][C]8.76315940439626[/C][C]0.0268405956037370[/C][/ROW]
[ROW][C]14[/C][C]8.82[/C][C]8.8042471268022[/C][C]0.0157528731978029[/C][/ROW]
[ROW][C]15[/C][C]8.82[/C][C]8.8348855162548[/C][C]-0.0148855162548056[/C][/ROW]
[ROW][C]16[/C][C]8.84[/C][C]8.83428227667721[/C][C]0.00571772332278542[/C][/ROW]
[ROW][C]17[/C][C]8.86[/C][C]8.85451398896337[/C][C]0.00548601103662882[/C][/ROW]
[ROW][C]18[/C][C]8.86[/C][C]8.87473631104638[/C][C]-0.0147363110463772[/C][/ROW]
[ROW][C]19[/C][C]8.85[/C][C]8.87413911805027[/C][C]-0.0241391180502664[/C][/ROW]
[ROW][C]20[/C][C]8.86[/C][C]8.86316087375381[/C][C]-0.0031608737538118[/C][/ROW]
[ROW][C]21[/C][C]8.86[/C][C]8.87303277848889[/C][C]-0.0130327784888955[/C][/ROW]
[ROW][C]22[/C][C]8.87[/C][C]8.87250462161104[/C][C]-0.00250462161103648[/C][/ROW]
[ROW][C]23[/C][C]8.88[/C][C]8.88240312114193[/C][C]-0.00240312114193308[/C][/ROW]
[ROW][C]24[/C][C]8.9[/C][C]8.89230573400683[/C][C]0.00769426599316603[/C][/ROW]
[ROW][C]25[/C][C]8.91[/C][C]8.91261754622[/C][C]-0.00261754622000332[/C][/ROW]
[ROW][C]26[/C][C]8.96[/C][C]8.92251146945054[/C][C]0.0374885305494583[/C][/ROW]
[ROW][C]27[/C][C]8.98[/C][C]8.97403070230388[/C][C]0.00596929769612231[/C][/ROW]
[ROW][C]28[/C][C]8.99[/C][C]8.99427260970965[/C][C]-0.00427260970964483[/C][/ROW]
[ROW][C]29[/C][C]9[/C][C]9.00409946104404[/C][C]-0.00409946104403502[/C][/ROW]
[ROW][C]30[/C][C]9[/C][C]9.01393332927499[/C][C]-0.0139333292749892[/C][/ROW]
[ROW][C]31[/C][C]9[/C][C]9.01336867733263[/C][C]-0.0133686773326307[/C][/ROW]
[ROW][C]32[/C][C]9.01[/C][C]9.01282690806316[/C][C]-0.00282690806315955[/C][/ROW]
[ROW][C]33[/C][C]9.01[/C][C]9.0227123468483[/C][C]-0.0127123468483035[/C][/ROW]
[ROW][C]34[/C][C]8.99[/C][C]9.02219717554946[/C][C]-0.0321971755494594[/C][/ROW]
[ROW][C]35[/C][C]8.99[/C][C]9.00089237629053[/C][C]-0.0108923762905277[/C][/ROW]
[ROW][C]36[/C][C]8.99[/C][C]9.00045095979143[/C][C]-0.0104509597914308[/C][/ROW]
[ROW][C]37[/C][C]9[/C][C]9.0000274318155[/C][C]-2.74318155053521e-05[/C][/ROW]
[ROW][C]38[/C][C]9[/C][C]9.01002632013375[/C][C]-0.0100263201337540[/C][/ROW]
[ROW][C]39[/C][C]9.02[/C][C]9.00962000079496[/C][C]0.0103799992050408[/C][/ROW]
[ROW][C]40[/C][C]9.05[/C][C]9.0300406530739[/C][C]0.0199593469260986[/C][/ROW]
[ROW][C]41[/C][C]9.05[/C][C]9.06084951101357[/C][C]-0.0108495110135660[/C][/ROW]
[ROW][C]42[/C][C]9.05[/C][C]9.06040983164143[/C][C]-0.0104098316414252[/C][/ROW]
[ROW][C]43[/C][C]9.06[/C][C]9.05998797039492[/C][C]1.20296050827307e-05[/C][/ROW]
[ROW][C]44[/C][C]9.06[/C][C]9.06998845789792[/C][C]-0.00998845789792213[/C][/ROW]
[ROW][C]45[/C][C]9.08[/C][C]9.06958367293649[/C][C]0.0104163270635116[/C][/ROW]
[ROW][C]46[/C][C]9.07[/C][C]9.09000579741173[/C][C]-0.0200057974117342[/C][/ROW]
[ROW][C]47[/C][C]9.06[/C][C]9.07919505705356[/C][C]-0.0191950570535617[/C][/ROW]
[ROW][C]48[/C][C]9.08[/C][C]9.06841717216797[/C][C]0.0115828278320276[/C][/ROW]
[ROW][C]49[/C][C]9.07[/C][C]9.08888656940278[/C][C]-0.0188865694027793[/C][/ROW]
[ROW][C]50[/C][C]9.11[/C][C]9.07812118606278[/C][C]0.0318788139372153[/C][/ROW]
[ROW][C]51[/C][C]9.15[/C][C]9.11941308363116[/C][C]0.0305869163688435[/C][/ROW]
[ROW][C]52[/C][C]9.15[/C][C]9.1606526267007[/C][C]-0.0106526267006952[/C][/ROW]
[ROW][C]53[/C][C]9.17[/C][C]9.16022092611866[/C][C]0.0097790738813437[/C][/ROW]
[ROW][C]54[/C][C]9.2[/C][C]9.18061722573611[/C][C]0.019382774263887[/C][/ROW]
[ROW][C]55[/C][C]9.23[/C][C]9.21140271791249[/C][C]0.0185972820875122[/C][/ROW]
[ROW][C]56[/C][C]9.26[/C][C]9.24215637780569[/C][C]0.0178436221943112[/C][/ROW]
[ROW][C]57[/C][C]9.27[/C][C]9.2728794954276[/C][C]-0.00287949542760479[/C][/ROW]
[ROW][C]58[/C][C]9.28[/C][C]9.28276280309556[/C][C]-0.00276280309556221[/C][/ROW]
[ROW][C]59[/C][C]9.29[/C][C]9.29265083975188[/C][C]-0.00265083975187963[/C][/ROW]
[ROW][C]60[/C][C]9.29[/C][C]9.30254341375302[/C][C]-0.0125434137530220[/C][/ROW]
[ROW][C]61[/C][C]9.11[/C][C]9.30203508851361[/C][C]-0.192035088513615[/C][/ROW]
[ROW][C]62[/C][C]9.06[/C][C]9.11425281454377[/C][C]-0.0542528145437657[/C][/ROW]
[ROW][C]63[/C][C]9.11[/C][C]9.06205420454138[/C][C]0.0479457954586184[/C][/ROW]
[ROW][C]64[/C][C]9.13[/C][C]9.11399722088724[/C][C]0.0160027791127568[/C][/ROW]
[ROW][C]65[/C][C]9.13[/C][C]9.13464573784474[/C][C]-0.00464573784473643[/C][/ROW]
[ROW][C]66[/C][C]9.19[/C][C]9.1344574680604[/C][C]0.0555425319396008[/C][/ROW]
[ROW][C]67[/C][C]9.2[/C][C]9.19670834420954[/C][C]0.00329165579046276[/C][/ROW]
[ROW][C]68[/C][C]9.23[/C][C]9.2068417394519[/C][C]0.0231582605480938[/C][/ROW]
[ROW][C]69[/C][C]9.24[/C][C]9.23778023423245[/C][C]0.00221976576755445[/C][/ROW]
[ROW][C]70[/C][C]9.28[/C][C]9.24787019084134[/C][C]0.0321298091586559[/C][/ROW]
[ROW][C]71[/C][C]9.32[/C][C]9.28917226005904[/C][C]0.0308277399409587[/C][/ROW]
[ROW][C]72[/C][C]9.32[/C][C]9.33042156256906[/C][C]-0.0104215625690607[/C][/ROW]
[ROW][C]73[/C][C]9.32[/C][C]9.32999922592353[/C][C]-0.00999922592353464[/C][/ROW]
[ROW][C]74[/C][C]9.36[/C][C]9.32959400458495[/C][C]0.0304059954150535[/C][/ROW]
[ROW][C]75[/C][C]9.37[/C][C]9.37082621578383[/C][C]-0.000826215783833462[/C][/ROW]
[ROW][C]76[/C][C]9.38[/C][C]9.38079273316543[/C][C]-0.000792733165432935[/C][/ROW]
[ROW][C]77[/C][C]9.41[/C][C]9.39076060743921[/C][C]0.0192393925607863[/C][/ROW]
[ROW][C]78[/C][C]9.44[/C][C]9.42154028903324[/C][C]0.0184597109667592[/C][/ROW]
[ROW][C]79[/C][C]9.44[/C][C]9.45228837381951[/C][C]-0.0122883738195139[/C][/ROW]
[ROW][C]80[/C][C]9.44[/C][C]9.45179038414248[/C][C]-0.0117903841424827[/C][/ROW]
[ROW][C]81[/C][C]9.47[/C][C]9.45131257563198[/C][C]0.0186874243680180[/C][/ROW]
[ROW][C]82[/C][C]9.48[/C][C]9.48206988856551[/C][C]-0.00206988856551149[/C][/ROW]
[ROW][C]83[/C][C]9.56[/C][C]9.49198600577082[/C][C]0.0680139942291831[/C][/ROW]
[ROW][C]84[/C][C]9.58[/C][C]9.57474229130682[/C][C]0.0052577086931791[/C][/ROW]
[ROW][C]85[/C][C]9.56[/C][C]9.59495536137553[/C][C]-0.0349553613755287[/C][/ROW]
[ROW][C]86[/C][C]9.58[/C][C]9.57353878588901[/C][C]0.00646121411098655[/C][/ROW]
[ROW][C]87[/C][C]9.7[/C][C]9.59380062834072[/C][C]0.106199371659283[/C][/ROW]
[ROW][C]88[/C][C]9.74[/C][C]9.71810438663861[/C][C]0.0218956133613855[/C][/ROW]
[ROW][C]89[/C][C]9.76[/C][C]9.75899171229996[/C][C]0.00100828770004213[/C][/ROW]
[ROW][C]90[/C][C]9.78[/C][C]9.77903257343207[/C][C]0.000967426567928698[/C][/ROW]
[ROW][C]91[/C][C]9.84[/C][C]9.79907177865574[/C][C]0.0409282213442612[/C][/ROW]
[ROW][C]92[/C][C]9.88[/C][C]9.86073040591009[/C][C]0.0192695940899146[/C][/ROW]
[ROW][C]93[/C][C]9.96[/C][C]9.90151131142926[/C][C]0.0584886885707387[/C][/ROW]
[ROW][C]94[/C][C]9.97[/C][C]9.98388158137377[/C][C]-0.0138815813737683[/C][/ROW]
[ROW][C]95[/C][C]9.96[/C][C]9.99331902652912[/C][C]-0.0333190265291226[/C][/ROW]
[ROW][C]96[/C][C]9.96[/C][C]9.98196876395542[/C][C]-0.0219687639554156[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=72296&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=72296&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
38.578.570
48.598.580.00999999999999979
58.618.600405252708250.0095947472917537
68.628.62079408244074-0.00079408244073953
78.628.63076190203477-0.0107619020347709
88.638.63032577304022-0.000325773040222188
98.718.640312570999540.0696874290004601
108.728.72313667293286-0.00313667293285746
118.748.733009558412770.00699044158723439
128.758.75329284795127-0.00329284795127194
138.798.763159404396260.0268405956037370
148.828.80424712680220.0157528731978029
158.828.8348855162548-0.0148855162548056
168.848.834282276677210.00571772332278542
178.868.854513988963370.00548601103662882
188.868.87473631104638-0.0147363110463772
198.858.87413911805027-0.0241391180502664
208.868.86316087375381-0.0031608737538118
218.868.87303277848889-0.0130327784888955
228.878.87250462161104-0.00250462161103648
238.888.88240312114193-0.00240312114193308
248.98.892305734006830.00769426599316603
258.918.91261754622-0.00261754622000332
268.968.922511469450540.0374885305494583
278.988.974030702303880.00596929769612231
288.998.99427260970965-0.00427260970964483
2999.00409946104404-0.00409946104403502
3099.01393332927499-0.0139333292749892
3199.01336867733263-0.0133686773326307
329.019.01282690806316-0.00282690806315955
339.019.0227123468483-0.0127123468483035
348.999.02219717554946-0.0321971755494594
358.999.00089237629053-0.0108923762905277
368.999.00045095979143-0.0104509597914308
3799.0000274318155-2.74318155053521e-05
3899.01002632013375-0.0100263201337540
399.029.009620000794960.0103799992050408
409.059.03004065307390.0199593469260986
419.059.06084951101357-0.0108495110135660
429.059.06040983164143-0.0104098316414252
439.069.059987970394921.20296050827307e-05
449.069.06998845789792-0.00998845789792213
459.089.069583672936490.0104163270635116
469.079.09000579741173-0.0200057974117342
479.069.07919505705356-0.0191950570535617
489.089.068417172167970.0115828278320276
499.079.08888656940278-0.0188865694027793
509.119.078121186062780.0318788139372153
519.159.119413083631160.0305869163688435
529.159.1606526267007-0.0106526267006952
539.179.160220926118660.0097790738813437
549.29.180617225736110.019382774263887
559.239.211402717912490.0185972820875122
569.269.242156377805690.0178436221943112
579.279.2728794954276-0.00287949542760479
589.289.28276280309556-0.00276280309556221
599.299.29265083975188-0.00265083975187963
609.299.30254341375302-0.0125434137530220
619.119.30203508851361-0.192035088513615
629.069.11425281454377-0.0542528145437657
639.119.062054204541380.0479457954586184
649.139.113997220887240.0160027791127568
659.139.13464573784474-0.00464573784473643
669.199.13445746806040.0555425319396008
679.29.196708344209540.00329165579046276
689.239.20684173945190.0231582605480938
699.249.237780234232450.00221976576755445
709.289.247870190841340.0321298091586559
719.329.289172260059040.0308277399409587
729.329.33042156256906-0.0104215625690607
739.329.32999922592353-0.00999922592353464
749.369.329594004584950.0304059954150535
759.379.37082621578383-0.000826215783833462
769.389.38079273316543-0.000792733165432935
779.419.390760607439210.0192393925607863
789.449.421540289033240.0184597109667592
799.449.45228837381951-0.0122883738195139
809.449.45179038414248-0.0117903841424827
819.479.451312575631980.0186874243680180
829.489.48206988856551-0.00206988856551149
839.569.491986005770820.0680139942291831
849.589.574742291306820.0052577086931791
859.569.59495536137553-0.0349553613755287
869.589.573538785889010.00646121411098655
879.79.593800628340720.106199371659283
889.749.718104386638610.0218956133613855
899.769.758991712299960.00100828770004213
909.789.779032573432070.000967426567928698
919.849.799071778655740.0409282213442612
929.889.860730405910090.0192695940899146
939.969.901511311429260.0584886885707387
949.979.98388158137377-0.0138815813737683
959.969.99331902652912-0.0333190265291226
969.969.98196876395542-0.0219687639554156







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
979.981078473846449.919718338867410.0424386088255
9810.00215694769299.9136048368184610.0907090585673
9910.02323542153939.9125936697225910.1338771733561
10010.04431389538589.9140150251028910.1746127656686
10110.06539236923229.9168580697787210.2139266686857
10210.08647084307869.9206158114559410.2523258747013
10310.10754931692519.9249937842333610.2901048496168
10410.12862779077159.929804507835210.3274510737078
10510.14970626461809.9349208270383110.3644917021976
10610.17078473846449.9402524233531610.4013170535756
10710.19186321231089.9457328466538610.4379935779678
10810.21294168615739.951311839469210.4745715328454

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
97 & 9.98107847384644 & 9.9197183388674 & 10.0424386088255 \tabularnewline
98 & 10.0021569476929 & 9.91360483681846 & 10.0907090585673 \tabularnewline
99 & 10.0232354215393 & 9.91259366972259 & 10.1338771733561 \tabularnewline
100 & 10.0443138953858 & 9.91401502510289 & 10.1746127656686 \tabularnewline
101 & 10.0653923692322 & 9.91685806977872 & 10.2139266686857 \tabularnewline
102 & 10.0864708430786 & 9.92061581145594 & 10.2523258747013 \tabularnewline
103 & 10.1075493169251 & 9.92499378423336 & 10.2901048496168 \tabularnewline
104 & 10.1286277907715 & 9.9298045078352 & 10.3274510737078 \tabularnewline
105 & 10.1497062646180 & 9.93492082703831 & 10.3644917021976 \tabularnewline
106 & 10.1707847384644 & 9.94025242335316 & 10.4013170535756 \tabularnewline
107 & 10.1918632123108 & 9.94573284665386 & 10.4379935779678 \tabularnewline
108 & 10.2129416861573 & 9.9513118394692 & 10.4745715328454 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=72296&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]9.98107847384644[/C][C]9.9197183388674[/C][C]10.0424386088255[/C][/ROW]
[ROW][C]98[/C][C]10.0021569476929[/C][C]9.91360483681846[/C][C]10.0907090585673[/C][/ROW]
[ROW][C]99[/C][C]10.0232354215393[/C][C]9.91259366972259[/C][C]10.1338771733561[/C][/ROW]
[ROW][C]100[/C][C]10.0443138953858[/C][C]9.91401502510289[/C][C]10.1746127656686[/C][/ROW]
[ROW][C]101[/C][C]10.0653923692322[/C][C]9.91685806977872[/C][C]10.2139266686857[/C][/ROW]
[ROW][C]102[/C][C]10.0864708430786[/C][C]9.92061581145594[/C][C]10.2523258747013[/C][/ROW]
[ROW][C]103[/C][C]10.1075493169251[/C][C]9.92499378423336[/C][C]10.2901048496168[/C][/ROW]
[ROW][C]104[/C][C]10.1286277907715[/C][C]9.9298045078352[/C][C]10.3274510737078[/C][/ROW]
[ROW][C]105[/C][C]10.1497062646180[/C][C]9.93492082703831[/C][C]10.3644917021976[/C][/ROW]
[ROW][C]106[/C][C]10.1707847384644[/C][C]9.94025242335316[/C][C]10.4013170535756[/C][/ROW]
[ROW][C]107[/C][C]10.1918632123108[/C][C]9.94573284665386[/C][C]10.4379935779678[/C][/ROW]
[ROW][C]108[/C][C]10.2129416861573[/C][C]9.9513118394692[/C][C]10.4745715328454[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=72296&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=72296&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
979.981078473846449.919718338867410.0424386088255
9810.00215694769299.9136048368184610.0907090585673
9910.02323542153939.9125936697225910.1338771733561
10010.04431389538589.9140150251028910.1746127656686
10110.06539236923229.9168580697787210.2139266686857
10210.08647084307869.9206158114559410.2523258747013
10310.10754931692519.9249937842333610.2901048496168
10410.12862779077159.929804507835210.3274510737078
10510.14970626461809.9349208270383110.3644917021976
10610.17078473846449.9402524233531610.4013170535756
10710.19186321231089.9457328466538610.4379935779678
10810.21294168615739.951311839469210.4745715328454



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=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')