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of Irreproducible Research!

Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationSun, 26 May 2013 19:57:39 -0400
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2013/May/26/t1369612696cr4ausxqwfo8464.htm/, Retrieved Mon, 29 Apr 2024 10:39:25 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=210692, Retrieved Mon, 29 Apr 2024 10:39:25 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact75
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [Standard Deviation Plot] [] [2013-04-29 18:07:56] [2350abd9e4ab4c416741d11e9cf0d058]
- RMPD    [Exponential Smoothing] [] [2013-05-26 23:57:39] [fd383db316336f22794dc1afa7a19318] [Current]
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Dataseries X:
530.3
527.76
521.41
1601.93
1577.49
1551.43
1551.43
1516.88
1485.95
1438.22
1385.06
1329.49
1329.49
1276.16
1242.34
1181.59
1160.21
1135.18
1135.18
1084.96
1077.35
1061.13
1029.98
1013.08
1013.08
996.04
975.02
951.89
944.4
932.47
932.47
920.44
900.18
886.9
867.74
859.03
859.03
844.99
834.82
825.62
816.92
813.21
813.21
811.03
804.16
788.62
778.76
765.91
765.91
753.85
742.22
732.11
729.94
731.22
731.22
729.11
726.94
720.52
709.36
703.21
703.21
695.88
681.63
672.1
665.49
658.93
658.93
656
650.66
645.93
638.74
634.67




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time3 seconds
R Server'Gwilym Jenkins' @ jenkins.wessa.net

\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 & 'Gwilym Jenkins' @ jenkins.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=210692&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]'Gwilym Jenkins' @ jenkins.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=210692&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=210692&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'Gwilym Jenkins' @ jenkins.wessa.net







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.989270808318865
beta0
gammaFALSE

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.989270808318865 \tabularnewline
beta & 0 \tabularnewline
gamma & FALSE \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=210692&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]0.989270808318865[/C][/ROW]
[ROW][C]beta[/C][C]0[/C][/ROW]
[ROW][C]gamma[/C][C]FALSE[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=210692&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=210692&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
alpha0.989270808318865
beta0
gammaFALSE







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
3521.41525.22-3.81000000000006
41601.93518.9108782203051083.0191217797
51577.491587.77008024809-10.2800802480911
61551.431575.06029695148-23.6302969514793
71551.431549.143533985472.28646601452533
81516.881548.86546806786-31.9854680678577
91485.951514.68317821791-28.733178217911
101438.221483.71828377671-45.4982837767081
111385.061436.1681598078-51.1081598078031
121329.491383.06834924305-53.578349243048
131329.491327.524852378991.96514762101242
141276.161326.92891555449-50.7689155544924
151242.341274.16470942643-31.8247094264277
161181.591240.14145340763-58.5514534076326
171160.211179.67820976682-19.4682097668194
181135.181157.87887815428-22.6988781542768
191135.181132.883540614662.29645938533599
201084.961132.61536084707-47.655360847067
211077.351082.93130350116-5.58130350116198
221061.131074.86988287509-13.7398828750943
231029.981058.73741783704-28.7574178370432
241013.081027.74854384823-14.6685438482281
251013.081010.697381618632.38261838136918
26996.041010.51443643068-14.4744364306835
27975.02993.655299002941-18.6352990029412
28951.89972.679941695038-20.7899416950379
29944.4949.573059269486-5.17305926948575
30932.47941.91550274448-9.44550274448022
31932.47930.031342609472.43865739052978
32920.44929.903835177412-9.46383517741242
33900.18918.001539301657-17.8215393016573
34886.9897.83121071122-10.9312107112204
35867.74884.477283055028-16.7372830550275
36859.03865.379577518119-6.34957751811885
37859.03856.5581258342862.47187416571387
38844.99856.463478788264-11.4734787882644
39834.82842.573101153169-7.7531011531687
40825.62832.363184508396-6.74318450839564
41816.92823.152348919132-6.23234891913194
42813.21814.446868066177-1.23686806617707
43813.21810.6832705945662.52672940543368
44811.03810.6428902358830.387109764117213
45804.16808.485846625139-4.32584662513921
46788.62801.666412837624-13.0464128376243
47778.76786.219977464086-7.45997746408614
48765.91776.300039528149-10.3900395281491
49765.91763.4814767256722.42852327432786
50753.85763.343943908288-9.49394390828763
51742.22751.411862344002-9.19186234400195
52732.11739.778621252995-7.66862125299542
53729.94729.6522781073530.287721892646573
54731.22727.3969129766633.82308702333705
55731.22728.6389813665132.58101863348702
56729.11728.6523077563490.457692243651195
57726.94726.5650893321870.374910667813083
58720.52724.395977511582-3.87597751158182
59709.36718.021586105674-8.66158610567356
60703.21706.91293181759-3.70293181759041
61703.21700.7097294652532.50027053474685
62695.88700.643174118178-4.76317411817809
63681.63693.391105008125-11.7611050081246
64672.1679.216187150014-7.11618715001418
65665.49669.636350935971-4.14635093597144
66658.93662.994486993969-4.06448699396935
67658.93656.4336086600442.49639133995618
68656656.363215738803-0.363215738802523
69650.66653.463897011283-2.80389701128331
70645.93648.150083548488-2.22008354848822
71638.74643.41381970194-4.67381970193981
72634.67636.250146307465-1.58014630746527

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
3 & 521.41 & 525.22 & -3.81000000000006 \tabularnewline
4 & 1601.93 & 518.910878220305 & 1083.0191217797 \tabularnewline
5 & 1577.49 & 1587.77008024809 & -10.2800802480911 \tabularnewline
6 & 1551.43 & 1575.06029695148 & -23.6302969514793 \tabularnewline
7 & 1551.43 & 1549.14353398547 & 2.28646601452533 \tabularnewline
8 & 1516.88 & 1548.86546806786 & -31.9854680678577 \tabularnewline
9 & 1485.95 & 1514.68317821791 & -28.733178217911 \tabularnewline
10 & 1438.22 & 1483.71828377671 & -45.4982837767081 \tabularnewline
11 & 1385.06 & 1436.1681598078 & -51.1081598078031 \tabularnewline
12 & 1329.49 & 1383.06834924305 & -53.578349243048 \tabularnewline
13 & 1329.49 & 1327.52485237899 & 1.96514762101242 \tabularnewline
14 & 1276.16 & 1326.92891555449 & -50.7689155544924 \tabularnewline
15 & 1242.34 & 1274.16470942643 & -31.8247094264277 \tabularnewline
16 & 1181.59 & 1240.14145340763 & -58.5514534076326 \tabularnewline
17 & 1160.21 & 1179.67820976682 & -19.4682097668194 \tabularnewline
18 & 1135.18 & 1157.87887815428 & -22.6988781542768 \tabularnewline
19 & 1135.18 & 1132.88354061466 & 2.29645938533599 \tabularnewline
20 & 1084.96 & 1132.61536084707 & -47.655360847067 \tabularnewline
21 & 1077.35 & 1082.93130350116 & -5.58130350116198 \tabularnewline
22 & 1061.13 & 1074.86988287509 & -13.7398828750943 \tabularnewline
23 & 1029.98 & 1058.73741783704 & -28.7574178370432 \tabularnewline
24 & 1013.08 & 1027.74854384823 & -14.6685438482281 \tabularnewline
25 & 1013.08 & 1010.69738161863 & 2.38261838136918 \tabularnewline
26 & 996.04 & 1010.51443643068 & -14.4744364306835 \tabularnewline
27 & 975.02 & 993.655299002941 & -18.6352990029412 \tabularnewline
28 & 951.89 & 972.679941695038 & -20.7899416950379 \tabularnewline
29 & 944.4 & 949.573059269486 & -5.17305926948575 \tabularnewline
30 & 932.47 & 941.91550274448 & -9.44550274448022 \tabularnewline
31 & 932.47 & 930.03134260947 & 2.43865739052978 \tabularnewline
32 & 920.44 & 929.903835177412 & -9.46383517741242 \tabularnewline
33 & 900.18 & 918.001539301657 & -17.8215393016573 \tabularnewline
34 & 886.9 & 897.83121071122 & -10.9312107112204 \tabularnewline
35 & 867.74 & 884.477283055028 & -16.7372830550275 \tabularnewline
36 & 859.03 & 865.379577518119 & -6.34957751811885 \tabularnewline
37 & 859.03 & 856.558125834286 & 2.47187416571387 \tabularnewline
38 & 844.99 & 856.463478788264 & -11.4734787882644 \tabularnewline
39 & 834.82 & 842.573101153169 & -7.7531011531687 \tabularnewline
40 & 825.62 & 832.363184508396 & -6.74318450839564 \tabularnewline
41 & 816.92 & 823.152348919132 & -6.23234891913194 \tabularnewline
42 & 813.21 & 814.446868066177 & -1.23686806617707 \tabularnewline
43 & 813.21 & 810.683270594566 & 2.52672940543368 \tabularnewline
44 & 811.03 & 810.642890235883 & 0.387109764117213 \tabularnewline
45 & 804.16 & 808.485846625139 & -4.32584662513921 \tabularnewline
46 & 788.62 & 801.666412837624 & -13.0464128376243 \tabularnewline
47 & 778.76 & 786.219977464086 & -7.45997746408614 \tabularnewline
48 & 765.91 & 776.300039528149 & -10.3900395281491 \tabularnewline
49 & 765.91 & 763.481476725672 & 2.42852327432786 \tabularnewline
50 & 753.85 & 763.343943908288 & -9.49394390828763 \tabularnewline
51 & 742.22 & 751.411862344002 & -9.19186234400195 \tabularnewline
52 & 732.11 & 739.778621252995 & -7.66862125299542 \tabularnewline
53 & 729.94 & 729.652278107353 & 0.287721892646573 \tabularnewline
54 & 731.22 & 727.396912976663 & 3.82308702333705 \tabularnewline
55 & 731.22 & 728.638981366513 & 2.58101863348702 \tabularnewline
56 & 729.11 & 728.652307756349 & 0.457692243651195 \tabularnewline
57 & 726.94 & 726.565089332187 & 0.374910667813083 \tabularnewline
58 & 720.52 & 724.395977511582 & -3.87597751158182 \tabularnewline
59 & 709.36 & 718.021586105674 & -8.66158610567356 \tabularnewline
60 & 703.21 & 706.91293181759 & -3.70293181759041 \tabularnewline
61 & 703.21 & 700.709729465253 & 2.50027053474685 \tabularnewline
62 & 695.88 & 700.643174118178 & -4.76317411817809 \tabularnewline
63 & 681.63 & 693.391105008125 & -11.7611050081246 \tabularnewline
64 & 672.1 & 679.216187150014 & -7.11618715001418 \tabularnewline
65 & 665.49 & 669.636350935971 & -4.14635093597144 \tabularnewline
66 & 658.93 & 662.994486993969 & -4.06448699396935 \tabularnewline
67 & 658.93 & 656.433608660044 & 2.49639133995618 \tabularnewline
68 & 656 & 656.363215738803 & -0.363215738802523 \tabularnewline
69 & 650.66 & 653.463897011283 & -2.80389701128331 \tabularnewline
70 & 645.93 & 648.150083548488 & -2.22008354848822 \tabularnewline
71 & 638.74 & 643.41381970194 & -4.67381970193981 \tabularnewline
72 & 634.67 & 636.250146307465 & -1.58014630746527 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=210692&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]521.41[/C][C]525.22[/C][C]-3.81000000000006[/C][/ROW]
[ROW][C]4[/C][C]1601.93[/C][C]518.910878220305[/C][C]1083.0191217797[/C][/ROW]
[ROW][C]5[/C][C]1577.49[/C][C]1587.77008024809[/C][C]-10.2800802480911[/C][/ROW]
[ROW][C]6[/C][C]1551.43[/C][C]1575.06029695148[/C][C]-23.6302969514793[/C][/ROW]
[ROW][C]7[/C][C]1551.43[/C][C]1549.14353398547[/C][C]2.28646601452533[/C][/ROW]
[ROW][C]8[/C][C]1516.88[/C][C]1548.86546806786[/C][C]-31.9854680678577[/C][/ROW]
[ROW][C]9[/C][C]1485.95[/C][C]1514.68317821791[/C][C]-28.733178217911[/C][/ROW]
[ROW][C]10[/C][C]1438.22[/C][C]1483.71828377671[/C][C]-45.4982837767081[/C][/ROW]
[ROW][C]11[/C][C]1385.06[/C][C]1436.1681598078[/C][C]-51.1081598078031[/C][/ROW]
[ROW][C]12[/C][C]1329.49[/C][C]1383.06834924305[/C][C]-53.578349243048[/C][/ROW]
[ROW][C]13[/C][C]1329.49[/C][C]1327.52485237899[/C][C]1.96514762101242[/C][/ROW]
[ROW][C]14[/C][C]1276.16[/C][C]1326.92891555449[/C][C]-50.7689155544924[/C][/ROW]
[ROW][C]15[/C][C]1242.34[/C][C]1274.16470942643[/C][C]-31.8247094264277[/C][/ROW]
[ROW][C]16[/C][C]1181.59[/C][C]1240.14145340763[/C][C]-58.5514534076326[/C][/ROW]
[ROW][C]17[/C][C]1160.21[/C][C]1179.67820976682[/C][C]-19.4682097668194[/C][/ROW]
[ROW][C]18[/C][C]1135.18[/C][C]1157.87887815428[/C][C]-22.6988781542768[/C][/ROW]
[ROW][C]19[/C][C]1135.18[/C][C]1132.88354061466[/C][C]2.29645938533599[/C][/ROW]
[ROW][C]20[/C][C]1084.96[/C][C]1132.61536084707[/C][C]-47.655360847067[/C][/ROW]
[ROW][C]21[/C][C]1077.35[/C][C]1082.93130350116[/C][C]-5.58130350116198[/C][/ROW]
[ROW][C]22[/C][C]1061.13[/C][C]1074.86988287509[/C][C]-13.7398828750943[/C][/ROW]
[ROW][C]23[/C][C]1029.98[/C][C]1058.73741783704[/C][C]-28.7574178370432[/C][/ROW]
[ROW][C]24[/C][C]1013.08[/C][C]1027.74854384823[/C][C]-14.6685438482281[/C][/ROW]
[ROW][C]25[/C][C]1013.08[/C][C]1010.69738161863[/C][C]2.38261838136918[/C][/ROW]
[ROW][C]26[/C][C]996.04[/C][C]1010.51443643068[/C][C]-14.4744364306835[/C][/ROW]
[ROW][C]27[/C][C]975.02[/C][C]993.655299002941[/C][C]-18.6352990029412[/C][/ROW]
[ROW][C]28[/C][C]951.89[/C][C]972.679941695038[/C][C]-20.7899416950379[/C][/ROW]
[ROW][C]29[/C][C]944.4[/C][C]949.573059269486[/C][C]-5.17305926948575[/C][/ROW]
[ROW][C]30[/C][C]932.47[/C][C]941.91550274448[/C][C]-9.44550274448022[/C][/ROW]
[ROW][C]31[/C][C]932.47[/C][C]930.03134260947[/C][C]2.43865739052978[/C][/ROW]
[ROW][C]32[/C][C]920.44[/C][C]929.903835177412[/C][C]-9.46383517741242[/C][/ROW]
[ROW][C]33[/C][C]900.18[/C][C]918.001539301657[/C][C]-17.8215393016573[/C][/ROW]
[ROW][C]34[/C][C]886.9[/C][C]897.83121071122[/C][C]-10.9312107112204[/C][/ROW]
[ROW][C]35[/C][C]867.74[/C][C]884.477283055028[/C][C]-16.7372830550275[/C][/ROW]
[ROW][C]36[/C][C]859.03[/C][C]865.379577518119[/C][C]-6.34957751811885[/C][/ROW]
[ROW][C]37[/C][C]859.03[/C][C]856.558125834286[/C][C]2.47187416571387[/C][/ROW]
[ROW][C]38[/C][C]844.99[/C][C]856.463478788264[/C][C]-11.4734787882644[/C][/ROW]
[ROW][C]39[/C][C]834.82[/C][C]842.573101153169[/C][C]-7.7531011531687[/C][/ROW]
[ROW][C]40[/C][C]825.62[/C][C]832.363184508396[/C][C]-6.74318450839564[/C][/ROW]
[ROW][C]41[/C][C]816.92[/C][C]823.152348919132[/C][C]-6.23234891913194[/C][/ROW]
[ROW][C]42[/C][C]813.21[/C][C]814.446868066177[/C][C]-1.23686806617707[/C][/ROW]
[ROW][C]43[/C][C]813.21[/C][C]810.683270594566[/C][C]2.52672940543368[/C][/ROW]
[ROW][C]44[/C][C]811.03[/C][C]810.642890235883[/C][C]0.387109764117213[/C][/ROW]
[ROW][C]45[/C][C]804.16[/C][C]808.485846625139[/C][C]-4.32584662513921[/C][/ROW]
[ROW][C]46[/C][C]788.62[/C][C]801.666412837624[/C][C]-13.0464128376243[/C][/ROW]
[ROW][C]47[/C][C]778.76[/C][C]786.219977464086[/C][C]-7.45997746408614[/C][/ROW]
[ROW][C]48[/C][C]765.91[/C][C]776.300039528149[/C][C]-10.3900395281491[/C][/ROW]
[ROW][C]49[/C][C]765.91[/C][C]763.481476725672[/C][C]2.42852327432786[/C][/ROW]
[ROW][C]50[/C][C]753.85[/C][C]763.343943908288[/C][C]-9.49394390828763[/C][/ROW]
[ROW][C]51[/C][C]742.22[/C][C]751.411862344002[/C][C]-9.19186234400195[/C][/ROW]
[ROW][C]52[/C][C]732.11[/C][C]739.778621252995[/C][C]-7.66862125299542[/C][/ROW]
[ROW][C]53[/C][C]729.94[/C][C]729.652278107353[/C][C]0.287721892646573[/C][/ROW]
[ROW][C]54[/C][C]731.22[/C][C]727.396912976663[/C][C]3.82308702333705[/C][/ROW]
[ROW][C]55[/C][C]731.22[/C][C]728.638981366513[/C][C]2.58101863348702[/C][/ROW]
[ROW][C]56[/C][C]729.11[/C][C]728.652307756349[/C][C]0.457692243651195[/C][/ROW]
[ROW][C]57[/C][C]726.94[/C][C]726.565089332187[/C][C]0.374910667813083[/C][/ROW]
[ROW][C]58[/C][C]720.52[/C][C]724.395977511582[/C][C]-3.87597751158182[/C][/ROW]
[ROW][C]59[/C][C]709.36[/C][C]718.021586105674[/C][C]-8.66158610567356[/C][/ROW]
[ROW][C]60[/C][C]703.21[/C][C]706.91293181759[/C][C]-3.70293181759041[/C][/ROW]
[ROW][C]61[/C][C]703.21[/C][C]700.709729465253[/C][C]2.50027053474685[/C][/ROW]
[ROW][C]62[/C][C]695.88[/C][C]700.643174118178[/C][C]-4.76317411817809[/C][/ROW]
[ROW][C]63[/C][C]681.63[/C][C]693.391105008125[/C][C]-11.7611050081246[/C][/ROW]
[ROW][C]64[/C][C]672.1[/C][C]679.216187150014[/C][C]-7.11618715001418[/C][/ROW]
[ROW][C]65[/C][C]665.49[/C][C]669.636350935971[/C][C]-4.14635093597144[/C][/ROW]
[ROW][C]66[/C][C]658.93[/C][C]662.994486993969[/C][C]-4.06448699396935[/C][/ROW]
[ROW][C]67[/C][C]658.93[/C][C]656.433608660044[/C][C]2.49639133995618[/C][/ROW]
[ROW][C]68[/C][C]656[/C][C]656.363215738803[/C][C]-0.363215738802523[/C][/ROW]
[ROW][C]69[/C][C]650.66[/C][C]653.463897011283[/C][C]-2.80389701128331[/C][/ROW]
[ROW][C]70[/C][C]645.93[/C][C]648.150083548488[/C][C]-2.22008354848822[/C][/ROW]
[ROW][C]71[/C][C]638.74[/C][C]643.41381970194[/C][C]-4.67381970193981[/C][/ROW]
[ROW][C]72[/C][C]634.67[/C][C]636.250146307465[/C][C]-1.58014630746527[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=210692&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=210692&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
3521.41525.22-3.81000000000006
41601.93518.9108782203051083.0191217797
51577.491587.77008024809-10.2800802480911
61551.431575.06029695148-23.6302969514793
71551.431549.143533985472.28646601452533
81516.881548.86546806786-31.9854680678577
91485.951514.68317821791-28.733178217911
101438.221483.71828377671-45.4982837767081
111385.061436.1681598078-51.1081598078031
121329.491383.06834924305-53.578349243048
131329.491327.524852378991.96514762101242
141276.161326.92891555449-50.7689155544924
151242.341274.16470942643-31.8247094264277
161181.591240.14145340763-58.5514534076326
171160.211179.67820976682-19.4682097668194
181135.181157.87887815428-22.6988781542768
191135.181132.883540614662.29645938533599
201084.961132.61536084707-47.655360847067
211077.351082.93130350116-5.58130350116198
221061.131074.86988287509-13.7398828750943
231029.981058.73741783704-28.7574178370432
241013.081027.74854384823-14.6685438482281
251013.081010.697381618632.38261838136918
26996.041010.51443643068-14.4744364306835
27975.02993.655299002941-18.6352990029412
28951.89972.679941695038-20.7899416950379
29944.4949.573059269486-5.17305926948575
30932.47941.91550274448-9.44550274448022
31932.47930.031342609472.43865739052978
32920.44929.903835177412-9.46383517741242
33900.18918.001539301657-17.8215393016573
34886.9897.83121071122-10.9312107112204
35867.74884.477283055028-16.7372830550275
36859.03865.379577518119-6.34957751811885
37859.03856.5581258342862.47187416571387
38844.99856.463478788264-11.4734787882644
39834.82842.573101153169-7.7531011531687
40825.62832.363184508396-6.74318450839564
41816.92823.152348919132-6.23234891913194
42813.21814.446868066177-1.23686806617707
43813.21810.6832705945662.52672940543368
44811.03810.6428902358830.387109764117213
45804.16808.485846625139-4.32584662513921
46788.62801.666412837624-13.0464128376243
47778.76786.219977464086-7.45997746408614
48765.91776.300039528149-10.3900395281491
49765.91763.4814767256722.42852327432786
50753.85763.343943908288-9.49394390828763
51742.22751.411862344002-9.19186234400195
52732.11739.778621252995-7.66862125299542
53729.94729.6522781073530.287721892646573
54731.22727.3969129766633.82308702333705
55731.22728.6389813665132.58101863348702
56729.11728.6523077563490.457692243651195
57726.94726.5650893321870.374910667813083
58720.52724.395977511582-3.87597751158182
59709.36718.021586105674-8.66158610567356
60703.21706.91293181759-3.70293181759041
61703.21700.7097294652532.50027053474685
62695.88700.643174118178-4.76317411817809
63681.63693.391105008125-11.7611050081246
64672.1679.216187150014-7.11618715001418
65665.49669.636350935971-4.14635093597144
66658.93662.994486993969-4.06448699396935
67658.93656.4336086600442.49639133995618
68656656.363215738803-0.363215738802523
69650.66653.463897011283-2.80389701128331
70645.93648.150083548488-2.22008354848822
71638.74643.41381970194-4.67381970193981
72634.67636.250146307465-1.58014630746527







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
73632.146953692617374.045973702006890.247933683228
74629.606953692617266.549897373874992.66401001136
75627.066953692617183.2147976614141070.91910972382
76624.526953692617112.4731999867541136.58070739848
77621.98695369261749.8039786269641194.16992875827
78619.446953692617-7.121212771095661246.01512015633
79616.906953692617-59.68892088571341293.50282827095
80614.366953692617-108.8040411399561337.53794852519
81611.826953692617-155.0958573111041378.74976469634
82609.286953692617-199.0229548873581417.59686227259
83606.746953692617-240.9317699871061454.42567737234
84604.206953692617-281.0915998191351489.50550720437

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
73 & 632.146953692617 & 374.045973702006 & 890.247933683228 \tabularnewline
74 & 629.606953692617 & 266.549897373874 & 992.66401001136 \tabularnewline
75 & 627.066953692617 & 183.214797661414 & 1070.91910972382 \tabularnewline
76 & 624.526953692617 & 112.473199986754 & 1136.58070739848 \tabularnewline
77 & 621.986953692617 & 49.803978626964 & 1194.16992875827 \tabularnewline
78 & 619.446953692617 & -7.12121277109566 & 1246.01512015633 \tabularnewline
79 & 616.906953692617 & -59.6889208857134 & 1293.50282827095 \tabularnewline
80 & 614.366953692617 & -108.804041139956 & 1337.53794852519 \tabularnewline
81 & 611.826953692617 & -155.095857311104 & 1378.74976469634 \tabularnewline
82 & 609.286953692617 & -199.022954887358 & 1417.59686227259 \tabularnewline
83 & 606.746953692617 & -240.931769987106 & 1454.42567737234 \tabularnewline
84 & 604.206953692617 & -281.091599819135 & 1489.50550720437 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=210692&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]632.146953692617[/C][C]374.045973702006[/C][C]890.247933683228[/C][/ROW]
[ROW][C]74[/C][C]629.606953692617[/C][C]266.549897373874[/C][C]992.66401001136[/C][/ROW]
[ROW][C]75[/C][C]627.066953692617[/C][C]183.214797661414[/C][C]1070.91910972382[/C][/ROW]
[ROW][C]76[/C][C]624.526953692617[/C][C]112.473199986754[/C][C]1136.58070739848[/C][/ROW]
[ROW][C]77[/C][C]621.986953692617[/C][C]49.803978626964[/C][C]1194.16992875827[/C][/ROW]
[ROW][C]78[/C][C]619.446953692617[/C][C]-7.12121277109566[/C][C]1246.01512015633[/C][/ROW]
[ROW][C]79[/C][C]616.906953692617[/C][C]-59.6889208857134[/C][C]1293.50282827095[/C][/ROW]
[ROW][C]80[/C][C]614.366953692617[/C][C]-108.804041139956[/C][C]1337.53794852519[/C][/ROW]
[ROW][C]81[/C][C]611.826953692617[/C][C]-155.095857311104[/C][C]1378.74976469634[/C][/ROW]
[ROW][C]82[/C][C]609.286953692617[/C][C]-199.022954887358[/C][C]1417.59686227259[/C][/ROW]
[ROW][C]83[/C][C]606.746953692617[/C][C]-240.931769987106[/C][C]1454.42567737234[/C][/ROW]
[ROW][C]84[/C][C]604.206953692617[/C][C]-281.091599819135[/C][C]1489.50550720437[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=210692&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=210692&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
73632.146953692617374.045973702006890.247933683228
74629.606953692617266.549897373874992.66401001136
75627.066953692617183.2147976614141070.91910972382
76624.526953692617112.4731999867541136.58070739848
77621.98695369261749.8039786269641194.16992875827
78619.446953692617-7.121212771095661246.01512015633
79616.906953692617-59.68892088571341293.50282827095
80614.366953692617-108.8040411399561337.53794852519
81611.826953692617-155.0958573111041378.74976469634
82609.286953692617-199.0229548873581417.59686227259
83606.746953692617-240.9317699871061454.42567737234
84604.206953692617-281.0915998191351489.50550720437



Parameters (Session):
par1 = additive ; par2 = 12 ;
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')