Free Statistics

of Irreproducible Research!

Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationMon, 17 Dec 2012 05:33:13 -0500
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2012/Dec/17/t13557404091oa766al4qt6exy.htm/, Retrieved Fri, 29 Mar 2024 02:02:33 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=200753, Retrieved Fri, 29 Mar 2024 02:02:33 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact77
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [] [2012-12-17 10:33:13] [76c30f62b7052b57088120e90a652e05] [Current]
Feedback Forum

Post a new message
Dataseries X:
10
9.99
9.95
9.96
9.97
9.95
9.94
9.9
9.9
9.92
9.87
9.96
9.94
9.96
9.96
9.89
9.82
9.83
9.83
9.82
9.77
9.66
9.69
9.67
9.7
9.77
9.79
9.81
9.77
9.78
9.77
9.79
9.77
9.77
9.8
9.8
9.8
9.8
9.76
9.78
9.77
9.79
9.81
9.82
9.84
9.87
9.99
9.99
9.99
10.08
10.06
10.08
10.07
10.04
10.04
10.12
10.1
10.11
10.13
10.16
10.15
10.25
10.41
10.46
10.46
10.5
10.5
10.48
10.5
10.5
10.53
10.53




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'Gertrude Mary Cox' @ cox.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 & 2 seconds \tabularnewline
R Server & 'Gertrude Mary Cox' @ cox.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=200753&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]'Gertrude Mary Cox' @ cox.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=200753&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=200753&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'Gertrude Mary Cox' @ cox.wessa.net







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha1
beta0.0734210921061535
gammaFALSE

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 1 \tabularnewline
beta & 0.0734210921061535 \tabularnewline
gamma & FALSE \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=200753&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]0.0734210921061535[/C][/ROW]
[ROW][C]gamma[/C][C]FALSE[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=200753&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=200753&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
beta0.0734210921061535
gammaFALSE







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
39.959.98-0.0300000000000011
49.969.937797367236810.0222026327631859
59.979.949427508781920.0205724912180791
69.959.9609379635545-0.0109379635544968
79.949.94013488632491-0.000134886324907768
89.99.93012498282362-0.0301249828236223
99.99.887913173685030.0120868263149667
109.929.888800601673180.0311993983268248
119.879.91109129557139-0.0410912955713858
129.969.858074327774480.101925672225523
139.949.95555782194293-0.0155578219429309
149.969.934415549665090.0255844503349145
159.969.956293987949610.00370601205038845
169.899.95656608740171-0.0665660874017107
179.829.88167873256744-0.0616787325674437
189.839.807150212662620.0228497873373819
199.839.818827869003320.0111721309966786
209.829.819648139062250.000351860937749748
219.779.80967397307657-0.0396739730765709
229.669.7567610666451-0.0967610666450973
239.699.639656763458660.050343236541341
249.679.67335301886568-0.00335301886568118
259.79.653106836558710.0468931634412879
269.779.686549783830880.0834502161691173
279.799.762676789838510.0273232101614855
289.819.784682889768420.025317110231585
299.779.80654169965059-0.0365416996505914
309.789.763858768154830.0161412318451699
319.779.77504387502484-0.00504387502484072
329.799.764673548212070.0253264517879295
339.779.78653304396151-0.0165330439615126
349.779.765319169818020.00468083018198051
359.89.765662841481940.0343371585180563
369.89.798183913160160.00181608683983825
379.89.79831725223930.00168274776069666
389.89.798440801417630.00155919858236686
399.769.79855527948036-0.0385552794803612
409.789.755724508754450.024275491245545
419.779.77750684183311-0.00750684183311456
429.799.766955681307460.0230443186925395
439.819.788647620352710.0213523796472934
449.829.810215335385480.00978466461452143
459.849.820933736147370.0190662638526309
469.879.842333602061810.0276663979381873
479.999.874364899213080.115635100786923
489.9910.0028549545987-0.0128549545986587
499.9910.0019111297931-0.0119111297930505
5010.0810.00103660163540.0789633983645732
5110.0610.0968341805798-0.036834180579767
5210.0810.07412977481480.00587022518523383
5310.0710.0945607731588-0.0245607731587736
5410.0410.0827574943705-0.0427574943704858
5510.0410.0496181924381-0.00961819243808115
5610.1210.04891201424520.0710879857548097
5710.110.1341313717949-0.0341313717949348
5810.1110.1116254092027-0.00162540920267062
5910.1310.12150606988390.00849393011610999
6010.1610.14212970350930.0178702964907114
6110.1510.1734417601939-0.0234417601938972
6210.2510.16172064055960.0882793594404294
6310.4110.26820220754010.141797792459881
6410.4610.43861315632080.0213868436792364
6510.4610.4901834017404-0.0301834017403984
6610.510.48796730342110.01203269657886
6710.510.5288507571449-0.0288507571449408
6810.4810.5267325030473-0.0467325030472701
6910.510.5033013516367-0.00330135163668643
7010.510.5230589627941-0.023058962794094
7110.5310.52136594856290.00863405143708285
7210.5310.5519998700487-0.0219998700487274

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
3 & 9.95 & 9.98 & -0.0300000000000011 \tabularnewline
4 & 9.96 & 9.93779736723681 & 0.0222026327631859 \tabularnewline
5 & 9.97 & 9.94942750878192 & 0.0205724912180791 \tabularnewline
6 & 9.95 & 9.9609379635545 & -0.0109379635544968 \tabularnewline
7 & 9.94 & 9.94013488632491 & -0.000134886324907768 \tabularnewline
8 & 9.9 & 9.93012498282362 & -0.0301249828236223 \tabularnewline
9 & 9.9 & 9.88791317368503 & 0.0120868263149667 \tabularnewline
10 & 9.92 & 9.88880060167318 & 0.0311993983268248 \tabularnewline
11 & 9.87 & 9.91109129557139 & -0.0410912955713858 \tabularnewline
12 & 9.96 & 9.85807432777448 & 0.101925672225523 \tabularnewline
13 & 9.94 & 9.95555782194293 & -0.0155578219429309 \tabularnewline
14 & 9.96 & 9.93441554966509 & 0.0255844503349145 \tabularnewline
15 & 9.96 & 9.95629398794961 & 0.00370601205038845 \tabularnewline
16 & 9.89 & 9.95656608740171 & -0.0665660874017107 \tabularnewline
17 & 9.82 & 9.88167873256744 & -0.0616787325674437 \tabularnewline
18 & 9.83 & 9.80715021266262 & 0.0228497873373819 \tabularnewline
19 & 9.83 & 9.81882786900332 & 0.0111721309966786 \tabularnewline
20 & 9.82 & 9.81964813906225 & 0.000351860937749748 \tabularnewline
21 & 9.77 & 9.80967397307657 & -0.0396739730765709 \tabularnewline
22 & 9.66 & 9.7567610666451 & -0.0967610666450973 \tabularnewline
23 & 9.69 & 9.63965676345866 & 0.050343236541341 \tabularnewline
24 & 9.67 & 9.67335301886568 & -0.00335301886568118 \tabularnewline
25 & 9.7 & 9.65310683655871 & 0.0468931634412879 \tabularnewline
26 & 9.77 & 9.68654978383088 & 0.0834502161691173 \tabularnewline
27 & 9.79 & 9.76267678983851 & 0.0273232101614855 \tabularnewline
28 & 9.81 & 9.78468288976842 & 0.025317110231585 \tabularnewline
29 & 9.77 & 9.80654169965059 & -0.0365416996505914 \tabularnewline
30 & 9.78 & 9.76385876815483 & 0.0161412318451699 \tabularnewline
31 & 9.77 & 9.77504387502484 & -0.00504387502484072 \tabularnewline
32 & 9.79 & 9.76467354821207 & 0.0253264517879295 \tabularnewline
33 & 9.77 & 9.78653304396151 & -0.0165330439615126 \tabularnewline
34 & 9.77 & 9.76531916981802 & 0.00468083018198051 \tabularnewline
35 & 9.8 & 9.76566284148194 & 0.0343371585180563 \tabularnewline
36 & 9.8 & 9.79818391316016 & 0.00181608683983825 \tabularnewline
37 & 9.8 & 9.7983172522393 & 0.00168274776069666 \tabularnewline
38 & 9.8 & 9.79844080141763 & 0.00155919858236686 \tabularnewline
39 & 9.76 & 9.79855527948036 & -0.0385552794803612 \tabularnewline
40 & 9.78 & 9.75572450875445 & 0.024275491245545 \tabularnewline
41 & 9.77 & 9.77750684183311 & -0.00750684183311456 \tabularnewline
42 & 9.79 & 9.76695568130746 & 0.0230443186925395 \tabularnewline
43 & 9.81 & 9.78864762035271 & 0.0213523796472934 \tabularnewline
44 & 9.82 & 9.81021533538548 & 0.00978466461452143 \tabularnewline
45 & 9.84 & 9.82093373614737 & 0.0190662638526309 \tabularnewline
46 & 9.87 & 9.84233360206181 & 0.0276663979381873 \tabularnewline
47 & 9.99 & 9.87436489921308 & 0.115635100786923 \tabularnewline
48 & 9.99 & 10.0028549545987 & -0.0128549545986587 \tabularnewline
49 & 9.99 & 10.0019111297931 & -0.0119111297930505 \tabularnewline
50 & 10.08 & 10.0010366016354 & 0.0789633983645732 \tabularnewline
51 & 10.06 & 10.0968341805798 & -0.036834180579767 \tabularnewline
52 & 10.08 & 10.0741297748148 & 0.00587022518523383 \tabularnewline
53 & 10.07 & 10.0945607731588 & -0.0245607731587736 \tabularnewline
54 & 10.04 & 10.0827574943705 & -0.0427574943704858 \tabularnewline
55 & 10.04 & 10.0496181924381 & -0.00961819243808115 \tabularnewline
56 & 10.12 & 10.0489120142452 & 0.0710879857548097 \tabularnewline
57 & 10.1 & 10.1341313717949 & -0.0341313717949348 \tabularnewline
58 & 10.11 & 10.1116254092027 & -0.00162540920267062 \tabularnewline
59 & 10.13 & 10.1215060698839 & 0.00849393011610999 \tabularnewline
60 & 10.16 & 10.1421297035093 & 0.0178702964907114 \tabularnewline
61 & 10.15 & 10.1734417601939 & -0.0234417601938972 \tabularnewline
62 & 10.25 & 10.1617206405596 & 0.0882793594404294 \tabularnewline
63 & 10.41 & 10.2682022075401 & 0.141797792459881 \tabularnewline
64 & 10.46 & 10.4386131563208 & 0.0213868436792364 \tabularnewline
65 & 10.46 & 10.4901834017404 & -0.0301834017403984 \tabularnewline
66 & 10.5 & 10.4879673034211 & 0.01203269657886 \tabularnewline
67 & 10.5 & 10.5288507571449 & -0.0288507571449408 \tabularnewline
68 & 10.48 & 10.5267325030473 & -0.0467325030472701 \tabularnewline
69 & 10.5 & 10.5033013516367 & -0.00330135163668643 \tabularnewline
70 & 10.5 & 10.5230589627941 & -0.023058962794094 \tabularnewline
71 & 10.53 & 10.5213659485629 & 0.00863405143708285 \tabularnewline
72 & 10.53 & 10.5519998700487 & -0.0219998700487274 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=200753&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]9.95[/C][C]9.98[/C][C]-0.0300000000000011[/C][/ROW]
[ROW][C]4[/C][C]9.96[/C][C]9.93779736723681[/C][C]0.0222026327631859[/C][/ROW]
[ROW][C]5[/C][C]9.97[/C][C]9.94942750878192[/C][C]0.0205724912180791[/C][/ROW]
[ROW][C]6[/C][C]9.95[/C][C]9.9609379635545[/C][C]-0.0109379635544968[/C][/ROW]
[ROW][C]7[/C][C]9.94[/C][C]9.94013488632491[/C][C]-0.000134886324907768[/C][/ROW]
[ROW][C]8[/C][C]9.9[/C][C]9.93012498282362[/C][C]-0.0301249828236223[/C][/ROW]
[ROW][C]9[/C][C]9.9[/C][C]9.88791317368503[/C][C]0.0120868263149667[/C][/ROW]
[ROW][C]10[/C][C]9.92[/C][C]9.88880060167318[/C][C]0.0311993983268248[/C][/ROW]
[ROW][C]11[/C][C]9.87[/C][C]9.91109129557139[/C][C]-0.0410912955713858[/C][/ROW]
[ROW][C]12[/C][C]9.96[/C][C]9.85807432777448[/C][C]0.101925672225523[/C][/ROW]
[ROW][C]13[/C][C]9.94[/C][C]9.95555782194293[/C][C]-0.0155578219429309[/C][/ROW]
[ROW][C]14[/C][C]9.96[/C][C]9.93441554966509[/C][C]0.0255844503349145[/C][/ROW]
[ROW][C]15[/C][C]9.96[/C][C]9.95629398794961[/C][C]0.00370601205038845[/C][/ROW]
[ROW][C]16[/C][C]9.89[/C][C]9.95656608740171[/C][C]-0.0665660874017107[/C][/ROW]
[ROW][C]17[/C][C]9.82[/C][C]9.88167873256744[/C][C]-0.0616787325674437[/C][/ROW]
[ROW][C]18[/C][C]9.83[/C][C]9.80715021266262[/C][C]0.0228497873373819[/C][/ROW]
[ROW][C]19[/C][C]9.83[/C][C]9.81882786900332[/C][C]0.0111721309966786[/C][/ROW]
[ROW][C]20[/C][C]9.82[/C][C]9.81964813906225[/C][C]0.000351860937749748[/C][/ROW]
[ROW][C]21[/C][C]9.77[/C][C]9.80967397307657[/C][C]-0.0396739730765709[/C][/ROW]
[ROW][C]22[/C][C]9.66[/C][C]9.7567610666451[/C][C]-0.0967610666450973[/C][/ROW]
[ROW][C]23[/C][C]9.69[/C][C]9.63965676345866[/C][C]0.050343236541341[/C][/ROW]
[ROW][C]24[/C][C]9.67[/C][C]9.67335301886568[/C][C]-0.00335301886568118[/C][/ROW]
[ROW][C]25[/C][C]9.7[/C][C]9.65310683655871[/C][C]0.0468931634412879[/C][/ROW]
[ROW][C]26[/C][C]9.77[/C][C]9.68654978383088[/C][C]0.0834502161691173[/C][/ROW]
[ROW][C]27[/C][C]9.79[/C][C]9.76267678983851[/C][C]0.0273232101614855[/C][/ROW]
[ROW][C]28[/C][C]9.81[/C][C]9.78468288976842[/C][C]0.025317110231585[/C][/ROW]
[ROW][C]29[/C][C]9.77[/C][C]9.80654169965059[/C][C]-0.0365416996505914[/C][/ROW]
[ROW][C]30[/C][C]9.78[/C][C]9.76385876815483[/C][C]0.0161412318451699[/C][/ROW]
[ROW][C]31[/C][C]9.77[/C][C]9.77504387502484[/C][C]-0.00504387502484072[/C][/ROW]
[ROW][C]32[/C][C]9.79[/C][C]9.76467354821207[/C][C]0.0253264517879295[/C][/ROW]
[ROW][C]33[/C][C]9.77[/C][C]9.78653304396151[/C][C]-0.0165330439615126[/C][/ROW]
[ROW][C]34[/C][C]9.77[/C][C]9.76531916981802[/C][C]0.00468083018198051[/C][/ROW]
[ROW][C]35[/C][C]9.8[/C][C]9.76566284148194[/C][C]0.0343371585180563[/C][/ROW]
[ROW][C]36[/C][C]9.8[/C][C]9.79818391316016[/C][C]0.00181608683983825[/C][/ROW]
[ROW][C]37[/C][C]9.8[/C][C]9.7983172522393[/C][C]0.00168274776069666[/C][/ROW]
[ROW][C]38[/C][C]9.8[/C][C]9.79844080141763[/C][C]0.00155919858236686[/C][/ROW]
[ROW][C]39[/C][C]9.76[/C][C]9.79855527948036[/C][C]-0.0385552794803612[/C][/ROW]
[ROW][C]40[/C][C]9.78[/C][C]9.75572450875445[/C][C]0.024275491245545[/C][/ROW]
[ROW][C]41[/C][C]9.77[/C][C]9.77750684183311[/C][C]-0.00750684183311456[/C][/ROW]
[ROW][C]42[/C][C]9.79[/C][C]9.76695568130746[/C][C]0.0230443186925395[/C][/ROW]
[ROW][C]43[/C][C]9.81[/C][C]9.78864762035271[/C][C]0.0213523796472934[/C][/ROW]
[ROW][C]44[/C][C]9.82[/C][C]9.81021533538548[/C][C]0.00978466461452143[/C][/ROW]
[ROW][C]45[/C][C]9.84[/C][C]9.82093373614737[/C][C]0.0190662638526309[/C][/ROW]
[ROW][C]46[/C][C]9.87[/C][C]9.84233360206181[/C][C]0.0276663979381873[/C][/ROW]
[ROW][C]47[/C][C]9.99[/C][C]9.87436489921308[/C][C]0.115635100786923[/C][/ROW]
[ROW][C]48[/C][C]9.99[/C][C]10.0028549545987[/C][C]-0.0128549545986587[/C][/ROW]
[ROW][C]49[/C][C]9.99[/C][C]10.0019111297931[/C][C]-0.0119111297930505[/C][/ROW]
[ROW][C]50[/C][C]10.08[/C][C]10.0010366016354[/C][C]0.0789633983645732[/C][/ROW]
[ROW][C]51[/C][C]10.06[/C][C]10.0968341805798[/C][C]-0.036834180579767[/C][/ROW]
[ROW][C]52[/C][C]10.08[/C][C]10.0741297748148[/C][C]0.00587022518523383[/C][/ROW]
[ROW][C]53[/C][C]10.07[/C][C]10.0945607731588[/C][C]-0.0245607731587736[/C][/ROW]
[ROW][C]54[/C][C]10.04[/C][C]10.0827574943705[/C][C]-0.0427574943704858[/C][/ROW]
[ROW][C]55[/C][C]10.04[/C][C]10.0496181924381[/C][C]-0.00961819243808115[/C][/ROW]
[ROW][C]56[/C][C]10.12[/C][C]10.0489120142452[/C][C]0.0710879857548097[/C][/ROW]
[ROW][C]57[/C][C]10.1[/C][C]10.1341313717949[/C][C]-0.0341313717949348[/C][/ROW]
[ROW][C]58[/C][C]10.11[/C][C]10.1116254092027[/C][C]-0.00162540920267062[/C][/ROW]
[ROW][C]59[/C][C]10.13[/C][C]10.1215060698839[/C][C]0.00849393011610999[/C][/ROW]
[ROW][C]60[/C][C]10.16[/C][C]10.1421297035093[/C][C]0.0178702964907114[/C][/ROW]
[ROW][C]61[/C][C]10.15[/C][C]10.1734417601939[/C][C]-0.0234417601938972[/C][/ROW]
[ROW][C]62[/C][C]10.25[/C][C]10.1617206405596[/C][C]0.0882793594404294[/C][/ROW]
[ROW][C]63[/C][C]10.41[/C][C]10.2682022075401[/C][C]0.141797792459881[/C][/ROW]
[ROW][C]64[/C][C]10.46[/C][C]10.4386131563208[/C][C]0.0213868436792364[/C][/ROW]
[ROW][C]65[/C][C]10.46[/C][C]10.4901834017404[/C][C]-0.0301834017403984[/C][/ROW]
[ROW][C]66[/C][C]10.5[/C][C]10.4879673034211[/C][C]0.01203269657886[/C][/ROW]
[ROW][C]67[/C][C]10.5[/C][C]10.5288507571449[/C][C]-0.0288507571449408[/C][/ROW]
[ROW][C]68[/C][C]10.48[/C][C]10.5267325030473[/C][C]-0.0467325030472701[/C][/ROW]
[ROW][C]69[/C][C]10.5[/C][C]10.5033013516367[/C][C]-0.00330135163668643[/C][/ROW]
[ROW][C]70[/C][C]10.5[/C][C]10.5230589627941[/C][C]-0.023058962794094[/C][/ROW]
[ROW][C]71[/C][C]10.53[/C][C]10.5213659485629[/C][C]0.00863405143708285[/C][/ROW]
[ROW][C]72[/C][C]10.53[/C][C]10.5519998700487[/C][C]-0.0219998700487274[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=200753&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=200753&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
39.959.98-0.0300000000000011
49.969.937797367236810.0222026327631859
59.979.949427508781920.0205724912180791
69.959.9609379635545-0.0109379635544968
79.949.94013488632491-0.000134886324907768
89.99.93012498282362-0.0301249828236223
99.99.887913173685030.0120868263149667
109.929.888800601673180.0311993983268248
119.879.91109129557139-0.0410912955713858
129.969.858074327774480.101925672225523
139.949.95555782194293-0.0155578219429309
149.969.934415549665090.0255844503349145
159.969.956293987949610.00370601205038845
169.899.95656608740171-0.0665660874017107
179.829.88167873256744-0.0616787325674437
189.839.807150212662620.0228497873373819
199.839.818827869003320.0111721309966786
209.829.819648139062250.000351860937749748
219.779.80967397307657-0.0396739730765709
229.669.7567610666451-0.0967610666450973
239.699.639656763458660.050343236541341
249.679.67335301886568-0.00335301886568118
259.79.653106836558710.0468931634412879
269.779.686549783830880.0834502161691173
279.799.762676789838510.0273232101614855
289.819.784682889768420.025317110231585
299.779.80654169965059-0.0365416996505914
309.789.763858768154830.0161412318451699
319.779.77504387502484-0.00504387502484072
329.799.764673548212070.0253264517879295
339.779.78653304396151-0.0165330439615126
349.779.765319169818020.00468083018198051
359.89.765662841481940.0343371585180563
369.89.798183913160160.00181608683983825
379.89.79831725223930.00168274776069666
389.89.798440801417630.00155919858236686
399.769.79855527948036-0.0385552794803612
409.789.755724508754450.024275491245545
419.779.77750684183311-0.00750684183311456
429.799.766955681307460.0230443186925395
439.819.788647620352710.0213523796472934
449.829.810215335385480.00978466461452143
459.849.820933736147370.0190662638526309
469.879.842333602061810.0276663979381873
479.999.874364899213080.115635100786923
489.9910.0028549545987-0.0128549545986587
499.9910.0019111297931-0.0119111297930505
5010.0810.00103660163540.0789633983645732
5110.0610.0968341805798-0.036834180579767
5210.0810.07412977481480.00587022518523383
5310.0710.0945607731588-0.0245607731587736
5410.0410.0827574943705-0.0427574943704858
5510.0410.0496181924381-0.00961819243808115
5610.1210.04891201424520.0710879857548097
5710.110.1341313717949-0.0341313717949348
5810.1110.1116254092027-0.00162540920267062
5910.1310.12150606988390.00849393011610999
6010.1610.14212970350930.0178702964907114
6110.1510.1734417601939-0.0234417601938972
6210.2510.16172064055960.0882793594404294
6310.4110.26820220754010.141797792459881
6410.4610.43861315632080.0213868436792364
6510.4610.4901834017404-0.0301834017403984
6610.510.48796730342110.01203269657886
6710.510.5288507571449-0.0288507571449408
6810.4810.5267325030473-0.0467325030472701
6910.510.5033013516367-0.00330135163668643
7010.510.5230589627941-0.023058962794094
7110.5310.52136594856290.00863405143708285
7210.5310.5519998700487-0.0219998700487274







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
7310.550384615563610.468638219647410.6321310114797
7410.570769231127110.450843260722710.6906952015315
7510.591153846690710.438932490647110.7433752027342
7610.611538462254210.429544430320910.7935324941876
7710.631923077817810.42143378239510.8424123732405
7810.652307693381310.41399039531110.8906249914517
7910.672692308944910.406868971529610.9385156463602
8010.693076924508410.39985597404310.9862978749739
8110.71346154007210.392811235798611.0341118443454
8210.733846155635610.385638792028611.0820535192425
8310.754230771199110.378270902397211.130190640001
8410.774615386762710.370658671125811.1785721023995

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
73 & 10.5503846155636 & 10.4686382196474 & 10.6321310114797 \tabularnewline
74 & 10.5707692311271 & 10.4508432607227 & 10.6906952015315 \tabularnewline
75 & 10.5911538466907 & 10.4389324906471 & 10.7433752027342 \tabularnewline
76 & 10.6115384622542 & 10.4295444303209 & 10.7935324941876 \tabularnewline
77 & 10.6319230778178 & 10.421433782395 & 10.8424123732405 \tabularnewline
78 & 10.6523076933813 & 10.413990395311 & 10.8906249914517 \tabularnewline
79 & 10.6726923089449 & 10.4068689715296 & 10.9385156463602 \tabularnewline
80 & 10.6930769245084 & 10.399855974043 & 10.9862978749739 \tabularnewline
81 & 10.713461540072 & 10.3928112357986 & 11.0341118443454 \tabularnewline
82 & 10.7338461556356 & 10.3856387920286 & 11.0820535192425 \tabularnewline
83 & 10.7542307711991 & 10.3782709023972 & 11.130190640001 \tabularnewline
84 & 10.7746153867627 & 10.3706586711258 & 11.1785721023995 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=200753&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]10.5503846155636[/C][C]10.4686382196474[/C][C]10.6321310114797[/C][/ROW]
[ROW][C]74[/C][C]10.5707692311271[/C][C]10.4508432607227[/C][C]10.6906952015315[/C][/ROW]
[ROW][C]75[/C][C]10.5911538466907[/C][C]10.4389324906471[/C][C]10.7433752027342[/C][/ROW]
[ROW][C]76[/C][C]10.6115384622542[/C][C]10.4295444303209[/C][C]10.7935324941876[/C][/ROW]
[ROW][C]77[/C][C]10.6319230778178[/C][C]10.421433782395[/C][C]10.8424123732405[/C][/ROW]
[ROW][C]78[/C][C]10.6523076933813[/C][C]10.413990395311[/C][C]10.8906249914517[/C][/ROW]
[ROW][C]79[/C][C]10.6726923089449[/C][C]10.4068689715296[/C][C]10.9385156463602[/C][/ROW]
[ROW][C]80[/C][C]10.6930769245084[/C][C]10.399855974043[/C][C]10.9862978749739[/C][/ROW]
[ROW][C]81[/C][C]10.713461540072[/C][C]10.3928112357986[/C][C]11.0341118443454[/C][/ROW]
[ROW][C]82[/C][C]10.7338461556356[/C][C]10.3856387920286[/C][C]11.0820535192425[/C][/ROW]
[ROW][C]83[/C][C]10.7542307711991[/C][C]10.3782709023972[/C][C]11.130190640001[/C][/ROW]
[ROW][C]84[/C][C]10.7746153867627[/C][C]10.3706586711258[/C][C]11.1785721023995[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=200753&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=200753&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
7310.550384615563610.468638219647410.6321310114797
7410.570769231127110.450843260722710.6906952015315
7510.591153846690710.438932490647110.7433752027342
7610.611538462254210.429544430320910.7935324941876
7710.631923077817810.42143378239510.8424123732405
7810.652307693381310.41399039531110.8906249914517
7910.672692308944910.406868971529610.9385156463602
8010.693076924508410.39985597404310.9862978749739
8110.71346154007210.392811235798611.0341118443454
8210.733846155635610.385638792028611.0820535192425
8310.754230771199110.378270902397211.130190640001
8410.774615386762710.370658671125811.1785721023995



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')