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Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationThu, 18 Dec 2014 11:57:24 +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/2014/Dec/18/t1418903870qgakr370vr3k7ac.htm/, Retrieved Fri, 17 May 2024 00:15:00 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=270834, Retrieved Fri, 17 May 2024 00:15:00 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact71
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [] [2014-12-18 11:57:24] [f1a1c306ccf782003dcf1365fad9efec] [Current]
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Dataseries X:
1850,07
1841,55
1845
1844,01
1842,67
1842,67
1842,67
1842,9
1840,37
1841,59
1844,33
1844,33
1844,33
1845,39
1861,84
1862,85
1869,46
1870,8
1870,8
1871,52
1875,52
1880,38
1885,05
1886,42
1886,42
1891,65
1903,11
1905,29
1904,26
1905,37
1905,37
1905,12
1908,62
1915,08
1916,36
1916,68
1916,24
1922,05
1922,63
1922,47
1920,64
1920,66
1920,66
1921,19
1921,44
1921,73
1921,81
1921,81
1921,81
1921,48
1917,07
1912,64
1901,15
1898,12
1900,02
1900,02
1900,82
1901,9
1902,19
1901,84
1903,73
1889,7
1891,27
1894,48
1894,27
1893,98
1893,98
1895,62
1901,72
1905,4
1898,14
1898,09




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 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 & 2 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ jenkins.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=270834&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' @ jenkins.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=270834&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=270834&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' @ jenkins.wessa.net







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha1
beta0.27127582424833
gammaFALSE

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 1 \tabularnewline
beta & 0.27127582424833 \tabularnewline
gamma & FALSE \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=270834&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]0.27127582424833[/C][/ROW]
[ROW][C]gamma[/C][C]FALSE[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=270834&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=270834&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
beta0.27127582424833
gammaFALSE







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
318451833.0311.97
41844.011839.727171616254.28282838374753
51842.671839.898999416172.77100058383235
61842.671839.310704883543.35929511646054
71842.671840.222000435152.4479995648494
81842.91840.886083534862.01391646513525
91840.371841.66241038391-1.29241038391183
101841.591838.781810691752.80818930825126
111844.331840.763604560993.56639543900997
121844.331844.4710814233-0.141081423302921
131844.331844.43280944391-0.102809443910246
141845.391844.404919727270.985080272727146
151861.841845.7321481902116.107851809792
161862.851866.55181896678-3.70181896677923
171869.461866.557604975352.90239502465215
181870.81873.95495457795-3.15495457795487
191870.81874.43909167435-3.63909167435395
201871.521873.45189408088-1.93189408087846
211875.521873.647817921731.87218207827232
221880.381878.155695658152.22430434184616
231885.051883.619095651871.43090434813234
241886.421888.67726540833-2.25726540832738
251886.421889.43492387414-3.01492387413623
261891.651888.617047915133.03295208486611
271903.111894.669814491868.44018550813803
281905.291908.41943277239-3.1294327723906
291904.261909.75049331763-5.49049331763058
301905.371907.23105521736-1.86105521736067
311905.371907.8361959293-2.46619592929937
321905.121907.16717659582-2.0471765958207
331908.621906.361827077412.25817292259239
341915.081910.474414798284.60558520172094
351916.361918.18379872002-1.82379872002184
361916.681918.96904621898-2.28904621898482
371916.241918.66808331919-2.42808331918741
381922.051917.569403015434.48059698456882
391922.631924.59488065554-1.96488065554445
401922.471924.64185603616-2.17185603616235
411920.641923.8926839998-3.25268399980359
421920.661921.18030946674-0.520309466737444
431920.661921.05916208728-0.399162087284139
441921.191920.950879063050.239120936952531
451921.441921.54574679231-0.105746792314221
461921.731921.76706024407-0.0370602440675611
471921.811922.04700669581-0.23700669581126
481921.811922.06271250905-0.252712509052799
491921.811921.99415771486-0.184157714861612
501921.481921.94420017897-0.464200178970714
511917.071921.4882738928-4.41827389280434
521912.641915.87970300078-3.23970300077872
531901.151910.57084989892-9.42084989892282
541898.121896.525201077471.59479892252693
551900.021893.927831469696.09216853030853
561900.021897.480489509212.5395104907891
571900.821898.169397310792.65060268921297
581901.91899.688441740062.21155825994219
591902.191901.36838402990.821615970103039
601901.841901.8812685794-0.0412685794024128
611903.731901.520073411512.20992658849082
621889.71904.00957306833-14.3095730683303
631891.271886.097731839585.17226816042262
641894.481889.070843148035.40915685197069
651894.271893.748216631540.52178336846373
661893.981893.67976384490.300236155104812
671893.981893.471210655340.50878934465959
681895.621893.609232904182.01076709581821
691901.721895.794705405475.92529459452885
701905.41903.502094580521.89790541948378
711898.141907.69695043753-9.55695043753212
721898.091897.844380830290.245619169709698

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
3 & 1845 & 1833.03 & 11.97 \tabularnewline
4 & 1844.01 & 1839.72717161625 & 4.28282838374753 \tabularnewline
5 & 1842.67 & 1839.89899941617 & 2.77100058383235 \tabularnewline
6 & 1842.67 & 1839.31070488354 & 3.35929511646054 \tabularnewline
7 & 1842.67 & 1840.22200043515 & 2.4479995648494 \tabularnewline
8 & 1842.9 & 1840.88608353486 & 2.01391646513525 \tabularnewline
9 & 1840.37 & 1841.66241038391 & -1.29241038391183 \tabularnewline
10 & 1841.59 & 1838.78181069175 & 2.80818930825126 \tabularnewline
11 & 1844.33 & 1840.76360456099 & 3.56639543900997 \tabularnewline
12 & 1844.33 & 1844.4710814233 & -0.141081423302921 \tabularnewline
13 & 1844.33 & 1844.43280944391 & -0.102809443910246 \tabularnewline
14 & 1845.39 & 1844.40491972727 & 0.985080272727146 \tabularnewline
15 & 1861.84 & 1845.73214819021 & 16.107851809792 \tabularnewline
16 & 1862.85 & 1866.55181896678 & -3.70181896677923 \tabularnewline
17 & 1869.46 & 1866.55760497535 & 2.90239502465215 \tabularnewline
18 & 1870.8 & 1873.95495457795 & -3.15495457795487 \tabularnewline
19 & 1870.8 & 1874.43909167435 & -3.63909167435395 \tabularnewline
20 & 1871.52 & 1873.45189408088 & -1.93189408087846 \tabularnewline
21 & 1875.52 & 1873.64781792173 & 1.87218207827232 \tabularnewline
22 & 1880.38 & 1878.15569565815 & 2.22430434184616 \tabularnewline
23 & 1885.05 & 1883.61909565187 & 1.43090434813234 \tabularnewline
24 & 1886.42 & 1888.67726540833 & -2.25726540832738 \tabularnewline
25 & 1886.42 & 1889.43492387414 & -3.01492387413623 \tabularnewline
26 & 1891.65 & 1888.61704791513 & 3.03295208486611 \tabularnewline
27 & 1903.11 & 1894.66981449186 & 8.44018550813803 \tabularnewline
28 & 1905.29 & 1908.41943277239 & -3.1294327723906 \tabularnewline
29 & 1904.26 & 1909.75049331763 & -5.49049331763058 \tabularnewline
30 & 1905.37 & 1907.23105521736 & -1.86105521736067 \tabularnewline
31 & 1905.37 & 1907.8361959293 & -2.46619592929937 \tabularnewline
32 & 1905.12 & 1907.16717659582 & -2.0471765958207 \tabularnewline
33 & 1908.62 & 1906.36182707741 & 2.25817292259239 \tabularnewline
34 & 1915.08 & 1910.47441479828 & 4.60558520172094 \tabularnewline
35 & 1916.36 & 1918.18379872002 & -1.82379872002184 \tabularnewline
36 & 1916.68 & 1918.96904621898 & -2.28904621898482 \tabularnewline
37 & 1916.24 & 1918.66808331919 & -2.42808331918741 \tabularnewline
38 & 1922.05 & 1917.56940301543 & 4.48059698456882 \tabularnewline
39 & 1922.63 & 1924.59488065554 & -1.96488065554445 \tabularnewline
40 & 1922.47 & 1924.64185603616 & -2.17185603616235 \tabularnewline
41 & 1920.64 & 1923.8926839998 & -3.25268399980359 \tabularnewline
42 & 1920.66 & 1921.18030946674 & -0.520309466737444 \tabularnewline
43 & 1920.66 & 1921.05916208728 & -0.399162087284139 \tabularnewline
44 & 1921.19 & 1920.95087906305 & 0.239120936952531 \tabularnewline
45 & 1921.44 & 1921.54574679231 & -0.105746792314221 \tabularnewline
46 & 1921.73 & 1921.76706024407 & -0.0370602440675611 \tabularnewline
47 & 1921.81 & 1922.04700669581 & -0.23700669581126 \tabularnewline
48 & 1921.81 & 1922.06271250905 & -0.252712509052799 \tabularnewline
49 & 1921.81 & 1921.99415771486 & -0.184157714861612 \tabularnewline
50 & 1921.48 & 1921.94420017897 & -0.464200178970714 \tabularnewline
51 & 1917.07 & 1921.4882738928 & -4.41827389280434 \tabularnewline
52 & 1912.64 & 1915.87970300078 & -3.23970300077872 \tabularnewline
53 & 1901.15 & 1910.57084989892 & -9.42084989892282 \tabularnewline
54 & 1898.12 & 1896.52520107747 & 1.59479892252693 \tabularnewline
55 & 1900.02 & 1893.92783146969 & 6.09216853030853 \tabularnewline
56 & 1900.02 & 1897.48048950921 & 2.5395104907891 \tabularnewline
57 & 1900.82 & 1898.16939731079 & 2.65060268921297 \tabularnewline
58 & 1901.9 & 1899.68844174006 & 2.21155825994219 \tabularnewline
59 & 1902.19 & 1901.3683840299 & 0.821615970103039 \tabularnewline
60 & 1901.84 & 1901.8812685794 & -0.0412685794024128 \tabularnewline
61 & 1903.73 & 1901.52007341151 & 2.20992658849082 \tabularnewline
62 & 1889.7 & 1904.00957306833 & -14.3095730683303 \tabularnewline
63 & 1891.27 & 1886.09773183958 & 5.17226816042262 \tabularnewline
64 & 1894.48 & 1889.07084314803 & 5.40915685197069 \tabularnewline
65 & 1894.27 & 1893.74821663154 & 0.52178336846373 \tabularnewline
66 & 1893.98 & 1893.6797638449 & 0.300236155104812 \tabularnewline
67 & 1893.98 & 1893.47121065534 & 0.50878934465959 \tabularnewline
68 & 1895.62 & 1893.60923290418 & 2.01076709581821 \tabularnewline
69 & 1901.72 & 1895.79470540547 & 5.92529459452885 \tabularnewline
70 & 1905.4 & 1903.50209458052 & 1.89790541948378 \tabularnewline
71 & 1898.14 & 1907.69695043753 & -9.55695043753212 \tabularnewline
72 & 1898.09 & 1897.84438083029 & 0.245619169709698 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=270834&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]1845[/C][C]1833.03[/C][C]11.97[/C][/ROW]
[ROW][C]4[/C][C]1844.01[/C][C]1839.72717161625[/C][C]4.28282838374753[/C][/ROW]
[ROW][C]5[/C][C]1842.67[/C][C]1839.89899941617[/C][C]2.77100058383235[/C][/ROW]
[ROW][C]6[/C][C]1842.67[/C][C]1839.31070488354[/C][C]3.35929511646054[/C][/ROW]
[ROW][C]7[/C][C]1842.67[/C][C]1840.22200043515[/C][C]2.4479995648494[/C][/ROW]
[ROW][C]8[/C][C]1842.9[/C][C]1840.88608353486[/C][C]2.01391646513525[/C][/ROW]
[ROW][C]9[/C][C]1840.37[/C][C]1841.66241038391[/C][C]-1.29241038391183[/C][/ROW]
[ROW][C]10[/C][C]1841.59[/C][C]1838.78181069175[/C][C]2.80818930825126[/C][/ROW]
[ROW][C]11[/C][C]1844.33[/C][C]1840.76360456099[/C][C]3.56639543900997[/C][/ROW]
[ROW][C]12[/C][C]1844.33[/C][C]1844.4710814233[/C][C]-0.141081423302921[/C][/ROW]
[ROW][C]13[/C][C]1844.33[/C][C]1844.43280944391[/C][C]-0.102809443910246[/C][/ROW]
[ROW][C]14[/C][C]1845.39[/C][C]1844.40491972727[/C][C]0.985080272727146[/C][/ROW]
[ROW][C]15[/C][C]1861.84[/C][C]1845.73214819021[/C][C]16.107851809792[/C][/ROW]
[ROW][C]16[/C][C]1862.85[/C][C]1866.55181896678[/C][C]-3.70181896677923[/C][/ROW]
[ROW][C]17[/C][C]1869.46[/C][C]1866.55760497535[/C][C]2.90239502465215[/C][/ROW]
[ROW][C]18[/C][C]1870.8[/C][C]1873.95495457795[/C][C]-3.15495457795487[/C][/ROW]
[ROW][C]19[/C][C]1870.8[/C][C]1874.43909167435[/C][C]-3.63909167435395[/C][/ROW]
[ROW][C]20[/C][C]1871.52[/C][C]1873.45189408088[/C][C]-1.93189408087846[/C][/ROW]
[ROW][C]21[/C][C]1875.52[/C][C]1873.64781792173[/C][C]1.87218207827232[/C][/ROW]
[ROW][C]22[/C][C]1880.38[/C][C]1878.15569565815[/C][C]2.22430434184616[/C][/ROW]
[ROW][C]23[/C][C]1885.05[/C][C]1883.61909565187[/C][C]1.43090434813234[/C][/ROW]
[ROW][C]24[/C][C]1886.42[/C][C]1888.67726540833[/C][C]-2.25726540832738[/C][/ROW]
[ROW][C]25[/C][C]1886.42[/C][C]1889.43492387414[/C][C]-3.01492387413623[/C][/ROW]
[ROW][C]26[/C][C]1891.65[/C][C]1888.61704791513[/C][C]3.03295208486611[/C][/ROW]
[ROW][C]27[/C][C]1903.11[/C][C]1894.66981449186[/C][C]8.44018550813803[/C][/ROW]
[ROW][C]28[/C][C]1905.29[/C][C]1908.41943277239[/C][C]-3.1294327723906[/C][/ROW]
[ROW][C]29[/C][C]1904.26[/C][C]1909.75049331763[/C][C]-5.49049331763058[/C][/ROW]
[ROW][C]30[/C][C]1905.37[/C][C]1907.23105521736[/C][C]-1.86105521736067[/C][/ROW]
[ROW][C]31[/C][C]1905.37[/C][C]1907.8361959293[/C][C]-2.46619592929937[/C][/ROW]
[ROW][C]32[/C][C]1905.12[/C][C]1907.16717659582[/C][C]-2.0471765958207[/C][/ROW]
[ROW][C]33[/C][C]1908.62[/C][C]1906.36182707741[/C][C]2.25817292259239[/C][/ROW]
[ROW][C]34[/C][C]1915.08[/C][C]1910.47441479828[/C][C]4.60558520172094[/C][/ROW]
[ROW][C]35[/C][C]1916.36[/C][C]1918.18379872002[/C][C]-1.82379872002184[/C][/ROW]
[ROW][C]36[/C][C]1916.68[/C][C]1918.96904621898[/C][C]-2.28904621898482[/C][/ROW]
[ROW][C]37[/C][C]1916.24[/C][C]1918.66808331919[/C][C]-2.42808331918741[/C][/ROW]
[ROW][C]38[/C][C]1922.05[/C][C]1917.56940301543[/C][C]4.48059698456882[/C][/ROW]
[ROW][C]39[/C][C]1922.63[/C][C]1924.59488065554[/C][C]-1.96488065554445[/C][/ROW]
[ROW][C]40[/C][C]1922.47[/C][C]1924.64185603616[/C][C]-2.17185603616235[/C][/ROW]
[ROW][C]41[/C][C]1920.64[/C][C]1923.8926839998[/C][C]-3.25268399980359[/C][/ROW]
[ROW][C]42[/C][C]1920.66[/C][C]1921.18030946674[/C][C]-0.520309466737444[/C][/ROW]
[ROW][C]43[/C][C]1920.66[/C][C]1921.05916208728[/C][C]-0.399162087284139[/C][/ROW]
[ROW][C]44[/C][C]1921.19[/C][C]1920.95087906305[/C][C]0.239120936952531[/C][/ROW]
[ROW][C]45[/C][C]1921.44[/C][C]1921.54574679231[/C][C]-0.105746792314221[/C][/ROW]
[ROW][C]46[/C][C]1921.73[/C][C]1921.76706024407[/C][C]-0.0370602440675611[/C][/ROW]
[ROW][C]47[/C][C]1921.81[/C][C]1922.04700669581[/C][C]-0.23700669581126[/C][/ROW]
[ROW][C]48[/C][C]1921.81[/C][C]1922.06271250905[/C][C]-0.252712509052799[/C][/ROW]
[ROW][C]49[/C][C]1921.81[/C][C]1921.99415771486[/C][C]-0.184157714861612[/C][/ROW]
[ROW][C]50[/C][C]1921.48[/C][C]1921.94420017897[/C][C]-0.464200178970714[/C][/ROW]
[ROW][C]51[/C][C]1917.07[/C][C]1921.4882738928[/C][C]-4.41827389280434[/C][/ROW]
[ROW][C]52[/C][C]1912.64[/C][C]1915.87970300078[/C][C]-3.23970300077872[/C][/ROW]
[ROW][C]53[/C][C]1901.15[/C][C]1910.57084989892[/C][C]-9.42084989892282[/C][/ROW]
[ROW][C]54[/C][C]1898.12[/C][C]1896.52520107747[/C][C]1.59479892252693[/C][/ROW]
[ROW][C]55[/C][C]1900.02[/C][C]1893.92783146969[/C][C]6.09216853030853[/C][/ROW]
[ROW][C]56[/C][C]1900.02[/C][C]1897.48048950921[/C][C]2.5395104907891[/C][/ROW]
[ROW][C]57[/C][C]1900.82[/C][C]1898.16939731079[/C][C]2.65060268921297[/C][/ROW]
[ROW][C]58[/C][C]1901.9[/C][C]1899.68844174006[/C][C]2.21155825994219[/C][/ROW]
[ROW][C]59[/C][C]1902.19[/C][C]1901.3683840299[/C][C]0.821615970103039[/C][/ROW]
[ROW][C]60[/C][C]1901.84[/C][C]1901.8812685794[/C][C]-0.0412685794024128[/C][/ROW]
[ROW][C]61[/C][C]1903.73[/C][C]1901.52007341151[/C][C]2.20992658849082[/C][/ROW]
[ROW][C]62[/C][C]1889.7[/C][C]1904.00957306833[/C][C]-14.3095730683303[/C][/ROW]
[ROW][C]63[/C][C]1891.27[/C][C]1886.09773183958[/C][C]5.17226816042262[/C][/ROW]
[ROW][C]64[/C][C]1894.48[/C][C]1889.07084314803[/C][C]5.40915685197069[/C][/ROW]
[ROW][C]65[/C][C]1894.27[/C][C]1893.74821663154[/C][C]0.52178336846373[/C][/ROW]
[ROW][C]66[/C][C]1893.98[/C][C]1893.6797638449[/C][C]0.300236155104812[/C][/ROW]
[ROW][C]67[/C][C]1893.98[/C][C]1893.47121065534[/C][C]0.50878934465959[/C][/ROW]
[ROW][C]68[/C][C]1895.62[/C][C]1893.60923290418[/C][C]2.01076709581821[/C][/ROW]
[ROW][C]69[/C][C]1901.72[/C][C]1895.79470540547[/C][C]5.92529459452885[/C][/ROW]
[ROW][C]70[/C][C]1905.4[/C][C]1903.50209458052[/C][C]1.89790541948378[/C][/ROW]
[ROW][C]71[/C][C]1898.14[/C][C]1907.69695043753[/C][C]-9.55695043753212[/C][/ROW]
[ROW][C]72[/C][C]1898.09[/C][C]1897.84438083029[/C][C]0.245619169709698[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=270834&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=270834&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
318451833.0311.97
41844.011839.727171616254.28282838374753
51842.671839.898999416172.77100058383235
61842.671839.310704883543.35929511646054
71842.671840.222000435152.4479995648494
81842.91840.886083534862.01391646513525
91840.371841.66241038391-1.29241038391183
101841.591838.781810691752.80818930825126
111844.331840.763604560993.56639543900997
121844.331844.4710814233-0.141081423302921
131844.331844.43280944391-0.102809443910246
141845.391844.404919727270.985080272727146
151861.841845.7321481902116.107851809792
161862.851866.55181896678-3.70181896677923
171869.461866.557604975352.90239502465215
181870.81873.95495457795-3.15495457795487
191870.81874.43909167435-3.63909167435395
201871.521873.45189408088-1.93189408087846
211875.521873.647817921731.87218207827232
221880.381878.155695658152.22430434184616
231885.051883.619095651871.43090434813234
241886.421888.67726540833-2.25726540832738
251886.421889.43492387414-3.01492387413623
261891.651888.617047915133.03295208486611
271903.111894.669814491868.44018550813803
281905.291908.41943277239-3.1294327723906
291904.261909.75049331763-5.49049331763058
301905.371907.23105521736-1.86105521736067
311905.371907.8361959293-2.46619592929937
321905.121907.16717659582-2.0471765958207
331908.621906.361827077412.25817292259239
341915.081910.474414798284.60558520172094
351916.361918.18379872002-1.82379872002184
361916.681918.96904621898-2.28904621898482
371916.241918.66808331919-2.42808331918741
381922.051917.569403015434.48059698456882
391922.631924.59488065554-1.96488065554445
401922.471924.64185603616-2.17185603616235
411920.641923.8926839998-3.25268399980359
421920.661921.18030946674-0.520309466737444
431920.661921.05916208728-0.399162087284139
441921.191920.950879063050.239120936952531
451921.441921.54574679231-0.105746792314221
461921.731921.76706024407-0.0370602440675611
471921.811922.04700669581-0.23700669581126
481921.811922.06271250905-0.252712509052799
491921.811921.99415771486-0.184157714861612
501921.481921.94420017897-0.464200178970714
511917.071921.4882738928-4.41827389280434
521912.641915.87970300078-3.23970300077872
531901.151910.57084989892-9.42084989892282
541898.121896.525201077471.59479892252693
551900.021893.927831469696.09216853030853
561900.021897.480489509212.5395104907891
571900.821898.169397310792.65060268921297
581901.91899.688441740062.21155825994219
591902.191901.36838402990.821615970103039
601901.841901.8812685794-0.0412685794024128
611903.731901.520073411512.20992658849082
621889.71904.00957306833-14.3095730683303
631891.271886.097731839585.17226816042262
641894.481889.070843148035.40915685197069
651894.271893.748216631540.52178336846373
661893.981893.67976384490.300236155104812
671893.981893.471210655340.50878934465959
681895.621893.609232904182.01076709581821
691901.721895.794705405475.92529459452885
701905.41903.502094580521.89790541948378
711898.141907.69695043753-9.55695043753212
721898.091897.844380830290.245619169709698







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
731897.8610113731889.266860727721906.45516201829
741897.632022746011883.73141984521911.53262564681
751897.403034119011878.194371440151916.61169679788
761897.174045492021872.436058046361921.91203293767
771896.945056865021866.398643348971927.49147038107
781896.716068238031860.066518387581933.36561808848
791896.487079611031853.438768211661939.5353910104
801896.258090984031846.520208803371945.99597316469
811896.029102357041839.317907276041952.74029743804
821895.800113730041831.839688463591959.7605389965
831895.571125103051824.09345938221967.0487908239
841895.342136476051816.086900357171974.59737259493

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
73 & 1897.861011373 & 1889.26686072772 & 1906.45516201829 \tabularnewline
74 & 1897.63202274601 & 1883.7314198452 & 1911.53262564681 \tabularnewline
75 & 1897.40303411901 & 1878.19437144015 & 1916.61169679788 \tabularnewline
76 & 1897.17404549202 & 1872.43605804636 & 1921.91203293767 \tabularnewline
77 & 1896.94505686502 & 1866.39864334897 & 1927.49147038107 \tabularnewline
78 & 1896.71606823803 & 1860.06651838758 & 1933.36561808848 \tabularnewline
79 & 1896.48707961103 & 1853.43876821166 & 1939.5353910104 \tabularnewline
80 & 1896.25809098403 & 1846.52020880337 & 1945.99597316469 \tabularnewline
81 & 1896.02910235704 & 1839.31790727604 & 1952.74029743804 \tabularnewline
82 & 1895.80011373004 & 1831.83968846359 & 1959.7605389965 \tabularnewline
83 & 1895.57112510305 & 1824.0934593822 & 1967.0487908239 \tabularnewline
84 & 1895.34213647605 & 1816.08690035717 & 1974.59737259493 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=270834&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]1897.861011373[/C][C]1889.26686072772[/C][C]1906.45516201829[/C][/ROW]
[ROW][C]74[/C][C]1897.63202274601[/C][C]1883.7314198452[/C][C]1911.53262564681[/C][/ROW]
[ROW][C]75[/C][C]1897.40303411901[/C][C]1878.19437144015[/C][C]1916.61169679788[/C][/ROW]
[ROW][C]76[/C][C]1897.17404549202[/C][C]1872.43605804636[/C][C]1921.91203293767[/C][/ROW]
[ROW][C]77[/C][C]1896.94505686502[/C][C]1866.39864334897[/C][C]1927.49147038107[/C][/ROW]
[ROW][C]78[/C][C]1896.71606823803[/C][C]1860.06651838758[/C][C]1933.36561808848[/C][/ROW]
[ROW][C]79[/C][C]1896.48707961103[/C][C]1853.43876821166[/C][C]1939.5353910104[/C][/ROW]
[ROW][C]80[/C][C]1896.25809098403[/C][C]1846.52020880337[/C][C]1945.99597316469[/C][/ROW]
[ROW][C]81[/C][C]1896.02910235704[/C][C]1839.31790727604[/C][C]1952.74029743804[/C][/ROW]
[ROW][C]82[/C][C]1895.80011373004[/C][C]1831.83968846359[/C][C]1959.7605389965[/C][/ROW]
[ROW][C]83[/C][C]1895.57112510305[/C][C]1824.0934593822[/C][C]1967.0487908239[/C][/ROW]
[ROW][C]84[/C][C]1895.34213647605[/C][C]1816.08690035717[/C][C]1974.59737259493[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=270834&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=270834&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
731897.8610113731889.266860727721906.45516201829
741897.632022746011883.73141984521911.53262564681
751897.403034119011878.194371440151916.61169679788
761897.174045492021872.436058046361921.91203293767
771896.945056865021866.398643348971927.49147038107
781896.716068238031860.066518387581933.36561808848
791896.487079611031853.438768211661939.5353910104
801896.258090984031846.520208803371945.99597316469
811896.029102357041839.317907276041952.74029743804
821895.800113730041831.839688463591959.7605389965
831895.571125103051824.09345938221967.0487908239
841895.342136476051816.086900357171974.59737259493



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')