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Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationFri, 28 Nov 2014 13:15:11 +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/Nov/28/t1417180531k3e47y2u5blhek4.htm/, Retrieved Sun, 19 May 2024 14:56:34 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=260879, Retrieved Sun, 19 May 2024 14:56:34 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact88
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [Classical Decomposition] [] [2014-11-28 12:46:25] [b5b39717209e06ff52ecfc643c6cbf41]
- RMP     [Exponential Smoothing] [] [2014-11-28 13:15:11] [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=260879&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=260879&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=260879&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
alpha0.999955088014629
betaFALSE
gammaFALSE

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.999955088014629 \tabularnewline
beta & FALSE \tabularnewline
gamma & FALSE \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=260879&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]0.999955088014629[/C][/ROW]
[ROW][C]beta[/C][C]FALSE[/C][/ROW]
[ROW][C]gamma[/C][C]FALSE[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=260879&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=260879&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
alpha0.999955088014629
betaFALSE
gammaFALSE







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
21841.551850.07-8.51999999999998
318451841.550382650123.44961734988465
41844.011844.99984507084-0.989845070836054
51842.671844.01004445591-1.34004445590722
61842.671842.67006018406-6.01840570197965e-05
71842.671842.6700000027-2.70301825366914e-09
81842.91842.670.229999999999791
91840.371842.89998967024-2.52998967024359
101841.591840.370113626861.21988637314098
111844.331841.589945212482.74005478751883
121844.331844.32987693870.000123061300655536
131844.331844.329999994475.52699930267408e-09
141845.391844.331.0600000000004
151861.841845.389952393316.4500476067044
161862.851861.83926119571.01073880429749
171869.461862.849954605716.61004539428632
181870.81869.459703129741.34029687026191
191870.81870.799939804616.01953934165067e-05
201871.521870.79999999730.7200000027035
211875.521871.519967663374.0000323366296
221880.381875.519820350614.86017964939401
231885.051880.379781719684.67021828031716
241886.421885.049790251221.3702097487751
251886.421886.419938461166.15388401001837e-05
261891.651886.419999997245.23000000276397
271903.111891.6497651103211.4602348896835
281905.291903.10948529812.18051470190176
291904.261905.28990206876-1.02990206875552
301905.371904.260046254951.10995374505319
311905.371905.369950149774.98502263326372e-05
321905.121905.36999999776-0.249999997761051
331908.621905.1200112283.49998877200392
341915.081908.619842808566.46015719144475
351916.361915.079709861511.28029013848527
361916.681916.359942499630.320057500372059
371916.241916.67998562558-0.439985625582267
381922.051916.240019760635.80998023937195
391922.631922.049739062250.580260937747653
401922.471922.62997393933-0.159973939329348
411920.641922.47000718475-1.83000718474727
421920.661920.640082189260.0199178107438911
431920.661920.659999105458.94548293217667e-07
441921.191920.659999999960.53000000003999
451921.441921.189976196650.250023803352406
461921.731921.439988770930.290011229065385
471921.811921.729986975020.0800130249799622
481921.811921.809996406463.59354385182087e-06
491921.811921.809999999841.61435309564695e-10
501921.481921.81-0.329999999999927
511917.071921.48001482096-4.41001482095521
521912.641917.07019806252-4.43019806252096
531901.151912.64019896899-11.4901989689906
541898.121901.15051604765-3.03051604764823
551900.021898.120136106491.8998638935077
561900.021900.019914673348.53266594731394e-05
571900.821900.019999996170.80000000383211
581901.91900.819964070411.08003592958858
591902.191901.899951493440.290048506557923
601901.841902.18998697335-0.349986973345722
611903.731901.840015718611.8899842813903
621889.71903.72991511705-14.0299151170536
631891.271889.700630111341.56936988865755
641894.481891.269929516483.21007048351748
651894.271894.47985582936-0.209855829361231
661893.981894.27000942504-0.290009425041944
671893.981893.9800130249-1.30248990899418e-05
681895.621893.980000000591.63999999941484
691901.721895.619926344346.10007365565616
701905.41901.719726033583.68027396641901
711898.141905.39983471159-7.25983471158929
721898.091898.14032605359-0.0503260535904246

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
2 & 1841.55 & 1850.07 & -8.51999999999998 \tabularnewline
3 & 1845 & 1841.55038265012 & 3.44961734988465 \tabularnewline
4 & 1844.01 & 1844.99984507084 & -0.989845070836054 \tabularnewline
5 & 1842.67 & 1844.01004445591 & -1.34004445590722 \tabularnewline
6 & 1842.67 & 1842.67006018406 & -6.01840570197965e-05 \tabularnewline
7 & 1842.67 & 1842.6700000027 & -2.70301825366914e-09 \tabularnewline
8 & 1842.9 & 1842.67 & 0.229999999999791 \tabularnewline
9 & 1840.37 & 1842.89998967024 & -2.52998967024359 \tabularnewline
10 & 1841.59 & 1840.37011362686 & 1.21988637314098 \tabularnewline
11 & 1844.33 & 1841.58994521248 & 2.74005478751883 \tabularnewline
12 & 1844.33 & 1844.3298769387 & 0.000123061300655536 \tabularnewline
13 & 1844.33 & 1844.32999999447 & 5.52699930267408e-09 \tabularnewline
14 & 1845.39 & 1844.33 & 1.0600000000004 \tabularnewline
15 & 1861.84 & 1845.3899523933 & 16.4500476067044 \tabularnewline
16 & 1862.85 & 1861.8392611957 & 1.01073880429749 \tabularnewline
17 & 1869.46 & 1862.84995460571 & 6.61004539428632 \tabularnewline
18 & 1870.8 & 1869.45970312974 & 1.34029687026191 \tabularnewline
19 & 1870.8 & 1870.79993980461 & 6.01953934165067e-05 \tabularnewline
20 & 1871.52 & 1870.7999999973 & 0.7200000027035 \tabularnewline
21 & 1875.52 & 1871.51996766337 & 4.0000323366296 \tabularnewline
22 & 1880.38 & 1875.51982035061 & 4.86017964939401 \tabularnewline
23 & 1885.05 & 1880.37978171968 & 4.67021828031716 \tabularnewline
24 & 1886.42 & 1885.04979025122 & 1.3702097487751 \tabularnewline
25 & 1886.42 & 1886.41993846116 & 6.15388401001837e-05 \tabularnewline
26 & 1891.65 & 1886.41999999724 & 5.23000000276397 \tabularnewline
27 & 1903.11 & 1891.64976511032 & 11.4602348896835 \tabularnewline
28 & 1905.29 & 1903.1094852981 & 2.18051470190176 \tabularnewline
29 & 1904.26 & 1905.28990206876 & -1.02990206875552 \tabularnewline
30 & 1905.37 & 1904.26004625495 & 1.10995374505319 \tabularnewline
31 & 1905.37 & 1905.36995014977 & 4.98502263326372e-05 \tabularnewline
32 & 1905.12 & 1905.36999999776 & -0.249999997761051 \tabularnewline
33 & 1908.62 & 1905.120011228 & 3.49998877200392 \tabularnewline
34 & 1915.08 & 1908.61984280856 & 6.46015719144475 \tabularnewline
35 & 1916.36 & 1915.07970986151 & 1.28029013848527 \tabularnewline
36 & 1916.68 & 1916.35994249963 & 0.320057500372059 \tabularnewline
37 & 1916.24 & 1916.67998562558 & -0.439985625582267 \tabularnewline
38 & 1922.05 & 1916.24001976063 & 5.80998023937195 \tabularnewline
39 & 1922.63 & 1922.04973906225 & 0.580260937747653 \tabularnewline
40 & 1922.47 & 1922.62997393933 & -0.159973939329348 \tabularnewline
41 & 1920.64 & 1922.47000718475 & -1.83000718474727 \tabularnewline
42 & 1920.66 & 1920.64008218926 & 0.0199178107438911 \tabularnewline
43 & 1920.66 & 1920.65999910545 & 8.94548293217667e-07 \tabularnewline
44 & 1921.19 & 1920.65999999996 & 0.53000000003999 \tabularnewline
45 & 1921.44 & 1921.18997619665 & 0.250023803352406 \tabularnewline
46 & 1921.73 & 1921.43998877093 & 0.290011229065385 \tabularnewline
47 & 1921.81 & 1921.72998697502 & 0.0800130249799622 \tabularnewline
48 & 1921.81 & 1921.80999640646 & 3.59354385182087e-06 \tabularnewline
49 & 1921.81 & 1921.80999999984 & 1.61435309564695e-10 \tabularnewline
50 & 1921.48 & 1921.81 & -0.329999999999927 \tabularnewline
51 & 1917.07 & 1921.48001482096 & -4.41001482095521 \tabularnewline
52 & 1912.64 & 1917.07019806252 & -4.43019806252096 \tabularnewline
53 & 1901.15 & 1912.64019896899 & -11.4901989689906 \tabularnewline
54 & 1898.12 & 1901.15051604765 & -3.03051604764823 \tabularnewline
55 & 1900.02 & 1898.12013610649 & 1.8998638935077 \tabularnewline
56 & 1900.02 & 1900.01991467334 & 8.53266594731394e-05 \tabularnewline
57 & 1900.82 & 1900.01999999617 & 0.80000000383211 \tabularnewline
58 & 1901.9 & 1900.81996407041 & 1.08003592958858 \tabularnewline
59 & 1902.19 & 1901.89995149344 & 0.290048506557923 \tabularnewline
60 & 1901.84 & 1902.18998697335 & -0.349986973345722 \tabularnewline
61 & 1903.73 & 1901.84001571861 & 1.8899842813903 \tabularnewline
62 & 1889.7 & 1903.72991511705 & -14.0299151170536 \tabularnewline
63 & 1891.27 & 1889.70063011134 & 1.56936988865755 \tabularnewline
64 & 1894.48 & 1891.26992951648 & 3.21007048351748 \tabularnewline
65 & 1894.27 & 1894.47985582936 & -0.209855829361231 \tabularnewline
66 & 1893.98 & 1894.27000942504 & -0.290009425041944 \tabularnewline
67 & 1893.98 & 1893.9800130249 & -1.30248990899418e-05 \tabularnewline
68 & 1895.62 & 1893.98000000059 & 1.63999999941484 \tabularnewline
69 & 1901.72 & 1895.61992634434 & 6.10007365565616 \tabularnewline
70 & 1905.4 & 1901.71972603358 & 3.68027396641901 \tabularnewline
71 & 1898.14 & 1905.39983471159 & -7.25983471158929 \tabularnewline
72 & 1898.09 & 1898.14032605359 & -0.0503260535904246 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=260879&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]2[/C][C]1841.55[/C][C]1850.07[/C][C]-8.51999999999998[/C][/ROW]
[ROW][C]3[/C][C]1845[/C][C]1841.55038265012[/C][C]3.44961734988465[/C][/ROW]
[ROW][C]4[/C][C]1844.01[/C][C]1844.99984507084[/C][C]-0.989845070836054[/C][/ROW]
[ROW][C]5[/C][C]1842.67[/C][C]1844.01004445591[/C][C]-1.34004445590722[/C][/ROW]
[ROW][C]6[/C][C]1842.67[/C][C]1842.67006018406[/C][C]-6.01840570197965e-05[/C][/ROW]
[ROW][C]7[/C][C]1842.67[/C][C]1842.6700000027[/C][C]-2.70301825366914e-09[/C][/ROW]
[ROW][C]8[/C][C]1842.9[/C][C]1842.67[/C][C]0.229999999999791[/C][/ROW]
[ROW][C]9[/C][C]1840.37[/C][C]1842.89998967024[/C][C]-2.52998967024359[/C][/ROW]
[ROW][C]10[/C][C]1841.59[/C][C]1840.37011362686[/C][C]1.21988637314098[/C][/ROW]
[ROW][C]11[/C][C]1844.33[/C][C]1841.58994521248[/C][C]2.74005478751883[/C][/ROW]
[ROW][C]12[/C][C]1844.33[/C][C]1844.3298769387[/C][C]0.000123061300655536[/C][/ROW]
[ROW][C]13[/C][C]1844.33[/C][C]1844.32999999447[/C][C]5.52699930267408e-09[/C][/ROW]
[ROW][C]14[/C][C]1845.39[/C][C]1844.33[/C][C]1.0600000000004[/C][/ROW]
[ROW][C]15[/C][C]1861.84[/C][C]1845.3899523933[/C][C]16.4500476067044[/C][/ROW]
[ROW][C]16[/C][C]1862.85[/C][C]1861.8392611957[/C][C]1.01073880429749[/C][/ROW]
[ROW][C]17[/C][C]1869.46[/C][C]1862.84995460571[/C][C]6.61004539428632[/C][/ROW]
[ROW][C]18[/C][C]1870.8[/C][C]1869.45970312974[/C][C]1.34029687026191[/C][/ROW]
[ROW][C]19[/C][C]1870.8[/C][C]1870.79993980461[/C][C]6.01953934165067e-05[/C][/ROW]
[ROW][C]20[/C][C]1871.52[/C][C]1870.7999999973[/C][C]0.7200000027035[/C][/ROW]
[ROW][C]21[/C][C]1875.52[/C][C]1871.51996766337[/C][C]4.0000323366296[/C][/ROW]
[ROW][C]22[/C][C]1880.38[/C][C]1875.51982035061[/C][C]4.86017964939401[/C][/ROW]
[ROW][C]23[/C][C]1885.05[/C][C]1880.37978171968[/C][C]4.67021828031716[/C][/ROW]
[ROW][C]24[/C][C]1886.42[/C][C]1885.04979025122[/C][C]1.3702097487751[/C][/ROW]
[ROW][C]25[/C][C]1886.42[/C][C]1886.41993846116[/C][C]6.15388401001837e-05[/C][/ROW]
[ROW][C]26[/C][C]1891.65[/C][C]1886.41999999724[/C][C]5.23000000276397[/C][/ROW]
[ROW][C]27[/C][C]1903.11[/C][C]1891.64976511032[/C][C]11.4602348896835[/C][/ROW]
[ROW][C]28[/C][C]1905.29[/C][C]1903.1094852981[/C][C]2.18051470190176[/C][/ROW]
[ROW][C]29[/C][C]1904.26[/C][C]1905.28990206876[/C][C]-1.02990206875552[/C][/ROW]
[ROW][C]30[/C][C]1905.37[/C][C]1904.26004625495[/C][C]1.10995374505319[/C][/ROW]
[ROW][C]31[/C][C]1905.37[/C][C]1905.36995014977[/C][C]4.98502263326372e-05[/C][/ROW]
[ROW][C]32[/C][C]1905.12[/C][C]1905.36999999776[/C][C]-0.249999997761051[/C][/ROW]
[ROW][C]33[/C][C]1908.62[/C][C]1905.120011228[/C][C]3.49998877200392[/C][/ROW]
[ROW][C]34[/C][C]1915.08[/C][C]1908.61984280856[/C][C]6.46015719144475[/C][/ROW]
[ROW][C]35[/C][C]1916.36[/C][C]1915.07970986151[/C][C]1.28029013848527[/C][/ROW]
[ROW][C]36[/C][C]1916.68[/C][C]1916.35994249963[/C][C]0.320057500372059[/C][/ROW]
[ROW][C]37[/C][C]1916.24[/C][C]1916.67998562558[/C][C]-0.439985625582267[/C][/ROW]
[ROW][C]38[/C][C]1922.05[/C][C]1916.24001976063[/C][C]5.80998023937195[/C][/ROW]
[ROW][C]39[/C][C]1922.63[/C][C]1922.04973906225[/C][C]0.580260937747653[/C][/ROW]
[ROW][C]40[/C][C]1922.47[/C][C]1922.62997393933[/C][C]-0.159973939329348[/C][/ROW]
[ROW][C]41[/C][C]1920.64[/C][C]1922.47000718475[/C][C]-1.83000718474727[/C][/ROW]
[ROW][C]42[/C][C]1920.66[/C][C]1920.64008218926[/C][C]0.0199178107438911[/C][/ROW]
[ROW][C]43[/C][C]1920.66[/C][C]1920.65999910545[/C][C]8.94548293217667e-07[/C][/ROW]
[ROW][C]44[/C][C]1921.19[/C][C]1920.65999999996[/C][C]0.53000000003999[/C][/ROW]
[ROW][C]45[/C][C]1921.44[/C][C]1921.18997619665[/C][C]0.250023803352406[/C][/ROW]
[ROW][C]46[/C][C]1921.73[/C][C]1921.43998877093[/C][C]0.290011229065385[/C][/ROW]
[ROW][C]47[/C][C]1921.81[/C][C]1921.72998697502[/C][C]0.0800130249799622[/C][/ROW]
[ROW][C]48[/C][C]1921.81[/C][C]1921.80999640646[/C][C]3.59354385182087e-06[/C][/ROW]
[ROW][C]49[/C][C]1921.81[/C][C]1921.80999999984[/C][C]1.61435309564695e-10[/C][/ROW]
[ROW][C]50[/C][C]1921.48[/C][C]1921.81[/C][C]-0.329999999999927[/C][/ROW]
[ROW][C]51[/C][C]1917.07[/C][C]1921.48001482096[/C][C]-4.41001482095521[/C][/ROW]
[ROW][C]52[/C][C]1912.64[/C][C]1917.07019806252[/C][C]-4.43019806252096[/C][/ROW]
[ROW][C]53[/C][C]1901.15[/C][C]1912.64019896899[/C][C]-11.4901989689906[/C][/ROW]
[ROW][C]54[/C][C]1898.12[/C][C]1901.15051604765[/C][C]-3.03051604764823[/C][/ROW]
[ROW][C]55[/C][C]1900.02[/C][C]1898.12013610649[/C][C]1.8998638935077[/C][/ROW]
[ROW][C]56[/C][C]1900.02[/C][C]1900.01991467334[/C][C]8.53266594731394e-05[/C][/ROW]
[ROW][C]57[/C][C]1900.82[/C][C]1900.01999999617[/C][C]0.80000000383211[/C][/ROW]
[ROW][C]58[/C][C]1901.9[/C][C]1900.81996407041[/C][C]1.08003592958858[/C][/ROW]
[ROW][C]59[/C][C]1902.19[/C][C]1901.89995149344[/C][C]0.290048506557923[/C][/ROW]
[ROW][C]60[/C][C]1901.84[/C][C]1902.18998697335[/C][C]-0.349986973345722[/C][/ROW]
[ROW][C]61[/C][C]1903.73[/C][C]1901.84001571861[/C][C]1.8899842813903[/C][/ROW]
[ROW][C]62[/C][C]1889.7[/C][C]1903.72991511705[/C][C]-14.0299151170536[/C][/ROW]
[ROW][C]63[/C][C]1891.27[/C][C]1889.70063011134[/C][C]1.56936988865755[/C][/ROW]
[ROW][C]64[/C][C]1894.48[/C][C]1891.26992951648[/C][C]3.21007048351748[/C][/ROW]
[ROW][C]65[/C][C]1894.27[/C][C]1894.47985582936[/C][C]-0.209855829361231[/C][/ROW]
[ROW][C]66[/C][C]1893.98[/C][C]1894.27000942504[/C][C]-0.290009425041944[/C][/ROW]
[ROW][C]67[/C][C]1893.98[/C][C]1893.9800130249[/C][C]-1.30248990899418e-05[/C][/ROW]
[ROW][C]68[/C][C]1895.62[/C][C]1893.98000000059[/C][C]1.63999999941484[/C][/ROW]
[ROW][C]69[/C][C]1901.72[/C][C]1895.61992634434[/C][C]6.10007365565616[/C][/ROW]
[ROW][C]70[/C][C]1905.4[/C][C]1901.71972603358[/C][C]3.68027396641901[/C][/ROW]
[ROW][C]71[/C][C]1898.14[/C][C]1905.39983471159[/C][C]-7.25983471158929[/C][/ROW]
[ROW][C]72[/C][C]1898.09[/C][C]1898.14032605359[/C][C]-0.0503260535904246[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=260879&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=260879&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
21841.551850.07-8.51999999999998
318451841.550382650123.44961734988465
41844.011844.99984507084-0.989845070836054
51842.671844.01004445591-1.34004445590722
61842.671842.67006018406-6.01840570197965e-05
71842.671842.6700000027-2.70301825366914e-09
81842.91842.670.229999999999791
91840.371842.89998967024-2.52998967024359
101841.591840.370113626861.21988637314098
111844.331841.589945212482.74005478751883
121844.331844.32987693870.000123061300655536
131844.331844.329999994475.52699930267408e-09
141845.391844.331.0600000000004
151861.841845.389952393316.4500476067044
161862.851861.83926119571.01073880429749
171869.461862.849954605716.61004539428632
181870.81869.459703129741.34029687026191
191870.81870.799939804616.01953934165067e-05
201871.521870.79999999730.7200000027035
211875.521871.519967663374.0000323366296
221880.381875.519820350614.86017964939401
231885.051880.379781719684.67021828031716
241886.421885.049790251221.3702097487751
251886.421886.419938461166.15388401001837e-05
261891.651886.419999997245.23000000276397
271903.111891.6497651103211.4602348896835
281905.291903.10948529812.18051470190176
291904.261905.28990206876-1.02990206875552
301905.371904.260046254951.10995374505319
311905.371905.369950149774.98502263326372e-05
321905.121905.36999999776-0.249999997761051
331908.621905.1200112283.49998877200392
341915.081908.619842808566.46015719144475
351916.361915.079709861511.28029013848527
361916.681916.359942499630.320057500372059
371916.241916.67998562558-0.439985625582267
381922.051916.240019760635.80998023937195
391922.631922.049739062250.580260937747653
401922.471922.62997393933-0.159973939329348
411920.641922.47000718475-1.83000718474727
421920.661920.640082189260.0199178107438911
431920.661920.659999105458.94548293217667e-07
441921.191920.659999999960.53000000003999
451921.441921.189976196650.250023803352406
461921.731921.439988770930.290011229065385
471921.811921.729986975020.0800130249799622
481921.811921.809996406463.59354385182087e-06
491921.811921.809999999841.61435309564695e-10
501921.481921.81-0.329999999999927
511917.071921.48001482096-4.41001482095521
521912.641917.07019806252-4.43019806252096
531901.151912.64019896899-11.4901989689906
541898.121901.15051604765-3.03051604764823
551900.021898.120136106491.8998638935077
561900.021900.019914673348.53266594731394e-05
571900.821900.019999996170.80000000383211
581901.91900.819964070411.08003592958858
591902.191901.899951493440.290048506557923
601901.841902.18998697335-0.349986973345722
611903.731901.840015718611.8899842813903
621889.71903.72991511705-14.0299151170536
631891.271889.700630111341.56936988865755
641894.481891.269929516483.21007048351748
651894.271894.47985582936-0.209855829361231
661893.981894.27000942504-0.290009425041944
671893.981893.9800130249-1.30248990899418e-05
681895.621893.980000000591.63999999941484
691901.721895.619926344346.10007365565616
701905.41901.719726033583.68027396641901
711898.141905.39983471159-7.25983471158929
721898.091898.14032605359-0.0503260535904246







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
731898.090002260241889.916373721841906.26363079865
741898.090002260241886.531005499091909.64899902139
751898.090002260241883.933286229861912.24671829062
761898.090002260241881.743295821171914.43670869932
771898.090002260241879.813869900091916.36613462039
781898.090002260241878.069532318551918.11047220193
791898.090002260241876.465446326611919.71455819387
801898.090002260241874.972398103081921.2076064174
811898.090002260241873.570095559611922.60990896087
821898.090002260241872.24376409591923.93624042459
831898.090002260241870.982250050061925.19775447042
841898.090002260241869.776888116281926.4031164042

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
73 & 1898.09000226024 & 1889.91637372184 & 1906.26363079865 \tabularnewline
74 & 1898.09000226024 & 1886.53100549909 & 1909.64899902139 \tabularnewline
75 & 1898.09000226024 & 1883.93328622986 & 1912.24671829062 \tabularnewline
76 & 1898.09000226024 & 1881.74329582117 & 1914.43670869932 \tabularnewline
77 & 1898.09000226024 & 1879.81386990009 & 1916.36613462039 \tabularnewline
78 & 1898.09000226024 & 1878.06953231855 & 1918.11047220193 \tabularnewline
79 & 1898.09000226024 & 1876.46544632661 & 1919.71455819387 \tabularnewline
80 & 1898.09000226024 & 1874.97239810308 & 1921.2076064174 \tabularnewline
81 & 1898.09000226024 & 1873.57009555961 & 1922.60990896087 \tabularnewline
82 & 1898.09000226024 & 1872.2437640959 & 1923.93624042459 \tabularnewline
83 & 1898.09000226024 & 1870.98225005006 & 1925.19775447042 \tabularnewline
84 & 1898.09000226024 & 1869.77688811628 & 1926.4031164042 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=260879&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]1898.09000226024[/C][C]1889.91637372184[/C][C]1906.26363079865[/C][/ROW]
[ROW][C]74[/C][C]1898.09000226024[/C][C]1886.53100549909[/C][C]1909.64899902139[/C][/ROW]
[ROW][C]75[/C][C]1898.09000226024[/C][C]1883.93328622986[/C][C]1912.24671829062[/C][/ROW]
[ROW][C]76[/C][C]1898.09000226024[/C][C]1881.74329582117[/C][C]1914.43670869932[/C][/ROW]
[ROW][C]77[/C][C]1898.09000226024[/C][C]1879.81386990009[/C][C]1916.36613462039[/C][/ROW]
[ROW][C]78[/C][C]1898.09000226024[/C][C]1878.06953231855[/C][C]1918.11047220193[/C][/ROW]
[ROW][C]79[/C][C]1898.09000226024[/C][C]1876.46544632661[/C][C]1919.71455819387[/C][/ROW]
[ROW][C]80[/C][C]1898.09000226024[/C][C]1874.97239810308[/C][C]1921.2076064174[/C][/ROW]
[ROW][C]81[/C][C]1898.09000226024[/C][C]1873.57009555961[/C][C]1922.60990896087[/C][/ROW]
[ROW][C]82[/C][C]1898.09000226024[/C][C]1872.2437640959[/C][C]1923.93624042459[/C][/ROW]
[ROW][C]83[/C][C]1898.09000226024[/C][C]1870.98225005006[/C][C]1925.19775447042[/C][/ROW]
[ROW][C]84[/C][C]1898.09000226024[/C][C]1869.77688811628[/C][C]1926.4031164042[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=260879&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=260879&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
731898.090002260241889.916373721841906.26363079865
741898.090002260241886.531005499091909.64899902139
751898.090002260241883.933286229861912.24671829062
761898.090002260241881.743295821171914.43670869932
771898.090002260241879.813869900091916.36613462039
781898.090002260241878.069532318551918.11047220193
791898.090002260241876.465446326611919.71455819387
801898.090002260241874.972398103081921.2076064174
811898.090002260241873.570095559611922.60990896087
821898.090002260241872.24376409591923.93624042459
831898.090002260241870.982250050061925.19775447042
841898.090002260241869.776888116281926.4031164042



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