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Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationFri, 21 Dec 2012 04:08:57 -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/21/t1356080998l9bb3zsgeaxwim4.htm/, Retrieved Tue, 23 Apr 2024 07:51:34 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=203324, Retrieved Tue, 23 Apr 2024 07:51:34 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact96
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [] [2012-12-21 09:08:57] [225a918d0dc37b74f86c734a55ddeb4f] [Current]
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Dataseries X:
1855.87
1868.53
1865.71
1872.59
1875.95
1875.95
1875.95
1878.08
1878.26
1876.39
1876.77
1876.88
1876.88
1876.68
1865.52
1858.99
1856.87
1858.22
1858.22
1859.32
1859.52
1852.48
1850.07
1850.07
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




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=203324&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=203324&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=203324&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
alpha0.601766342255356
beta0.133327045838075
gamma1

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.601766342255356 \tabularnewline
beta & 0.133327045838075 \tabularnewline
gamma & 1 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=203324&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]0.601766342255356[/C][/ROW]
[ROW][C]beta[/C][C]0.133327045838075[/C][/ROW]
[ROW][C]gamma[/C][C]1[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=203324&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=203324&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
alpha0.601766342255356
beta0.133327045838075
gamma1







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
131876.881882.5043883547-5.62438835470061
141876.681878.71675836282-2.03675836282105
151865.521866.00671403747-0.486714037465617
161858.991859.03496764084-0.0449676408384221
171856.871857.06710819262-0.197108192621272
181858.221858.58271468335-0.362714683347576
191858.221861.52081353583-3.30081353582705
201859.321858.210200079241.10979992075659
211859.521856.576119849022.9438801509848
221852.481855.13816996393-2.65816996392618
231850.071853.15290863401-3.08290863401112
241850.071850.56679011239-0.496790112394592
251850.071847.090981597582.97901840241661
261841.551849.45726188339-7.90726188339454
2718451832.9087799510612.0912200489379
281844.011833.768032623710.2419673762956
291842.671838.841358922413.82864107759497
301842.671843.94801054808-1.27801054807787
311842.671846.32626433394-3.65626433394118
321842.91845.69068787926-2.79068787926008
331840.371843.25935557115-2.88935557114814
341841.591836.431762987885.15823701211684
351844.331839.959658037214.37034196278501
361844.331844.46517246104-0.135172461035154
371844.331844.196808583010.133191416987302
381845.391841.892608504013.49739149599509
391861.841842.463472533919.3765274660961
401862.851849.847196959613.0028030403996
411869.461857.1262590775412.3337409224578
421870.81869.098092065281.70190793471784
431870.81876.34228289745-5.54228289744674
441871.521878.78497020316-7.26497020315787
451875.521877.13139776058-1.61139776057985
461880.381877.8897173392.49028266100049
471885.051882.896364274062.1536357259447
481886.421887.49384517578-1.0738451757752
491886.421889.91233301671-3.49233301671211
501891.651889.620111806912.02988819309144
511903.111898.367707557894.74229244211142
521905.291895.968899752579.32110024742838
531904.261902.032694055972.22730594402515
541905.371904.144704207921.22529579208094
551905.371908.63480917937-3.2648091793742
561905.121912.36230099809-7.24230099808642
571908.621913.57596129377-4.95596129376668
581915.081914.288870532070.791129467932933
591916.361918.33644235338-1.97644235338294
601916.681919.02940867582-2.34940867582259
611916.241919.48096033578-3.24096033578053
621922.051921.323087420580.726912579415966
631922.631930.04617330651-7.41617330651206
641922.471920.858157033981.61184296602482
651920.641917.543176703593.09682329640714
661920.661917.93454641932.7254535807017
671920.661919.814792637270.845207362725205
681921.191923.03684440137-1.84684440136607
691921.441927.44595455106-6.00595455106441
701921.731928.76960363851-7.03960363851024
711921.811925.32839581317-3.5183958131704
721921.811923.14685732919-1.33685732919503

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 1876.88 & 1882.5043883547 & -5.62438835470061 \tabularnewline
14 & 1876.68 & 1878.71675836282 & -2.03675836282105 \tabularnewline
15 & 1865.52 & 1866.00671403747 & -0.486714037465617 \tabularnewline
16 & 1858.99 & 1859.03496764084 & -0.0449676408384221 \tabularnewline
17 & 1856.87 & 1857.06710819262 & -0.197108192621272 \tabularnewline
18 & 1858.22 & 1858.58271468335 & -0.362714683347576 \tabularnewline
19 & 1858.22 & 1861.52081353583 & -3.30081353582705 \tabularnewline
20 & 1859.32 & 1858.21020007924 & 1.10979992075659 \tabularnewline
21 & 1859.52 & 1856.57611984902 & 2.9438801509848 \tabularnewline
22 & 1852.48 & 1855.13816996393 & -2.65816996392618 \tabularnewline
23 & 1850.07 & 1853.15290863401 & -3.08290863401112 \tabularnewline
24 & 1850.07 & 1850.56679011239 & -0.496790112394592 \tabularnewline
25 & 1850.07 & 1847.09098159758 & 2.97901840241661 \tabularnewline
26 & 1841.55 & 1849.45726188339 & -7.90726188339454 \tabularnewline
27 & 1845 & 1832.90877995106 & 12.0912200489379 \tabularnewline
28 & 1844.01 & 1833.7680326237 & 10.2419673762956 \tabularnewline
29 & 1842.67 & 1838.84135892241 & 3.82864107759497 \tabularnewline
30 & 1842.67 & 1843.94801054808 & -1.27801054807787 \tabularnewline
31 & 1842.67 & 1846.32626433394 & -3.65626433394118 \tabularnewline
32 & 1842.9 & 1845.69068787926 & -2.79068787926008 \tabularnewline
33 & 1840.37 & 1843.25935557115 & -2.88935557114814 \tabularnewline
34 & 1841.59 & 1836.43176298788 & 5.15823701211684 \tabularnewline
35 & 1844.33 & 1839.95965803721 & 4.37034196278501 \tabularnewline
36 & 1844.33 & 1844.46517246104 & -0.135172461035154 \tabularnewline
37 & 1844.33 & 1844.19680858301 & 0.133191416987302 \tabularnewline
38 & 1845.39 & 1841.89260850401 & 3.49739149599509 \tabularnewline
39 & 1861.84 & 1842.4634725339 & 19.3765274660961 \tabularnewline
40 & 1862.85 & 1849.8471969596 & 13.0028030403996 \tabularnewline
41 & 1869.46 & 1857.12625907754 & 12.3337409224578 \tabularnewline
42 & 1870.8 & 1869.09809206528 & 1.70190793471784 \tabularnewline
43 & 1870.8 & 1876.34228289745 & -5.54228289744674 \tabularnewline
44 & 1871.52 & 1878.78497020316 & -7.26497020315787 \tabularnewline
45 & 1875.52 & 1877.13139776058 & -1.61139776057985 \tabularnewline
46 & 1880.38 & 1877.889717339 & 2.49028266100049 \tabularnewline
47 & 1885.05 & 1882.89636427406 & 2.1536357259447 \tabularnewline
48 & 1886.42 & 1887.49384517578 & -1.0738451757752 \tabularnewline
49 & 1886.42 & 1889.91233301671 & -3.49233301671211 \tabularnewline
50 & 1891.65 & 1889.62011180691 & 2.02988819309144 \tabularnewline
51 & 1903.11 & 1898.36770755789 & 4.74229244211142 \tabularnewline
52 & 1905.29 & 1895.96889975257 & 9.32110024742838 \tabularnewline
53 & 1904.26 & 1902.03269405597 & 2.22730594402515 \tabularnewline
54 & 1905.37 & 1904.14470420792 & 1.22529579208094 \tabularnewline
55 & 1905.37 & 1908.63480917937 & -3.2648091793742 \tabularnewline
56 & 1905.12 & 1912.36230099809 & -7.24230099808642 \tabularnewline
57 & 1908.62 & 1913.57596129377 & -4.95596129376668 \tabularnewline
58 & 1915.08 & 1914.28887053207 & 0.791129467932933 \tabularnewline
59 & 1916.36 & 1918.33644235338 & -1.97644235338294 \tabularnewline
60 & 1916.68 & 1919.02940867582 & -2.34940867582259 \tabularnewline
61 & 1916.24 & 1919.48096033578 & -3.24096033578053 \tabularnewline
62 & 1922.05 & 1921.32308742058 & 0.726912579415966 \tabularnewline
63 & 1922.63 & 1930.04617330651 & -7.41617330651206 \tabularnewline
64 & 1922.47 & 1920.85815703398 & 1.61184296602482 \tabularnewline
65 & 1920.64 & 1917.54317670359 & 3.09682329640714 \tabularnewline
66 & 1920.66 & 1917.9345464193 & 2.7254535807017 \tabularnewline
67 & 1920.66 & 1919.81479263727 & 0.845207362725205 \tabularnewline
68 & 1921.19 & 1923.03684440137 & -1.84684440136607 \tabularnewline
69 & 1921.44 & 1927.44595455106 & -6.00595455106441 \tabularnewline
70 & 1921.73 & 1928.76960363851 & -7.03960363851024 \tabularnewline
71 & 1921.81 & 1925.32839581317 & -3.5183958131704 \tabularnewline
72 & 1921.81 & 1923.14685732919 & -1.33685732919503 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=203324&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]13[/C][C]1876.88[/C][C]1882.5043883547[/C][C]-5.62438835470061[/C][/ROW]
[ROW][C]14[/C][C]1876.68[/C][C]1878.71675836282[/C][C]-2.03675836282105[/C][/ROW]
[ROW][C]15[/C][C]1865.52[/C][C]1866.00671403747[/C][C]-0.486714037465617[/C][/ROW]
[ROW][C]16[/C][C]1858.99[/C][C]1859.03496764084[/C][C]-0.0449676408384221[/C][/ROW]
[ROW][C]17[/C][C]1856.87[/C][C]1857.06710819262[/C][C]-0.197108192621272[/C][/ROW]
[ROW][C]18[/C][C]1858.22[/C][C]1858.58271468335[/C][C]-0.362714683347576[/C][/ROW]
[ROW][C]19[/C][C]1858.22[/C][C]1861.52081353583[/C][C]-3.30081353582705[/C][/ROW]
[ROW][C]20[/C][C]1859.32[/C][C]1858.21020007924[/C][C]1.10979992075659[/C][/ROW]
[ROW][C]21[/C][C]1859.52[/C][C]1856.57611984902[/C][C]2.9438801509848[/C][/ROW]
[ROW][C]22[/C][C]1852.48[/C][C]1855.13816996393[/C][C]-2.65816996392618[/C][/ROW]
[ROW][C]23[/C][C]1850.07[/C][C]1853.15290863401[/C][C]-3.08290863401112[/C][/ROW]
[ROW][C]24[/C][C]1850.07[/C][C]1850.56679011239[/C][C]-0.496790112394592[/C][/ROW]
[ROW][C]25[/C][C]1850.07[/C][C]1847.09098159758[/C][C]2.97901840241661[/C][/ROW]
[ROW][C]26[/C][C]1841.55[/C][C]1849.45726188339[/C][C]-7.90726188339454[/C][/ROW]
[ROW][C]27[/C][C]1845[/C][C]1832.90877995106[/C][C]12.0912200489379[/C][/ROW]
[ROW][C]28[/C][C]1844.01[/C][C]1833.7680326237[/C][C]10.2419673762956[/C][/ROW]
[ROW][C]29[/C][C]1842.67[/C][C]1838.84135892241[/C][C]3.82864107759497[/C][/ROW]
[ROW][C]30[/C][C]1842.67[/C][C]1843.94801054808[/C][C]-1.27801054807787[/C][/ROW]
[ROW][C]31[/C][C]1842.67[/C][C]1846.32626433394[/C][C]-3.65626433394118[/C][/ROW]
[ROW][C]32[/C][C]1842.9[/C][C]1845.69068787926[/C][C]-2.79068787926008[/C][/ROW]
[ROW][C]33[/C][C]1840.37[/C][C]1843.25935557115[/C][C]-2.88935557114814[/C][/ROW]
[ROW][C]34[/C][C]1841.59[/C][C]1836.43176298788[/C][C]5.15823701211684[/C][/ROW]
[ROW][C]35[/C][C]1844.33[/C][C]1839.95965803721[/C][C]4.37034196278501[/C][/ROW]
[ROW][C]36[/C][C]1844.33[/C][C]1844.46517246104[/C][C]-0.135172461035154[/C][/ROW]
[ROW][C]37[/C][C]1844.33[/C][C]1844.19680858301[/C][C]0.133191416987302[/C][/ROW]
[ROW][C]38[/C][C]1845.39[/C][C]1841.89260850401[/C][C]3.49739149599509[/C][/ROW]
[ROW][C]39[/C][C]1861.84[/C][C]1842.4634725339[/C][C]19.3765274660961[/C][/ROW]
[ROW][C]40[/C][C]1862.85[/C][C]1849.8471969596[/C][C]13.0028030403996[/C][/ROW]
[ROW][C]41[/C][C]1869.46[/C][C]1857.12625907754[/C][C]12.3337409224578[/C][/ROW]
[ROW][C]42[/C][C]1870.8[/C][C]1869.09809206528[/C][C]1.70190793471784[/C][/ROW]
[ROW][C]43[/C][C]1870.8[/C][C]1876.34228289745[/C][C]-5.54228289744674[/C][/ROW]
[ROW][C]44[/C][C]1871.52[/C][C]1878.78497020316[/C][C]-7.26497020315787[/C][/ROW]
[ROW][C]45[/C][C]1875.52[/C][C]1877.13139776058[/C][C]-1.61139776057985[/C][/ROW]
[ROW][C]46[/C][C]1880.38[/C][C]1877.889717339[/C][C]2.49028266100049[/C][/ROW]
[ROW][C]47[/C][C]1885.05[/C][C]1882.89636427406[/C][C]2.1536357259447[/C][/ROW]
[ROW][C]48[/C][C]1886.42[/C][C]1887.49384517578[/C][C]-1.0738451757752[/C][/ROW]
[ROW][C]49[/C][C]1886.42[/C][C]1889.91233301671[/C][C]-3.49233301671211[/C][/ROW]
[ROW][C]50[/C][C]1891.65[/C][C]1889.62011180691[/C][C]2.02988819309144[/C][/ROW]
[ROW][C]51[/C][C]1903.11[/C][C]1898.36770755789[/C][C]4.74229244211142[/C][/ROW]
[ROW][C]52[/C][C]1905.29[/C][C]1895.96889975257[/C][C]9.32110024742838[/C][/ROW]
[ROW][C]53[/C][C]1904.26[/C][C]1902.03269405597[/C][C]2.22730594402515[/C][/ROW]
[ROW][C]54[/C][C]1905.37[/C][C]1904.14470420792[/C][C]1.22529579208094[/C][/ROW]
[ROW][C]55[/C][C]1905.37[/C][C]1908.63480917937[/C][C]-3.2648091793742[/C][/ROW]
[ROW][C]56[/C][C]1905.12[/C][C]1912.36230099809[/C][C]-7.24230099808642[/C][/ROW]
[ROW][C]57[/C][C]1908.62[/C][C]1913.57596129377[/C][C]-4.95596129376668[/C][/ROW]
[ROW][C]58[/C][C]1915.08[/C][C]1914.28887053207[/C][C]0.791129467932933[/C][/ROW]
[ROW][C]59[/C][C]1916.36[/C][C]1918.33644235338[/C][C]-1.97644235338294[/C][/ROW]
[ROW][C]60[/C][C]1916.68[/C][C]1919.02940867582[/C][C]-2.34940867582259[/C][/ROW]
[ROW][C]61[/C][C]1916.24[/C][C]1919.48096033578[/C][C]-3.24096033578053[/C][/ROW]
[ROW][C]62[/C][C]1922.05[/C][C]1921.32308742058[/C][C]0.726912579415966[/C][/ROW]
[ROW][C]63[/C][C]1922.63[/C][C]1930.04617330651[/C][C]-7.41617330651206[/C][/ROW]
[ROW][C]64[/C][C]1922.47[/C][C]1920.85815703398[/C][C]1.61184296602482[/C][/ROW]
[ROW][C]65[/C][C]1920.64[/C][C]1917.54317670359[/C][C]3.09682329640714[/C][/ROW]
[ROW][C]66[/C][C]1920.66[/C][C]1917.9345464193[/C][C]2.7254535807017[/C][/ROW]
[ROW][C]67[/C][C]1920.66[/C][C]1919.81479263727[/C][C]0.845207362725205[/C][/ROW]
[ROW][C]68[/C][C]1921.19[/C][C]1923.03684440137[/C][C]-1.84684440136607[/C][/ROW]
[ROW][C]69[/C][C]1921.44[/C][C]1927.44595455106[/C][C]-6.00595455106441[/C][/ROW]
[ROW][C]70[/C][C]1921.73[/C][C]1928.76960363851[/C][C]-7.03960363851024[/C][/ROW]
[ROW][C]71[/C][C]1921.81[/C][C]1925.32839581317[/C][C]-3.5183958131704[/C][/ROW]
[ROW][C]72[/C][C]1921.81[/C][C]1923.14685732919[/C][C]-1.33685732919503[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=203324&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=203324&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
131876.881882.5043883547-5.62438835470061
141876.681878.71675836282-2.03675836282105
151865.521866.00671403747-0.486714037465617
161858.991859.03496764084-0.0449676408384221
171856.871857.06710819262-0.197108192621272
181858.221858.58271468335-0.362714683347576
191858.221861.52081353583-3.30081353582705
201859.321858.210200079241.10979992075659
211859.521856.576119849022.9438801509848
221852.481855.13816996393-2.65816996392618
231850.071853.15290863401-3.08290863401112
241850.071850.56679011239-0.496790112394592
251850.071847.090981597582.97901840241661
261841.551849.45726188339-7.90726188339454
2718451832.9087799510612.0912200489379
281844.011833.768032623710.2419673762956
291842.671838.841358922413.82864107759497
301842.671843.94801054808-1.27801054807787
311842.671846.32626433394-3.65626433394118
321842.91845.69068787926-2.79068787926008
331840.371843.25935557115-2.88935557114814
341841.591836.431762987885.15823701211684
351844.331839.959658037214.37034196278501
361844.331844.46517246104-0.135172461035154
371844.331844.196808583010.133191416987302
381845.391841.892608504013.49739149599509
391861.841842.463472533919.3765274660961
401862.851849.847196959613.0028030403996
411869.461857.1262590775412.3337409224578
421870.81869.098092065281.70190793471784
431870.81876.34228289745-5.54228289744674
441871.521878.78497020316-7.26497020315787
451875.521877.13139776058-1.61139776057985
461880.381877.8897173392.49028266100049
471885.051882.896364274062.1536357259447
481886.421887.49384517578-1.0738451757752
491886.421889.91233301671-3.49233301671211
501891.651889.620111806912.02988819309144
511903.111898.367707557894.74229244211142
521905.291895.968899752579.32110024742838
531904.261902.032694055972.22730594402515
541905.371904.144704207921.22529579208094
551905.371908.63480917937-3.2648091793742
561905.121912.36230099809-7.24230099808642
571908.621913.57596129377-4.95596129376668
581915.081914.288870532070.791129467932933
591916.361918.33644235338-1.97644235338294
601916.681919.02940867582-2.34940867582259
611916.241919.48096033578-3.24096033578053
621922.051921.323087420580.726912579415966
631922.631930.04617330651-7.41617330651206
641922.471920.858157033981.61184296602482
651920.641917.543176703593.09682329640714
661920.661917.93454641932.7254535807017
671920.661919.814792637270.845207362725205
681921.191923.03684440137-1.84684440136607
691921.441927.44595455106-6.00595455106441
701921.731928.76960363851-7.03960363851024
711921.811925.32839581317-3.5183958131704
721921.811923.14685732919-1.33685732919503







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
731922.135839805491911.584060024971932.68761958602
741926.051593506561913.279487335951938.82369967718
751929.579260763021914.48573133411944.67279019194
761927.529184094031910.012412667711945.04595552036
771922.786175295761902.745514910541942.82683568098
781919.868180806391897.204985666631942.53137594615
791917.842987353881892.46095162181943.22502308597
801917.89996759681889.705225862521946.09470933107
811920.327935860491889.229045116351951.42682660464
821923.899787470831889.807650679961957.99192426169
831925.707494297051888.53525682451962.8797317696
841926.404711667611886.067647202491966.74177613273

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
73 & 1922.13583980549 & 1911.58406002497 & 1932.68761958602 \tabularnewline
74 & 1926.05159350656 & 1913.27948733595 & 1938.82369967718 \tabularnewline
75 & 1929.57926076302 & 1914.4857313341 & 1944.67279019194 \tabularnewline
76 & 1927.52918409403 & 1910.01241266771 & 1945.04595552036 \tabularnewline
77 & 1922.78617529576 & 1902.74551491054 & 1942.82683568098 \tabularnewline
78 & 1919.86818080639 & 1897.20498566663 & 1942.53137594615 \tabularnewline
79 & 1917.84298735388 & 1892.4609516218 & 1943.22502308597 \tabularnewline
80 & 1917.8999675968 & 1889.70522586252 & 1946.09470933107 \tabularnewline
81 & 1920.32793586049 & 1889.22904511635 & 1951.42682660464 \tabularnewline
82 & 1923.89978747083 & 1889.80765067996 & 1957.99192426169 \tabularnewline
83 & 1925.70749429705 & 1888.5352568245 & 1962.8797317696 \tabularnewline
84 & 1926.40471166761 & 1886.06764720249 & 1966.74177613273 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=203324&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]1922.13583980549[/C][C]1911.58406002497[/C][C]1932.68761958602[/C][/ROW]
[ROW][C]74[/C][C]1926.05159350656[/C][C]1913.27948733595[/C][C]1938.82369967718[/C][/ROW]
[ROW][C]75[/C][C]1929.57926076302[/C][C]1914.4857313341[/C][C]1944.67279019194[/C][/ROW]
[ROW][C]76[/C][C]1927.52918409403[/C][C]1910.01241266771[/C][C]1945.04595552036[/C][/ROW]
[ROW][C]77[/C][C]1922.78617529576[/C][C]1902.74551491054[/C][C]1942.82683568098[/C][/ROW]
[ROW][C]78[/C][C]1919.86818080639[/C][C]1897.20498566663[/C][C]1942.53137594615[/C][/ROW]
[ROW][C]79[/C][C]1917.84298735388[/C][C]1892.4609516218[/C][C]1943.22502308597[/C][/ROW]
[ROW][C]80[/C][C]1917.8999675968[/C][C]1889.70522586252[/C][C]1946.09470933107[/C][/ROW]
[ROW][C]81[/C][C]1920.32793586049[/C][C]1889.22904511635[/C][C]1951.42682660464[/C][/ROW]
[ROW][C]82[/C][C]1923.89978747083[/C][C]1889.80765067996[/C][C]1957.99192426169[/C][/ROW]
[ROW][C]83[/C][C]1925.70749429705[/C][C]1888.5352568245[/C][C]1962.8797317696[/C][/ROW]
[ROW][C]84[/C][C]1926.40471166761[/C][C]1886.06764720249[/C][C]1966.74177613273[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=203324&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=203324&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
731922.135839805491911.584060024971932.68761958602
741926.051593506561913.279487335951938.82369967718
751929.579260763021914.48573133411944.67279019194
761927.529184094031910.012412667711945.04595552036
771922.786175295761902.745514910541942.82683568098
781919.868180806391897.204985666631942.53137594615
791917.842987353881892.46095162181943.22502308597
801917.89996759681889.705225862521946.09470933107
811920.327935860491889.229045116351951.42682660464
821923.899787470831889.807650679961957.99192426169
831925.707494297051888.53525682451962.8797317696
841926.404711667611886.067647202491966.74177613273



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