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Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationTue, 15 Jan 2013 16:43:31 -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/2013/Jan/15/t135828627193xlc0h9wmf2mow.htm/, Retrieved Sat, 27 Apr 2024 23:38:24 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=205557, Retrieved Sat, 27 Apr 2024 23:38:24 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact79
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [Bootstrap Plot - Central Tendency] [Density Plot 50 ...] [2012-11-30 18:46:17] [d96c033d49ad8a497ee2d15a2990df1c]
- RMP     [Exponential Smoothing] [Exponential Smoot...] [2013-01-15 21:43:31] [76c30f62b7052b57088120e90a652e05] [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'George Udny Yule' @ yule.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 & 'George Udny Yule' @ yule.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=205557&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]'George Udny Yule' @ yule.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=205557&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=205557&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'George Udny Yule' @ yule.wessa.net







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha1
beta0.347103365971636
gammaFALSE

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 1 \tabularnewline
beta & 0.347103365971636 \tabularnewline
gamma & FALSE \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=205557&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]0.347103365971636[/C][/ROW]
[ROW][C]gamma[/C][C]FALSE[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=205557&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=205557&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
beta0.347103365971636
gammaFALSE







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
31865.711881.19-15.48
41872.591872.99683989476-0.406839894759287
51875.951879.73562439788-3.78562439787652
61875.951881.78162142707-5.83162142706942
71875.951879.75744600066-3.80744600066123
81878.081878.43586867808-0.355868678076604
91878.261880.44234546207-2.18234546207213
101876.391879.86484600647-3.47484600647385
111876.771876.78871526139-0.0187152613939361
121876.881877.16221913117-0.282219131168858
131876.881877.1742599208-0.294259920798595
141876.681877.07212131182-0.392121311818983
151865.521876.73601468462-11.2160146846174
161858.991861.6828982348-2.69289823479926
171856.871854.218184193282.65181580671856
181858.221853.018638385735.2013616142699
191858.221856.174048509682.04595149032116
201859.321856.884205158582.43579484141583
211859.521858.829677746860.690322253144132
221852.481859.26929092453-6.78929092452722
231850.071849.872705192060.197294807936714
241850.071847.531186883992.53881311601322
251850.071848.412417462131.65758253787203
261841.551848.9877699404-7.43776994039899
2718451837.886094958767.11390504123619
281844.011843.805355343780.204644656220353
291842.671842.88638819278-0.216388192781778
301842.671841.471279122711.19872087728936
311842.671841.887359174080.78264082592159
321842.91842.15901643910.740983560897575
331840.371842.64621432722-2.2762143272198
341841.591839.326132672572.26386732743117
351844.331841.331928642032.99807135796664
361844.331845.11256930181-0.782569301806689
371844.331844.84093686304-0.510936863043526
381845.391844.663588958080.726411041918027
391861.841845.9757286758115.8642713241888
401862.851867.93227065112-5.08227065112419
411869.461867.178197401342.28180259866008
421870.81874.58021876382-3.78021876381786
431870.81874.60809210679-3.8080921067874
441871.521873.28629051859-1.7662905185914
451875.521873.39320513432.12679486569527
461880.381878.131422790922.24857720908153
471885.051883.771911508841.27808849116195
481886.421888.88554032613-2.46554032612971
491886.421889.39974297999-2.97974297999144
501891.651888.365464161913.28453583809392
511903.111894.735537606968.37446239303677
521905.291909.10234169179-3.81234169178879
531904.261909.95906505833-5.69906505833501
541905.371906.9509003937-1.58090039369563
551905.371907.51216454578-2.14216454577786
561905.121906.76861202147-1.64861202147335
571908.621905.946373239642.67362676036146
581915.081910.374398087514.70560191248819
591916.361918.46772835026-2.10772835025909
601916.681919.01612874533-2.33612874533014
611916.241918.52525059448-2.28525059448316
621922.051917.292032421054.75796757895068
631922.631924.75353898289-2.12353898288688
641922.471924.59645145416-2.12645145415513
651920.641923.69835299684-3.05835299684236
661920.661920.80678837731-0.146788377309122
671920.661920.77583763746-0.115837637459663
681921.191920.735630003590.454369996408786
691921.441921.423343358740.0166566412588054
701921.731921.679124934990.0508750650121783
711921.811921.9867838413-0.17678384129772
721921.811922.00542157493-0.195421574933789

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
3 & 1865.71 & 1881.19 & -15.48 \tabularnewline
4 & 1872.59 & 1872.99683989476 & -0.406839894759287 \tabularnewline
5 & 1875.95 & 1879.73562439788 & -3.78562439787652 \tabularnewline
6 & 1875.95 & 1881.78162142707 & -5.83162142706942 \tabularnewline
7 & 1875.95 & 1879.75744600066 & -3.80744600066123 \tabularnewline
8 & 1878.08 & 1878.43586867808 & -0.355868678076604 \tabularnewline
9 & 1878.26 & 1880.44234546207 & -2.18234546207213 \tabularnewline
10 & 1876.39 & 1879.86484600647 & -3.47484600647385 \tabularnewline
11 & 1876.77 & 1876.78871526139 & -0.0187152613939361 \tabularnewline
12 & 1876.88 & 1877.16221913117 & -0.282219131168858 \tabularnewline
13 & 1876.88 & 1877.1742599208 & -0.294259920798595 \tabularnewline
14 & 1876.68 & 1877.07212131182 & -0.392121311818983 \tabularnewline
15 & 1865.52 & 1876.73601468462 & -11.2160146846174 \tabularnewline
16 & 1858.99 & 1861.6828982348 & -2.69289823479926 \tabularnewline
17 & 1856.87 & 1854.21818419328 & 2.65181580671856 \tabularnewline
18 & 1858.22 & 1853.01863838573 & 5.2013616142699 \tabularnewline
19 & 1858.22 & 1856.17404850968 & 2.04595149032116 \tabularnewline
20 & 1859.32 & 1856.88420515858 & 2.43579484141583 \tabularnewline
21 & 1859.52 & 1858.82967774686 & 0.690322253144132 \tabularnewline
22 & 1852.48 & 1859.26929092453 & -6.78929092452722 \tabularnewline
23 & 1850.07 & 1849.87270519206 & 0.197294807936714 \tabularnewline
24 & 1850.07 & 1847.53118688399 & 2.53881311601322 \tabularnewline
25 & 1850.07 & 1848.41241746213 & 1.65758253787203 \tabularnewline
26 & 1841.55 & 1848.9877699404 & -7.43776994039899 \tabularnewline
27 & 1845 & 1837.88609495876 & 7.11390504123619 \tabularnewline
28 & 1844.01 & 1843.80535534378 & 0.204644656220353 \tabularnewline
29 & 1842.67 & 1842.88638819278 & -0.216388192781778 \tabularnewline
30 & 1842.67 & 1841.47127912271 & 1.19872087728936 \tabularnewline
31 & 1842.67 & 1841.88735917408 & 0.78264082592159 \tabularnewline
32 & 1842.9 & 1842.1590164391 & 0.740983560897575 \tabularnewline
33 & 1840.37 & 1842.64621432722 & -2.2762143272198 \tabularnewline
34 & 1841.59 & 1839.32613267257 & 2.26386732743117 \tabularnewline
35 & 1844.33 & 1841.33192864203 & 2.99807135796664 \tabularnewline
36 & 1844.33 & 1845.11256930181 & -0.782569301806689 \tabularnewline
37 & 1844.33 & 1844.84093686304 & -0.510936863043526 \tabularnewline
38 & 1845.39 & 1844.66358895808 & 0.726411041918027 \tabularnewline
39 & 1861.84 & 1845.97572867581 & 15.8642713241888 \tabularnewline
40 & 1862.85 & 1867.93227065112 & -5.08227065112419 \tabularnewline
41 & 1869.46 & 1867.17819740134 & 2.28180259866008 \tabularnewline
42 & 1870.8 & 1874.58021876382 & -3.78021876381786 \tabularnewline
43 & 1870.8 & 1874.60809210679 & -3.8080921067874 \tabularnewline
44 & 1871.52 & 1873.28629051859 & -1.7662905185914 \tabularnewline
45 & 1875.52 & 1873.3932051343 & 2.12679486569527 \tabularnewline
46 & 1880.38 & 1878.13142279092 & 2.24857720908153 \tabularnewline
47 & 1885.05 & 1883.77191150884 & 1.27808849116195 \tabularnewline
48 & 1886.42 & 1888.88554032613 & -2.46554032612971 \tabularnewline
49 & 1886.42 & 1889.39974297999 & -2.97974297999144 \tabularnewline
50 & 1891.65 & 1888.36546416191 & 3.28453583809392 \tabularnewline
51 & 1903.11 & 1894.73553760696 & 8.37446239303677 \tabularnewline
52 & 1905.29 & 1909.10234169179 & -3.81234169178879 \tabularnewline
53 & 1904.26 & 1909.95906505833 & -5.69906505833501 \tabularnewline
54 & 1905.37 & 1906.9509003937 & -1.58090039369563 \tabularnewline
55 & 1905.37 & 1907.51216454578 & -2.14216454577786 \tabularnewline
56 & 1905.12 & 1906.76861202147 & -1.64861202147335 \tabularnewline
57 & 1908.62 & 1905.94637323964 & 2.67362676036146 \tabularnewline
58 & 1915.08 & 1910.37439808751 & 4.70560191248819 \tabularnewline
59 & 1916.36 & 1918.46772835026 & -2.10772835025909 \tabularnewline
60 & 1916.68 & 1919.01612874533 & -2.33612874533014 \tabularnewline
61 & 1916.24 & 1918.52525059448 & -2.28525059448316 \tabularnewline
62 & 1922.05 & 1917.29203242105 & 4.75796757895068 \tabularnewline
63 & 1922.63 & 1924.75353898289 & -2.12353898288688 \tabularnewline
64 & 1922.47 & 1924.59645145416 & -2.12645145415513 \tabularnewline
65 & 1920.64 & 1923.69835299684 & -3.05835299684236 \tabularnewline
66 & 1920.66 & 1920.80678837731 & -0.146788377309122 \tabularnewline
67 & 1920.66 & 1920.77583763746 & -0.115837637459663 \tabularnewline
68 & 1921.19 & 1920.73563000359 & 0.454369996408786 \tabularnewline
69 & 1921.44 & 1921.42334335874 & 0.0166566412588054 \tabularnewline
70 & 1921.73 & 1921.67912493499 & 0.0508750650121783 \tabularnewline
71 & 1921.81 & 1921.9867838413 & -0.17678384129772 \tabularnewline
72 & 1921.81 & 1922.00542157493 & -0.195421574933789 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=205557&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]1865.71[/C][C]1881.19[/C][C]-15.48[/C][/ROW]
[ROW][C]4[/C][C]1872.59[/C][C]1872.99683989476[/C][C]-0.406839894759287[/C][/ROW]
[ROW][C]5[/C][C]1875.95[/C][C]1879.73562439788[/C][C]-3.78562439787652[/C][/ROW]
[ROW][C]6[/C][C]1875.95[/C][C]1881.78162142707[/C][C]-5.83162142706942[/C][/ROW]
[ROW][C]7[/C][C]1875.95[/C][C]1879.75744600066[/C][C]-3.80744600066123[/C][/ROW]
[ROW][C]8[/C][C]1878.08[/C][C]1878.43586867808[/C][C]-0.355868678076604[/C][/ROW]
[ROW][C]9[/C][C]1878.26[/C][C]1880.44234546207[/C][C]-2.18234546207213[/C][/ROW]
[ROW][C]10[/C][C]1876.39[/C][C]1879.86484600647[/C][C]-3.47484600647385[/C][/ROW]
[ROW][C]11[/C][C]1876.77[/C][C]1876.78871526139[/C][C]-0.0187152613939361[/C][/ROW]
[ROW][C]12[/C][C]1876.88[/C][C]1877.16221913117[/C][C]-0.282219131168858[/C][/ROW]
[ROW][C]13[/C][C]1876.88[/C][C]1877.1742599208[/C][C]-0.294259920798595[/C][/ROW]
[ROW][C]14[/C][C]1876.68[/C][C]1877.07212131182[/C][C]-0.392121311818983[/C][/ROW]
[ROW][C]15[/C][C]1865.52[/C][C]1876.73601468462[/C][C]-11.2160146846174[/C][/ROW]
[ROW][C]16[/C][C]1858.99[/C][C]1861.6828982348[/C][C]-2.69289823479926[/C][/ROW]
[ROW][C]17[/C][C]1856.87[/C][C]1854.21818419328[/C][C]2.65181580671856[/C][/ROW]
[ROW][C]18[/C][C]1858.22[/C][C]1853.01863838573[/C][C]5.2013616142699[/C][/ROW]
[ROW][C]19[/C][C]1858.22[/C][C]1856.17404850968[/C][C]2.04595149032116[/C][/ROW]
[ROW][C]20[/C][C]1859.32[/C][C]1856.88420515858[/C][C]2.43579484141583[/C][/ROW]
[ROW][C]21[/C][C]1859.52[/C][C]1858.82967774686[/C][C]0.690322253144132[/C][/ROW]
[ROW][C]22[/C][C]1852.48[/C][C]1859.26929092453[/C][C]-6.78929092452722[/C][/ROW]
[ROW][C]23[/C][C]1850.07[/C][C]1849.87270519206[/C][C]0.197294807936714[/C][/ROW]
[ROW][C]24[/C][C]1850.07[/C][C]1847.53118688399[/C][C]2.53881311601322[/C][/ROW]
[ROW][C]25[/C][C]1850.07[/C][C]1848.41241746213[/C][C]1.65758253787203[/C][/ROW]
[ROW][C]26[/C][C]1841.55[/C][C]1848.9877699404[/C][C]-7.43776994039899[/C][/ROW]
[ROW][C]27[/C][C]1845[/C][C]1837.88609495876[/C][C]7.11390504123619[/C][/ROW]
[ROW][C]28[/C][C]1844.01[/C][C]1843.80535534378[/C][C]0.204644656220353[/C][/ROW]
[ROW][C]29[/C][C]1842.67[/C][C]1842.88638819278[/C][C]-0.216388192781778[/C][/ROW]
[ROW][C]30[/C][C]1842.67[/C][C]1841.47127912271[/C][C]1.19872087728936[/C][/ROW]
[ROW][C]31[/C][C]1842.67[/C][C]1841.88735917408[/C][C]0.78264082592159[/C][/ROW]
[ROW][C]32[/C][C]1842.9[/C][C]1842.1590164391[/C][C]0.740983560897575[/C][/ROW]
[ROW][C]33[/C][C]1840.37[/C][C]1842.64621432722[/C][C]-2.2762143272198[/C][/ROW]
[ROW][C]34[/C][C]1841.59[/C][C]1839.32613267257[/C][C]2.26386732743117[/C][/ROW]
[ROW][C]35[/C][C]1844.33[/C][C]1841.33192864203[/C][C]2.99807135796664[/C][/ROW]
[ROW][C]36[/C][C]1844.33[/C][C]1845.11256930181[/C][C]-0.782569301806689[/C][/ROW]
[ROW][C]37[/C][C]1844.33[/C][C]1844.84093686304[/C][C]-0.510936863043526[/C][/ROW]
[ROW][C]38[/C][C]1845.39[/C][C]1844.66358895808[/C][C]0.726411041918027[/C][/ROW]
[ROW][C]39[/C][C]1861.84[/C][C]1845.97572867581[/C][C]15.8642713241888[/C][/ROW]
[ROW][C]40[/C][C]1862.85[/C][C]1867.93227065112[/C][C]-5.08227065112419[/C][/ROW]
[ROW][C]41[/C][C]1869.46[/C][C]1867.17819740134[/C][C]2.28180259866008[/C][/ROW]
[ROW][C]42[/C][C]1870.8[/C][C]1874.58021876382[/C][C]-3.78021876381786[/C][/ROW]
[ROW][C]43[/C][C]1870.8[/C][C]1874.60809210679[/C][C]-3.8080921067874[/C][/ROW]
[ROW][C]44[/C][C]1871.52[/C][C]1873.28629051859[/C][C]-1.7662905185914[/C][/ROW]
[ROW][C]45[/C][C]1875.52[/C][C]1873.3932051343[/C][C]2.12679486569527[/C][/ROW]
[ROW][C]46[/C][C]1880.38[/C][C]1878.13142279092[/C][C]2.24857720908153[/C][/ROW]
[ROW][C]47[/C][C]1885.05[/C][C]1883.77191150884[/C][C]1.27808849116195[/C][/ROW]
[ROW][C]48[/C][C]1886.42[/C][C]1888.88554032613[/C][C]-2.46554032612971[/C][/ROW]
[ROW][C]49[/C][C]1886.42[/C][C]1889.39974297999[/C][C]-2.97974297999144[/C][/ROW]
[ROW][C]50[/C][C]1891.65[/C][C]1888.36546416191[/C][C]3.28453583809392[/C][/ROW]
[ROW][C]51[/C][C]1903.11[/C][C]1894.73553760696[/C][C]8.37446239303677[/C][/ROW]
[ROW][C]52[/C][C]1905.29[/C][C]1909.10234169179[/C][C]-3.81234169178879[/C][/ROW]
[ROW][C]53[/C][C]1904.26[/C][C]1909.95906505833[/C][C]-5.69906505833501[/C][/ROW]
[ROW][C]54[/C][C]1905.37[/C][C]1906.9509003937[/C][C]-1.58090039369563[/C][/ROW]
[ROW][C]55[/C][C]1905.37[/C][C]1907.51216454578[/C][C]-2.14216454577786[/C][/ROW]
[ROW][C]56[/C][C]1905.12[/C][C]1906.76861202147[/C][C]-1.64861202147335[/C][/ROW]
[ROW][C]57[/C][C]1908.62[/C][C]1905.94637323964[/C][C]2.67362676036146[/C][/ROW]
[ROW][C]58[/C][C]1915.08[/C][C]1910.37439808751[/C][C]4.70560191248819[/C][/ROW]
[ROW][C]59[/C][C]1916.36[/C][C]1918.46772835026[/C][C]-2.10772835025909[/C][/ROW]
[ROW][C]60[/C][C]1916.68[/C][C]1919.01612874533[/C][C]-2.33612874533014[/C][/ROW]
[ROW][C]61[/C][C]1916.24[/C][C]1918.52525059448[/C][C]-2.28525059448316[/C][/ROW]
[ROW][C]62[/C][C]1922.05[/C][C]1917.29203242105[/C][C]4.75796757895068[/C][/ROW]
[ROW][C]63[/C][C]1922.63[/C][C]1924.75353898289[/C][C]-2.12353898288688[/C][/ROW]
[ROW][C]64[/C][C]1922.47[/C][C]1924.59645145416[/C][C]-2.12645145415513[/C][/ROW]
[ROW][C]65[/C][C]1920.64[/C][C]1923.69835299684[/C][C]-3.05835299684236[/C][/ROW]
[ROW][C]66[/C][C]1920.66[/C][C]1920.80678837731[/C][C]-0.146788377309122[/C][/ROW]
[ROW][C]67[/C][C]1920.66[/C][C]1920.77583763746[/C][C]-0.115837637459663[/C][/ROW]
[ROW][C]68[/C][C]1921.19[/C][C]1920.73563000359[/C][C]0.454369996408786[/C][/ROW]
[ROW][C]69[/C][C]1921.44[/C][C]1921.42334335874[/C][C]0.0166566412588054[/C][/ROW]
[ROW][C]70[/C][C]1921.73[/C][C]1921.67912493499[/C][C]0.0508750650121783[/C][/ROW]
[ROW][C]71[/C][C]1921.81[/C][C]1921.9867838413[/C][C]-0.17678384129772[/C][/ROW]
[ROW][C]72[/C][C]1921.81[/C][C]1922.00542157493[/C][C]-0.195421574933789[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=205557&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=205557&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
31865.711881.19-15.48
41872.591872.99683989476-0.406839894759287
51875.951879.73562439788-3.78562439787652
61875.951881.78162142707-5.83162142706942
71875.951879.75744600066-3.80744600066123
81878.081878.43586867808-0.355868678076604
91878.261880.44234546207-2.18234546207213
101876.391879.86484600647-3.47484600647385
111876.771876.78871526139-0.0187152613939361
121876.881877.16221913117-0.282219131168858
131876.881877.1742599208-0.294259920798595
141876.681877.07212131182-0.392121311818983
151865.521876.73601468462-11.2160146846174
161858.991861.6828982348-2.69289823479926
171856.871854.218184193282.65181580671856
181858.221853.018638385735.2013616142699
191858.221856.174048509682.04595149032116
201859.321856.884205158582.43579484141583
211859.521858.829677746860.690322253144132
221852.481859.26929092453-6.78929092452722
231850.071849.872705192060.197294807936714
241850.071847.531186883992.53881311601322
251850.071848.412417462131.65758253787203
261841.551848.9877699404-7.43776994039899
2718451837.886094958767.11390504123619
281844.011843.805355343780.204644656220353
291842.671842.88638819278-0.216388192781778
301842.671841.471279122711.19872087728936
311842.671841.887359174080.78264082592159
321842.91842.15901643910.740983560897575
331840.371842.64621432722-2.2762143272198
341841.591839.326132672572.26386732743117
351844.331841.331928642032.99807135796664
361844.331845.11256930181-0.782569301806689
371844.331844.84093686304-0.510936863043526
381845.391844.663588958080.726411041918027
391861.841845.9757286758115.8642713241888
401862.851867.93227065112-5.08227065112419
411869.461867.178197401342.28180259866008
421870.81874.58021876382-3.78021876381786
431870.81874.60809210679-3.8080921067874
441871.521873.28629051859-1.7662905185914
451875.521873.39320513432.12679486569527
461880.381878.131422790922.24857720908153
471885.051883.771911508841.27808849116195
481886.421888.88554032613-2.46554032612971
491886.421889.39974297999-2.97974297999144
501891.651888.365464161913.28453583809392
511903.111894.735537606968.37446239303677
521905.291909.10234169179-3.81234169178879
531904.261909.95906505833-5.69906505833501
541905.371906.9509003937-1.58090039369563
551905.371907.51216454578-2.14216454577786
561905.121906.76861202147-1.64861202147335
571908.621905.946373239642.67362676036146
581915.081910.374398087514.70560191248819
591916.361918.46772835026-2.10772835025909
601916.681919.01612874533-2.33612874533014
611916.241918.52525059448-2.28525059448316
621922.051917.292032421054.75796757895068
631922.631924.75353898289-2.12353898288688
641922.471924.59645145416-2.12645145415513
651920.641923.69835299684-3.05835299684236
661920.661920.80678837731-0.146788377309122
671920.661920.77583763746-0.115837637459663
681921.191920.735630003590.454369996408786
691921.441921.423343358740.0166566412588054
701921.731921.679124934990.0508750650121783
711921.811921.9867838413-0.17678384129772
721921.811922.00542157493-0.195421574933789







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
731921.937590088491913.669351608251930.20582856874
741922.065180176981908.193531372341935.93682898162
751922.192770265471902.478570953751941.9069695772
761922.320360353961896.368138003691948.27258270424
771922.447950442451889.836598932131955.05930195278
781922.575540530941882.888390252041962.26269080985
791922.703130619441875.536406859651969.86985437922
801922.830720707931867.795612987781977.86582842808
811922.958310796421859.68088443131986.23573716153
821923.085900884911851.206267589881994.96553417993
831923.21349097341842.384764007082004.04221793971
841923.341081061891833.228318458472013.4538436653

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
73 & 1921.93759008849 & 1913.66935160825 & 1930.20582856874 \tabularnewline
74 & 1922.06518017698 & 1908.19353137234 & 1935.93682898162 \tabularnewline
75 & 1922.19277026547 & 1902.47857095375 & 1941.9069695772 \tabularnewline
76 & 1922.32036035396 & 1896.36813800369 & 1948.27258270424 \tabularnewline
77 & 1922.44795044245 & 1889.83659893213 & 1955.05930195278 \tabularnewline
78 & 1922.57554053094 & 1882.88839025204 & 1962.26269080985 \tabularnewline
79 & 1922.70313061944 & 1875.53640685965 & 1969.86985437922 \tabularnewline
80 & 1922.83072070793 & 1867.79561298778 & 1977.86582842808 \tabularnewline
81 & 1922.95831079642 & 1859.6808844313 & 1986.23573716153 \tabularnewline
82 & 1923.08590088491 & 1851.20626758988 & 1994.96553417993 \tabularnewline
83 & 1923.2134909734 & 1842.38476400708 & 2004.04221793971 \tabularnewline
84 & 1923.34108106189 & 1833.22831845847 & 2013.4538436653 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=205557&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]1921.93759008849[/C][C]1913.66935160825[/C][C]1930.20582856874[/C][/ROW]
[ROW][C]74[/C][C]1922.06518017698[/C][C]1908.19353137234[/C][C]1935.93682898162[/C][/ROW]
[ROW][C]75[/C][C]1922.19277026547[/C][C]1902.47857095375[/C][C]1941.9069695772[/C][/ROW]
[ROW][C]76[/C][C]1922.32036035396[/C][C]1896.36813800369[/C][C]1948.27258270424[/C][/ROW]
[ROW][C]77[/C][C]1922.44795044245[/C][C]1889.83659893213[/C][C]1955.05930195278[/C][/ROW]
[ROW][C]78[/C][C]1922.57554053094[/C][C]1882.88839025204[/C][C]1962.26269080985[/C][/ROW]
[ROW][C]79[/C][C]1922.70313061944[/C][C]1875.53640685965[/C][C]1969.86985437922[/C][/ROW]
[ROW][C]80[/C][C]1922.83072070793[/C][C]1867.79561298778[/C][C]1977.86582842808[/C][/ROW]
[ROW][C]81[/C][C]1922.95831079642[/C][C]1859.6808844313[/C][C]1986.23573716153[/C][/ROW]
[ROW][C]82[/C][C]1923.08590088491[/C][C]1851.20626758988[/C][C]1994.96553417993[/C][/ROW]
[ROW][C]83[/C][C]1923.2134909734[/C][C]1842.38476400708[/C][C]2004.04221793971[/C][/ROW]
[ROW][C]84[/C][C]1923.34108106189[/C][C]1833.22831845847[/C][C]2013.4538436653[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=205557&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=205557&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
731921.937590088491913.669351608251930.20582856874
741922.065180176981908.193531372341935.93682898162
751922.192770265471902.478570953751941.9069695772
761922.320360353961896.368138003691948.27258270424
771922.447950442451889.836598932131955.05930195278
781922.575540530941882.888390252041962.26269080985
791922.703130619441875.536406859651969.86985437922
801922.830720707931867.795612987781977.86582842808
811922.958310796421859.68088443131986.23573716153
821923.085900884911851.206267589881994.96553417993
831923.21349097341842.384764007082004.04221793971
841923.341081061891833.228318458472013.4538436653



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')