Free Statistics

of Irreproducible Research!

Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationFri, 25 Nov 2016 12:58:31 +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/2016/Nov/25/t14800787611yhc3b89ru8w0vh.htm/, Retrieved Sun, 19 May 2024 02:23:52 +0200
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=, Retrieved Sun, 19 May 2024 02:23:52 +0200
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact0
Dataseries X:
1859000
1869000
1858000
1859000
1878000
1876000
1869000
1888000
1874000
1872000
1885000
1878000
1868000
1879000
1873000
1863000
1880000
1886000
1880000
1901000
1900000
1901000
1922000
1917000
1918000
1927000
1926000
1926000
1945000
1940000
1934000
1945000
1940000
1935000
1945000
1937000
1932000
1947000
1943000
1941000
1951000
1951000
1944000
1962000
1968000
1969000
1972000
1954000
1959000
1971000
1963000
1964000
1986000
1972000
1975000
1993000
1983000
1997000
2000000
1995000
1991000
2001000
1993000
1995000
2010000
2005000
2008000
2028000
2015000
2023000
2031000
2027000




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=&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=&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=&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
alpha0.669556047002446
beta0.023460721643144
gamma1

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.669556047002446 \tabularnewline
beta & 0.023460721643144 \tabularnewline
gamma & 1 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=&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]0.669556047002446[/C][/ROW]
[ROW][C]beta[/C][C]0.023460721643144[/C][/ROW]
[ROW][C]gamma[/C][C]1[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=&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
alpha0.669556047002446
beta0.023460721643144
gamma1







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
1318680001863966.079059834033.92094017053
1418790001877942.356654321057.64334568102
1518730001872317.46333303682.536666971166
1618630001861785.469868981214.53013101569
1718800001878170.420677271829.57932273252
1818860001883579.254246812420.74575318955
1918800001884671.93259781-4671.93259780621
2019010001901067.27729992-67.2772999231238
2119000001887294.6399912412705.3600087613
2219010001894523.578429366476.42157064308
2319220001913225.293502498774.70649751439
2419170001913353.67458783646.32541220076
2519180001908063.579344619936.42065539444
2619270001925699.661651671300.33834833279
2719260001920808.370090785191.62990921899
2819260001914237.146929611762.8530704
2919450001938819.611950816180.38804918993
3019400001948336.82837127-8336.82837127196
3119340001940713.91757328-6713.91757328133
3219450001958062.48566744-13062.4856674364
3319400001940404.20284183-404.202841829974
3419350001937186.04469724-2186.04469723767
3519450001951099.94065098-6099.94065098232
3619370001939593.34752411-2593.34752410697
3719320001932125.02926842-125.029268421
3819470001939933.681605557066.31839444651
3919430001940042.480021312957.51997868926
4019410001933965.311410497034.688589514
4119510001953281.5376348-2281.53763480019
4219510001951947.19609854-947.196098539513
4319440001949535.71959259-5535.71959258965
4419620001965321.19904132-3321.19904132257
4519680001958267.013047229732.98695277609
4619690001961305.616907767694.38309224206
4719720001980755.0383373-8755.03833729564
4819540001968801.08256038-14801.0825603807
4919590001953954.521525285045.47847471642
5019710001967662.554851223337.44514878234
5119630001963919.46082003-919.460820032982
5219640001956535.33610437464.66389570339
5319860001973009.342561912990.6574381019
5419720001982529.79470095-10529.794700952
5519750001972223.733506932776.26649307203
5619930001994474.64732624-1474.64732624008
5719830001993167.8330508-10167.8330507984
5819970001982092.7958331314907.2041668694
592e+062000934.01192799-934.01192799001
6019950001992339.666243882660.33375611505
6119910001996137.84010225-5137.84010225115
6220010002002698.36124226-1698.36124225636
6319930001994332.93958785-1332.939587845
6419950001989592.051774295407.94822570891
6520100002006632.296325433367.70367457462
6620050002001903.583820833096.41617916594
6720080002005298.119571892701.88042810932
6820280002026273.548101831726.4518981725
6920150002024466.73135537-9466.73135537049
7020230002022387.32137175612.6786282463
7120310002026438.681082364561.31891764095
7220270002022813.583018274186.4169817348

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 1868000 & 1863966.07905983 & 4033.92094017053 \tabularnewline
14 & 1879000 & 1877942.35665432 & 1057.64334568102 \tabularnewline
15 & 1873000 & 1872317.46333303 & 682.536666971166 \tabularnewline
16 & 1863000 & 1861785.46986898 & 1214.53013101569 \tabularnewline
17 & 1880000 & 1878170.42067727 & 1829.57932273252 \tabularnewline
18 & 1886000 & 1883579.25424681 & 2420.74575318955 \tabularnewline
19 & 1880000 & 1884671.93259781 & -4671.93259780621 \tabularnewline
20 & 1901000 & 1901067.27729992 & -67.2772999231238 \tabularnewline
21 & 1900000 & 1887294.63999124 & 12705.3600087613 \tabularnewline
22 & 1901000 & 1894523.57842936 & 6476.42157064308 \tabularnewline
23 & 1922000 & 1913225.29350249 & 8774.70649751439 \tabularnewline
24 & 1917000 & 1913353.6745878 & 3646.32541220076 \tabularnewline
25 & 1918000 & 1908063.57934461 & 9936.42065539444 \tabularnewline
26 & 1927000 & 1925699.66165167 & 1300.33834833279 \tabularnewline
27 & 1926000 & 1920808.37009078 & 5191.62990921899 \tabularnewline
28 & 1926000 & 1914237.1469296 & 11762.8530704 \tabularnewline
29 & 1945000 & 1938819.61195081 & 6180.38804918993 \tabularnewline
30 & 1940000 & 1948336.82837127 & -8336.82837127196 \tabularnewline
31 & 1934000 & 1940713.91757328 & -6713.91757328133 \tabularnewline
32 & 1945000 & 1958062.48566744 & -13062.4856674364 \tabularnewline
33 & 1940000 & 1940404.20284183 & -404.202841829974 \tabularnewline
34 & 1935000 & 1937186.04469724 & -2186.04469723767 \tabularnewline
35 & 1945000 & 1951099.94065098 & -6099.94065098232 \tabularnewline
36 & 1937000 & 1939593.34752411 & -2593.34752410697 \tabularnewline
37 & 1932000 & 1932125.02926842 & -125.029268421 \tabularnewline
38 & 1947000 & 1939933.68160555 & 7066.31839444651 \tabularnewline
39 & 1943000 & 1940042.48002131 & 2957.51997868926 \tabularnewline
40 & 1941000 & 1933965.31141049 & 7034.688589514 \tabularnewline
41 & 1951000 & 1953281.5376348 & -2281.53763480019 \tabularnewline
42 & 1951000 & 1951947.19609854 & -947.196098539513 \tabularnewline
43 & 1944000 & 1949535.71959259 & -5535.71959258965 \tabularnewline
44 & 1962000 & 1965321.19904132 & -3321.19904132257 \tabularnewline
45 & 1968000 & 1958267.01304722 & 9732.98695277609 \tabularnewline
46 & 1969000 & 1961305.61690776 & 7694.38309224206 \tabularnewline
47 & 1972000 & 1980755.0383373 & -8755.03833729564 \tabularnewline
48 & 1954000 & 1968801.08256038 & -14801.0825603807 \tabularnewline
49 & 1959000 & 1953954.52152528 & 5045.47847471642 \tabularnewline
50 & 1971000 & 1967662.55485122 & 3337.44514878234 \tabularnewline
51 & 1963000 & 1963919.46082003 & -919.460820032982 \tabularnewline
52 & 1964000 & 1956535.3361043 & 7464.66389570339 \tabularnewline
53 & 1986000 & 1973009.3425619 & 12990.6574381019 \tabularnewline
54 & 1972000 & 1982529.79470095 & -10529.794700952 \tabularnewline
55 & 1975000 & 1972223.73350693 & 2776.26649307203 \tabularnewline
56 & 1993000 & 1994474.64732624 & -1474.64732624008 \tabularnewline
57 & 1983000 & 1993167.8330508 & -10167.8330507984 \tabularnewline
58 & 1997000 & 1982092.79583313 & 14907.2041668694 \tabularnewline
59 & 2e+06 & 2000934.01192799 & -934.01192799001 \tabularnewline
60 & 1995000 & 1992339.66624388 & 2660.33375611505 \tabularnewline
61 & 1991000 & 1996137.84010225 & -5137.84010225115 \tabularnewline
62 & 2001000 & 2002698.36124226 & -1698.36124225636 \tabularnewline
63 & 1993000 & 1994332.93958785 & -1332.939587845 \tabularnewline
64 & 1995000 & 1989592.05177429 & 5407.94822570891 \tabularnewline
65 & 2010000 & 2006632.29632543 & 3367.70367457462 \tabularnewline
66 & 2005000 & 2001903.58382083 & 3096.41617916594 \tabularnewline
67 & 2008000 & 2005298.11957189 & 2701.88042810932 \tabularnewline
68 & 2028000 & 2026273.54810183 & 1726.4518981725 \tabularnewline
69 & 2015000 & 2024466.73135537 & -9466.73135537049 \tabularnewline
70 & 2023000 & 2022387.32137175 & 612.6786282463 \tabularnewline
71 & 2031000 & 2026438.68108236 & 4561.31891764095 \tabularnewline
72 & 2027000 & 2022813.58301827 & 4186.4169817348 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=&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]1868000[/C][C]1863966.07905983[/C][C]4033.92094017053[/C][/ROW]
[ROW][C]14[/C][C]1879000[/C][C]1877942.35665432[/C][C]1057.64334568102[/C][/ROW]
[ROW][C]15[/C][C]1873000[/C][C]1872317.46333303[/C][C]682.536666971166[/C][/ROW]
[ROW][C]16[/C][C]1863000[/C][C]1861785.46986898[/C][C]1214.53013101569[/C][/ROW]
[ROW][C]17[/C][C]1880000[/C][C]1878170.42067727[/C][C]1829.57932273252[/C][/ROW]
[ROW][C]18[/C][C]1886000[/C][C]1883579.25424681[/C][C]2420.74575318955[/C][/ROW]
[ROW][C]19[/C][C]1880000[/C][C]1884671.93259781[/C][C]-4671.93259780621[/C][/ROW]
[ROW][C]20[/C][C]1901000[/C][C]1901067.27729992[/C][C]-67.2772999231238[/C][/ROW]
[ROW][C]21[/C][C]1900000[/C][C]1887294.63999124[/C][C]12705.3600087613[/C][/ROW]
[ROW][C]22[/C][C]1901000[/C][C]1894523.57842936[/C][C]6476.42157064308[/C][/ROW]
[ROW][C]23[/C][C]1922000[/C][C]1913225.29350249[/C][C]8774.70649751439[/C][/ROW]
[ROW][C]24[/C][C]1917000[/C][C]1913353.6745878[/C][C]3646.32541220076[/C][/ROW]
[ROW][C]25[/C][C]1918000[/C][C]1908063.57934461[/C][C]9936.42065539444[/C][/ROW]
[ROW][C]26[/C][C]1927000[/C][C]1925699.66165167[/C][C]1300.33834833279[/C][/ROW]
[ROW][C]27[/C][C]1926000[/C][C]1920808.37009078[/C][C]5191.62990921899[/C][/ROW]
[ROW][C]28[/C][C]1926000[/C][C]1914237.1469296[/C][C]11762.8530704[/C][/ROW]
[ROW][C]29[/C][C]1945000[/C][C]1938819.61195081[/C][C]6180.38804918993[/C][/ROW]
[ROW][C]30[/C][C]1940000[/C][C]1948336.82837127[/C][C]-8336.82837127196[/C][/ROW]
[ROW][C]31[/C][C]1934000[/C][C]1940713.91757328[/C][C]-6713.91757328133[/C][/ROW]
[ROW][C]32[/C][C]1945000[/C][C]1958062.48566744[/C][C]-13062.4856674364[/C][/ROW]
[ROW][C]33[/C][C]1940000[/C][C]1940404.20284183[/C][C]-404.202841829974[/C][/ROW]
[ROW][C]34[/C][C]1935000[/C][C]1937186.04469724[/C][C]-2186.04469723767[/C][/ROW]
[ROW][C]35[/C][C]1945000[/C][C]1951099.94065098[/C][C]-6099.94065098232[/C][/ROW]
[ROW][C]36[/C][C]1937000[/C][C]1939593.34752411[/C][C]-2593.34752410697[/C][/ROW]
[ROW][C]37[/C][C]1932000[/C][C]1932125.02926842[/C][C]-125.029268421[/C][/ROW]
[ROW][C]38[/C][C]1947000[/C][C]1939933.68160555[/C][C]7066.31839444651[/C][/ROW]
[ROW][C]39[/C][C]1943000[/C][C]1940042.48002131[/C][C]2957.51997868926[/C][/ROW]
[ROW][C]40[/C][C]1941000[/C][C]1933965.31141049[/C][C]7034.688589514[/C][/ROW]
[ROW][C]41[/C][C]1951000[/C][C]1953281.5376348[/C][C]-2281.53763480019[/C][/ROW]
[ROW][C]42[/C][C]1951000[/C][C]1951947.19609854[/C][C]-947.196098539513[/C][/ROW]
[ROW][C]43[/C][C]1944000[/C][C]1949535.71959259[/C][C]-5535.71959258965[/C][/ROW]
[ROW][C]44[/C][C]1962000[/C][C]1965321.19904132[/C][C]-3321.19904132257[/C][/ROW]
[ROW][C]45[/C][C]1968000[/C][C]1958267.01304722[/C][C]9732.98695277609[/C][/ROW]
[ROW][C]46[/C][C]1969000[/C][C]1961305.61690776[/C][C]7694.38309224206[/C][/ROW]
[ROW][C]47[/C][C]1972000[/C][C]1980755.0383373[/C][C]-8755.03833729564[/C][/ROW]
[ROW][C]48[/C][C]1954000[/C][C]1968801.08256038[/C][C]-14801.0825603807[/C][/ROW]
[ROW][C]49[/C][C]1959000[/C][C]1953954.52152528[/C][C]5045.47847471642[/C][/ROW]
[ROW][C]50[/C][C]1971000[/C][C]1967662.55485122[/C][C]3337.44514878234[/C][/ROW]
[ROW][C]51[/C][C]1963000[/C][C]1963919.46082003[/C][C]-919.460820032982[/C][/ROW]
[ROW][C]52[/C][C]1964000[/C][C]1956535.3361043[/C][C]7464.66389570339[/C][/ROW]
[ROW][C]53[/C][C]1986000[/C][C]1973009.3425619[/C][C]12990.6574381019[/C][/ROW]
[ROW][C]54[/C][C]1972000[/C][C]1982529.79470095[/C][C]-10529.794700952[/C][/ROW]
[ROW][C]55[/C][C]1975000[/C][C]1972223.73350693[/C][C]2776.26649307203[/C][/ROW]
[ROW][C]56[/C][C]1993000[/C][C]1994474.64732624[/C][C]-1474.64732624008[/C][/ROW]
[ROW][C]57[/C][C]1983000[/C][C]1993167.8330508[/C][C]-10167.8330507984[/C][/ROW]
[ROW][C]58[/C][C]1997000[/C][C]1982092.79583313[/C][C]14907.2041668694[/C][/ROW]
[ROW][C]59[/C][C]2e+06[/C][C]2000934.01192799[/C][C]-934.01192799001[/C][/ROW]
[ROW][C]60[/C][C]1995000[/C][C]1992339.66624388[/C][C]2660.33375611505[/C][/ROW]
[ROW][C]61[/C][C]1991000[/C][C]1996137.84010225[/C][C]-5137.84010225115[/C][/ROW]
[ROW][C]62[/C][C]2001000[/C][C]2002698.36124226[/C][C]-1698.36124225636[/C][/ROW]
[ROW][C]63[/C][C]1993000[/C][C]1994332.93958785[/C][C]-1332.939587845[/C][/ROW]
[ROW][C]64[/C][C]1995000[/C][C]1989592.05177429[/C][C]5407.94822570891[/C][/ROW]
[ROW][C]65[/C][C]2010000[/C][C]2006632.29632543[/C][C]3367.70367457462[/C][/ROW]
[ROW][C]66[/C][C]2005000[/C][C]2001903.58382083[/C][C]3096.41617916594[/C][/ROW]
[ROW][C]67[/C][C]2008000[/C][C]2005298.11957189[/C][C]2701.88042810932[/C][/ROW]
[ROW][C]68[/C][C]2028000[/C][C]2026273.54810183[/C][C]1726.4518981725[/C][/ROW]
[ROW][C]69[/C][C]2015000[/C][C]2024466.73135537[/C][C]-9466.73135537049[/C][/ROW]
[ROW][C]70[/C][C]2023000[/C][C]2022387.32137175[/C][C]612.6786282463[/C][/ROW]
[ROW][C]71[/C][C]2031000[/C][C]2026438.68108236[/C][C]4561.31891764095[/C][/ROW]
[ROW][C]72[/C][C]2027000[/C][C]2022813.58301827[/C][C]4186.4169817348[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=&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
1318680001863966.079059834033.92094017053
1418790001877942.356654321057.64334568102
1518730001872317.46333303682.536666971166
1618630001861785.469868981214.53013101569
1718800001878170.420677271829.57932273252
1818860001883579.254246812420.74575318955
1918800001884671.93259781-4671.93259780621
2019010001901067.27729992-67.2772999231238
2119000001887294.6399912412705.3600087613
2219010001894523.578429366476.42157064308
2319220001913225.293502498774.70649751439
2419170001913353.67458783646.32541220076
2519180001908063.579344619936.42065539444
2619270001925699.661651671300.33834833279
2719260001920808.370090785191.62990921899
2819260001914237.146929611762.8530704
2919450001938819.611950816180.38804918993
3019400001948336.82837127-8336.82837127196
3119340001940713.91757328-6713.91757328133
3219450001958062.48566744-13062.4856674364
3319400001940404.20284183-404.202841829974
3419350001937186.04469724-2186.04469723767
3519450001951099.94065098-6099.94065098232
3619370001939593.34752411-2593.34752410697
3719320001932125.02926842-125.029268421
3819470001939933.681605557066.31839444651
3919430001940042.480021312957.51997868926
4019410001933965.311410497034.688589514
4119510001953281.5376348-2281.53763480019
4219510001951947.19609854-947.196098539513
4319440001949535.71959259-5535.71959258965
4419620001965321.19904132-3321.19904132257
4519680001958267.013047229732.98695277609
4619690001961305.616907767694.38309224206
4719720001980755.0383373-8755.03833729564
4819540001968801.08256038-14801.0825603807
4919590001953954.521525285045.47847471642
5019710001967662.554851223337.44514878234
5119630001963919.46082003-919.460820032982
5219640001956535.33610437464.66389570339
5319860001973009.342561912990.6574381019
5419720001982529.79470095-10529.794700952
5519750001972223.733506932776.26649307203
5619930001994474.64732624-1474.64732624008
5719830001993167.8330508-10167.8330507984
5819970001982092.7958331314907.2041668694
592e+062000934.01192799-934.01192799001
6019950001992339.666243882660.33375611505
6119910001996137.84010225-5137.84010225115
6220010002002698.36124226-1698.36124225636
6319930001994332.93958785-1332.939587845
6419950001989592.051774295407.94822570891
6520100002006632.296325433367.70367457462
6620050002001903.583820833096.41617916594
6720080002005298.119571892701.88042810932
6820280002026273.548101831726.4518981725
6920150002024466.73135537-9466.73135537049
7020230002022387.32137175612.6786282463
7120310002026438.681082364561.31891764095
7220270002022813.583018274186.4169817348







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
732025182.753682762012543.988981722037821.5183838
742036526.666242112021205.130235632051848.20224859
752029652.586836662011954.029778922047351.14389441
762028286.043405822008404.253422522048167.83338912
772041200.608551262019269.620214532063131.59688799
782034243.915087722010361.58307912058126.24709633
792035502.746086742009743.145896552061262.34627693
802054372.239294412026792.885792582081951.59279624
812047709.076465522018355.442519842077062.7104112
822055445.88968552024354.394201052086537.38516995
832060529.242802172027729.313422782093329.17218156
842053791.963356862019307.510568632088276.41614509

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
73 & 2025182.75368276 & 2012543.98898172 & 2037821.5183838 \tabularnewline
74 & 2036526.66624211 & 2021205.13023563 & 2051848.20224859 \tabularnewline
75 & 2029652.58683666 & 2011954.02977892 & 2047351.14389441 \tabularnewline
76 & 2028286.04340582 & 2008404.25342252 & 2048167.83338912 \tabularnewline
77 & 2041200.60855126 & 2019269.62021453 & 2063131.59688799 \tabularnewline
78 & 2034243.91508772 & 2010361.5830791 & 2058126.24709633 \tabularnewline
79 & 2035502.74608674 & 2009743.14589655 & 2061262.34627693 \tabularnewline
80 & 2054372.23929441 & 2026792.88579258 & 2081951.59279624 \tabularnewline
81 & 2047709.07646552 & 2018355.44251984 & 2077062.7104112 \tabularnewline
82 & 2055445.8896855 & 2024354.39420105 & 2086537.38516995 \tabularnewline
83 & 2060529.24280217 & 2027729.31342278 & 2093329.17218156 \tabularnewline
84 & 2053791.96335686 & 2019307.51056863 & 2088276.41614509 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=&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]2025182.75368276[/C][C]2012543.98898172[/C][C]2037821.5183838[/C][/ROW]
[ROW][C]74[/C][C]2036526.66624211[/C][C]2021205.13023563[/C][C]2051848.20224859[/C][/ROW]
[ROW][C]75[/C][C]2029652.58683666[/C][C]2011954.02977892[/C][C]2047351.14389441[/C][/ROW]
[ROW][C]76[/C][C]2028286.04340582[/C][C]2008404.25342252[/C][C]2048167.83338912[/C][/ROW]
[ROW][C]77[/C][C]2041200.60855126[/C][C]2019269.62021453[/C][C]2063131.59688799[/C][/ROW]
[ROW][C]78[/C][C]2034243.91508772[/C][C]2010361.5830791[/C][C]2058126.24709633[/C][/ROW]
[ROW][C]79[/C][C]2035502.74608674[/C][C]2009743.14589655[/C][C]2061262.34627693[/C][/ROW]
[ROW][C]80[/C][C]2054372.23929441[/C][C]2026792.88579258[/C][C]2081951.59279624[/C][/ROW]
[ROW][C]81[/C][C]2047709.07646552[/C][C]2018355.44251984[/C][C]2077062.7104112[/C][/ROW]
[ROW][C]82[/C][C]2055445.8896855[/C][C]2024354.39420105[/C][C]2086537.38516995[/C][/ROW]
[ROW][C]83[/C][C]2060529.24280217[/C][C]2027729.31342278[/C][C]2093329.17218156[/C][/ROW]
[ROW][C]84[/C][C]2053791.96335686[/C][C]2019307.51056863[/C][C]2088276.41614509[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=&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
732025182.753682762012543.988981722037821.5183838
742036526.666242112021205.130235632051848.20224859
752029652.586836662011954.029778922047351.14389441
762028286.043405822008404.253422522048167.83338912
772041200.608551262019269.620214532063131.59688799
782034243.915087722010361.58307912058126.24709633
792035502.746086742009743.145896552061262.34627693
802054372.239294412026792.885792582081951.59279624
812047709.076465522018355.442519842077062.7104112
822055445.88968552024354.394201052086537.38516995
832060529.242802172027729.313422782093329.17218156
842053791.963356862019307.510568632088276.41614509



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')