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Author's title

Author*The author of this computation has been verified*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationMon, 29 Nov 2010 17:05:06 +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/2010/Nov/29/t1291050441430t87s2iiw16o5.htm/, Retrieved Mon, 29 Apr 2024 09:39:25 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=102955, Retrieved Mon, 29 Apr 2024 09:39:25 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact176
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [Exponential Smoothing] [HPC Retail Sales] [2008-03-10 17:43:04] [74be16979710d4c4e7c6647856088456]
-  M D    [Exponential Smoothing] [W8 Single Exponen...] [2010-11-29 17:05:06] [59f7d3e7fcb6374015f4e6b9053b0f01] [Current]
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Dataseries X:
10057
10900
11771
11992
11993
14504
11727
11477
13578
11555
11846
11397
10066
10269
14279
13870
13695
14420
11424
9704
12464
14301
13464
9893
11572
12380
16692
16052
16459
14761
13654
13480
18068
16560
14530
10650
11651
13735
13360
17818
20613
16231
13862
12004
17734
15034
12609
12320
10833
11350
13648
14890
16325
18045
15616
11926
16855
15083
12520
12355




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'Sir Ronald Aylmer Fisher' @ 193.190.124.24

\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 & 'Sir Ronald Aylmer Fisher' @ 193.190.124.24 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=102955&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]'Sir Ronald Aylmer Fisher' @ 193.190.124.24[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=102955&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=102955&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'Sir Ronald Aylmer Fisher' @ 193.190.124.24







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.680282906594522
beta0
gamma0

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.680282906594522 \tabularnewline
beta & 0 \tabularnewline
gamma & 0 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=102955&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]0.680282906594522[/C][/ROW]
[ROW][C]beta[/C][C]0[/C][/ROW]
[ROW][C]gamma[/C][C]0[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=102955&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=102955&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
alpha0.680282906594522
beta0
gamma0







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
21090010057843
31177110630.47849025921140.52150974082
41199211406.3557779392585.644222060762
51199311804.7595315530188.240468446978
61450411932.81630456682571.18369543315
71172713681.9486222846-1954.94862228456
81147712352.0304912739-875.030491273861
91357811756.76220531121821.23779468875
101155512995.7191458819-1440.71914588191
111184612015.6225377350-169.622537734987
121139711900.2312247407-503.231224740692
131006611557.8916244850-1491.89162448497
141026910542.9832538563-273.983253856313
151427910356.59712956473922.40287043528
161387013024.9407550991845.059244900873
171369513599.820114464995.1798855351353
181442013664.5693636460755.43063635396
191142414178.4759126755-2754.47591267546
20970412304.653032656-2600.653032656
211246410535.47322855691928.52677144308
221430111847.41702607962453.58297392043
231346413516.547583149-52.5475831489912
24989313480.8003605499-3587.80036054988
251157211040.0811029941531.918897005868
261238011401.9364363218978.063563678164
271669212067.29636025504624.70363974499
281605215213.403194439838.596805561003
291645915783.8862667869675.113733213082
301476116243.154599499-1482.15459949899
311365415234.8701605294-1580.87016052938
321348014159.4312127759-679.431212775904
331806813697.22577251774370.77422748233
341656016670.5887680578-110.588768057776
351453016595.3571194867-2065.35711948673
361065015190.3299750866-4540.32997508661
371165112101.6211027365-450.621102736457
381373511795.07126919411939.92873080593
391336013114.7716247730245.228375227049
401781813281.59629665194536.40370334814
412061316367.63419345174245.36580654831
421623119255.6839838874-3024.68398388737
431386217198.0431717986-3336.04317179857
441200414928.5900263626-2924.59002636263
451773412939.04142263134794.95857736869
461503416200.9697806440-1166.96978064402
471260915407.1001863595-2798.10018635953
481232013503.6004586402-1183.60045864020
491083312698.4172983898-1865.41729838983
501135011429.4057966295-79.4057966294968
511364811375.38739049792272.61260950207
521489012921.40690205341968.59309794664
531632514260.60713662642064.39286337358
541804515664.97831407522380.02168592481
551561617284.0663843341-1668.06638433411
561192616149.3093360067-4223.30933600669
571685513276.26418546033578.73581453972
581508315710.8169873093-627.816987309274
591252015283.7238223731-2763.72382237311
601235513403.6097474646-1048.60974746461

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
2 & 10900 & 10057 & 843 \tabularnewline
3 & 11771 & 10630.4784902592 & 1140.52150974082 \tabularnewline
4 & 11992 & 11406.3557779392 & 585.644222060762 \tabularnewline
5 & 11993 & 11804.7595315530 & 188.240468446978 \tabularnewline
6 & 14504 & 11932.8163045668 & 2571.18369543315 \tabularnewline
7 & 11727 & 13681.9486222846 & -1954.94862228456 \tabularnewline
8 & 11477 & 12352.0304912739 & -875.030491273861 \tabularnewline
9 & 13578 & 11756.7622053112 & 1821.23779468875 \tabularnewline
10 & 11555 & 12995.7191458819 & -1440.71914588191 \tabularnewline
11 & 11846 & 12015.6225377350 & -169.622537734987 \tabularnewline
12 & 11397 & 11900.2312247407 & -503.231224740692 \tabularnewline
13 & 10066 & 11557.8916244850 & -1491.89162448497 \tabularnewline
14 & 10269 & 10542.9832538563 & -273.983253856313 \tabularnewline
15 & 14279 & 10356.5971295647 & 3922.40287043528 \tabularnewline
16 & 13870 & 13024.9407550991 & 845.059244900873 \tabularnewline
17 & 13695 & 13599.8201144649 & 95.1798855351353 \tabularnewline
18 & 14420 & 13664.5693636460 & 755.43063635396 \tabularnewline
19 & 11424 & 14178.4759126755 & -2754.47591267546 \tabularnewline
20 & 9704 & 12304.653032656 & -2600.653032656 \tabularnewline
21 & 12464 & 10535.4732285569 & 1928.52677144308 \tabularnewline
22 & 14301 & 11847.4170260796 & 2453.58297392043 \tabularnewline
23 & 13464 & 13516.547583149 & -52.5475831489912 \tabularnewline
24 & 9893 & 13480.8003605499 & -3587.80036054988 \tabularnewline
25 & 11572 & 11040.0811029941 & 531.918897005868 \tabularnewline
26 & 12380 & 11401.9364363218 & 978.063563678164 \tabularnewline
27 & 16692 & 12067.2963602550 & 4624.70363974499 \tabularnewline
28 & 16052 & 15213.403194439 & 838.596805561003 \tabularnewline
29 & 16459 & 15783.8862667869 & 675.113733213082 \tabularnewline
30 & 14761 & 16243.154599499 & -1482.15459949899 \tabularnewline
31 & 13654 & 15234.8701605294 & -1580.87016052938 \tabularnewline
32 & 13480 & 14159.4312127759 & -679.431212775904 \tabularnewline
33 & 18068 & 13697.2257725177 & 4370.77422748233 \tabularnewline
34 & 16560 & 16670.5887680578 & -110.588768057776 \tabularnewline
35 & 14530 & 16595.3571194867 & -2065.35711948673 \tabularnewline
36 & 10650 & 15190.3299750866 & -4540.32997508661 \tabularnewline
37 & 11651 & 12101.6211027365 & -450.621102736457 \tabularnewline
38 & 13735 & 11795.0712691941 & 1939.92873080593 \tabularnewline
39 & 13360 & 13114.7716247730 & 245.228375227049 \tabularnewline
40 & 17818 & 13281.5962966519 & 4536.40370334814 \tabularnewline
41 & 20613 & 16367.6341934517 & 4245.36580654831 \tabularnewline
42 & 16231 & 19255.6839838874 & -3024.68398388737 \tabularnewline
43 & 13862 & 17198.0431717986 & -3336.04317179857 \tabularnewline
44 & 12004 & 14928.5900263626 & -2924.59002636263 \tabularnewline
45 & 17734 & 12939.0414226313 & 4794.95857736869 \tabularnewline
46 & 15034 & 16200.9697806440 & -1166.96978064402 \tabularnewline
47 & 12609 & 15407.1001863595 & -2798.10018635953 \tabularnewline
48 & 12320 & 13503.6004586402 & -1183.60045864020 \tabularnewline
49 & 10833 & 12698.4172983898 & -1865.41729838983 \tabularnewline
50 & 11350 & 11429.4057966295 & -79.4057966294968 \tabularnewline
51 & 13648 & 11375.3873904979 & 2272.61260950207 \tabularnewline
52 & 14890 & 12921.4069020534 & 1968.59309794664 \tabularnewline
53 & 16325 & 14260.6071366264 & 2064.39286337358 \tabularnewline
54 & 18045 & 15664.9783140752 & 2380.02168592481 \tabularnewline
55 & 15616 & 17284.0663843341 & -1668.06638433411 \tabularnewline
56 & 11926 & 16149.3093360067 & -4223.30933600669 \tabularnewline
57 & 16855 & 13276.2641854603 & 3578.73581453972 \tabularnewline
58 & 15083 & 15710.8169873093 & -627.816987309274 \tabularnewline
59 & 12520 & 15283.7238223731 & -2763.72382237311 \tabularnewline
60 & 12355 & 13403.6097474646 & -1048.60974746461 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=102955&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]10900[/C][C]10057[/C][C]843[/C][/ROW]
[ROW][C]3[/C][C]11771[/C][C]10630.4784902592[/C][C]1140.52150974082[/C][/ROW]
[ROW][C]4[/C][C]11992[/C][C]11406.3557779392[/C][C]585.644222060762[/C][/ROW]
[ROW][C]5[/C][C]11993[/C][C]11804.7595315530[/C][C]188.240468446978[/C][/ROW]
[ROW][C]6[/C][C]14504[/C][C]11932.8163045668[/C][C]2571.18369543315[/C][/ROW]
[ROW][C]7[/C][C]11727[/C][C]13681.9486222846[/C][C]-1954.94862228456[/C][/ROW]
[ROW][C]8[/C][C]11477[/C][C]12352.0304912739[/C][C]-875.030491273861[/C][/ROW]
[ROW][C]9[/C][C]13578[/C][C]11756.7622053112[/C][C]1821.23779468875[/C][/ROW]
[ROW][C]10[/C][C]11555[/C][C]12995.7191458819[/C][C]-1440.71914588191[/C][/ROW]
[ROW][C]11[/C][C]11846[/C][C]12015.6225377350[/C][C]-169.622537734987[/C][/ROW]
[ROW][C]12[/C][C]11397[/C][C]11900.2312247407[/C][C]-503.231224740692[/C][/ROW]
[ROW][C]13[/C][C]10066[/C][C]11557.8916244850[/C][C]-1491.89162448497[/C][/ROW]
[ROW][C]14[/C][C]10269[/C][C]10542.9832538563[/C][C]-273.983253856313[/C][/ROW]
[ROW][C]15[/C][C]14279[/C][C]10356.5971295647[/C][C]3922.40287043528[/C][/ROW]
[ROW][C]16[/C][C]13870[/C][C]13024.9407550991[/C][C]845.059244900873[/C][/ROW]
[ROW][C]17[/C][C]13695[/C][C]13599.8201144649[/C][C]95.1798855351353[/C][/ROW]
[ROW][C]18[/C][C]14420[/C][C]13664.5693636460[/C][C]755.43063635396[/C][/ROW]
[ROW][C]19[/C][C]11424[/C][C]14178.4759126755[/C][C]-2754.47591267546[/C][/ROW]
[ROW][C]20[/C][C]9704[/C][C]12304.653032656[/C][C]-2600.653032656[/C][/ROW]
[ROW][C]21[/C][C]12464[/C][C]10535.4732285569[/C][C]1928.52677144308[/C][/ROW]
[ROW][C]22[/C][C]14301[/C][C]11847.4170260796[/C][C]2453.58297392043[/C][/ROW]
[ROW][C]23[/C][C]13464[/C][C]13516.547583149[/C][C]-52.5475831489912[/C][/ROW]
[ROW][C]24[/C][C]9893[/C][C]13480.8003605499[/C][C]-3587.80036054988[/C][/ROW]
[ROW][C]25[/C][C]11572[/C][C]11040.0811029941[/C][C]531.918897005868[/C][/ROW]
[ROW][C]26[/C][C]12380[/C][C]11401.9364363218[/C][C]978.063563678164[/C][/ROW]
[ROW][C]27[/C][C]16692[/C][C]12067.2963602550[/C][C]4624.70363974499[/C][/ROW]
[ROW][C]28[/C][C]16052[/C][C]15213.403194439[/C][C]838.596805561003[/C][/ROW]
[ROW][C]29[/C][C]16459[/C][C]15783.8862667869[/C][C]675.113733213082[/C][/ROW]
[ROW][C]30[/C][C]14761[/C][C]16243.154599499[/C][C]-1482.15459949899[/C][/ROW]
[ROW][C]31[/C][C]13654[/C][C]15234.8701605294[/C][C]-1580.87016052938[/C][/ROW]
[ROW][C]32[/C][C]13480[/C][C]14159.4312127759[/C][C]-679.431212775904[/C][/ROW]
[ROW][C]33[/C][C]18068[/C][C]13697.2257725177[/C][C]4370.77422748233[/C][/ROW]
[ROW][C]34[/C][C]16560[/C][C]16670.5887680578[/C][C]-110.588768057776[/C][/ROW]
[ROW][C]35[/C][C]14530[/C][C]16595.3571194867[/C][C]-2065.35711948673[/C][/ROW]
[ROW][C]36[/C][C]10650[/C][C]15190.3299750866[/C][C]-4540.32997508661[/C][/ROW]
[ROW][C]37[/C][C]11651[/C][C]12101.6211027365[/C][C]-450.621102736457[/C][/ROW]
[ROW][C]38[/C][C]13735[/C][C]11795.0712691941[/C][C]1939.92873080593[/C][/ROW]
[ROW][C]39[/C][C]13360[/C][C]13114.7716247730[/C][C]245.228375227049[/C][/ROW]
[ROW][C]40[/C][C]17818[/C][C]13281.5962966519[/C][C]4536.40370334814[/C][/ROW]
[ROW][C]41[/C][C]20613[/C][C]16367.6341934517[/C][C]4245.36580654831[/C][/ROW]
[ROW][C]42[/C][C]16231[/C][C]19255.6839838874[/C][C]-3024.68398388737[/C][/ROW]
[ROW][C]43[/C][C]13862[/C][C]17198.0431717986[/C][C]-3336.04317179857[/C][/ROW]
[ROW][C]44[/C][C]12004[/C][C]14928.5900263626[/C][C]-2924.59002636263[/C][/ROW]
[ROW][C]45[/C][C]17734[/C][C]12939.0414226313[/C][C]4794.95857736869[/C][/ROW]
[ROW][C]46[/C][C]15034[/C][C]16200.9697806440[/C][C]-1166.96978064402[/C][/ROW]
[ROW][C]47[/C][C]12609[/C][C]15407.1001863595[/C][C]-2798.10018635953[/C][/ROW]
[ROW][C]48[/C][C]12320[/C][C]13503.6004586402[/C][C]-1183.60045864020[/C][/ROW]
[ROW][C]49[/C][C]10833[/C][C]12698.4172983898[/C][C]-1865.41729838983[/C][/ROW]
[ROW][C]50[/C][C]11350[/C][C]11429.4057966295[/C][C]-79.4057966294968[/C][/ROW]
[ROW][C]51[/C][C]13648[/C][C]11375.3873904979[/C][C]2272.61260950207[/C][/ROW]
[ROW][C]52[/C][C]14890[/C][C]12921.4069020534[/C][C]1968.59309794664[/C][/ROW]
[ROW][C]53[/C][C]16325[/C][C]14260.6071366264[/C][C]2064.39286337358[/C][/ROW]
[ROW][C]54[/C][C]18045[/C][C]15664.9783140752[/C][C]2380.02168592481[/C][/ROW]
[ROW][C]55[/C][C]15616[/C][C]17284.0663843341[/C][C]-1668.06638433411[/C][/ROW]
[ROW][C]56[/C][C]11926[/C][C]16149.3093360067[/C][C]-4223.30933600669[/C][/ROW]
[ROW][C]57[/C][C]16855[/C][C]13276.2641854603[/C][C]3578.73581453972[/C][/ROW]
[ROW][C]58[/C][C]15083[/C][C]15710.8169873093[/C][C]-627.816987309274[/C][/ROW]
[ROW][C]59[/C][C]12520[/C][C]15283.7238223731[/C][C]-2763.72382237311[/C][/ROW]
[ROW][C]60[/C][C]12355[/C][C]13403.6097474646[/C][C]-1048.60974746461[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=102955&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=102955&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
21090010057843
31177110630.47849025921140.52150974082
41199211406.3557779392585.644222060762
51199311804.7595315530188.240468446978
61450411932.81630456682571.18369543315
71172713681.9486222846-1954.94862228456
81147712352.0304912739-875.030491273861
91357811756.76220531121821.23779468875
101155512995.7191458819-1440.71914588191
111184612015.6225377350-169.622537734987
121139711900.2312247407-503.231224740692
131006611557.8916244850-1491.89162448497
141026910542.9832538563-273.983253856313
151427910356.59712956473922.40287043528
161387013024.9407550991845.059244900873
171369513599.820114464995.1798855351353
181442013664.5693636460755.43063635396
191142414178.4759126755-2754.47591267546
20970412304.653032656-2600.653032656
211246410535.47322855691928.52677144308
221430111847.41702607962453.58297392043
231346413516.547583149-52.5475831489912
24989313480.8003605499-3587.80036054988
251157211040.0811029941531.918897005868
261238011401.9364363218978.063563678164
271669212067.29636025504624.70363974499
281605215213.403194439838.596805561003
291645915783.8862667869675.113733213082
301476116243.154599499-1482.15459949899
311365415234.8701605294-1580.87016052938
321348014159.4312127759-679.431212775904
331806813697.22577251774370.77422748233
341656016670.5887680578-110.588768057776
351453016595.3571194867-2065.35711948673
361065015190.3299750866-4540.32997508661
371165112101.6211027365-450.621102736457
381373511795.07126919411939.92873080593
391336013114.7716247730245.228375227049
401781813281.59629665194536.40370334814
412061316367.63419345174245.36580654831
421623119255.6839838874-3024.68398388737
431386217198.0431717986-3336.04317179857
441200414928.5900263626-2924.59002636263
451773412939.04142263134794.95857736869
461503416200.9697806440-1166.96978064402
471260915407.1001863595-2798.10018635953
481232013503.6004586402-1183.60045864020
491083312698.4172983898-1865.41729838983
501135011429.4057966295-79.4057966294968
511364811375.38739049792272.61260950207
521489012921.40690205341968.59309794664
531632514260.60713662642064.39286337358
541804515664.97831407522380.02168592481
551561617284.0663843341-1668.06638433411
561192616149.3093360067-4223.30933600669
571685513276.26418546033578.73581453972
581508315710.8169873093-627.816987309274
591252015283.7238223731-2763.72382237311
601235513403.6097474646-1048.60974746461







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
6112690.25846057608101.3215432534717279.1953778986
6212690.25846057607140.139242810118240.3776783420
6312690.25846057606322.424870440119058.0920507120
6412690.25846057605598.3767686756219782.1401524765
6512690.25846057604941.6929654562420438.8239556958
6612690.25846057604336.471981834221044.0449393179
6712690.25846057603772.2301004137621608.2868207383
6812690.25846057603241.6230494223522138.8938717297
6912690.25846057602739.2689402742322641.2479808778
7012690.25846057602261.0842970382023119.4326241139
7112690.25846057601803.8837180984523576.6332030536
7212690.25846057601365.1255106322424015.3914105198

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
61 & 12690.2584605760 & 8101.32154325347 & 17279.1953778986 \tabularnewline
62 & 12690.2584605760 & 7140.1392428101 & 18240.3776783420 \tabularnewline
63 & 12690.2584605760 & 6322.4248704401 & 19058.0920507120 \tabularnewline
64 & 12690.2584605760 & 5598.37676867562 & 19782.1401524765 \tabularnewline
65 & 12690.2584605760 & 4941.69296545624 & 20438.8239556958 \tabularnewline
66 & 12690.2584605760 & 4336.4719818342 & 21044.0449393179 \tabularnewline
67 & 12690.2584605760 & 3772.23010041376 & 21608.2868207383 \tabularnewline
68 & 12690.2584605760 & 3241.62304942235 & 22138.8938717297 \tabularnewline
69 & 12690.2584605760 & 2739.26894027423 & 22641.2479808778 \tabularnewline
70 & 12690.2584605760 & 2261.08429703820 & 23119.4326241139 \tabularnewline
71 & 12690.2584605760 & 1803.88371809845 & 23576.6332030536 \tabularnewline
72 & 12690.2584605760 & 1365.12551063224 & 24015.3914105198 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=102955&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]61[/C][C]12690.2584605760[/C][C]8101.32154325347[/C][C]17279.1953778986[/C][/ROW]
[ROW][C]62[/C][C]12690.2584605760[/C][C]7140.1392428101[/C][C]18240.3776783420[/C][/ROW]
[ROW][C]63[/C][C]12690.2584605760[/C][C]6322.4248704401[/C][C]19058.0920507120[/C][/ROW]
[ROW][C]64[/C][C]12690.2584605760[/C][C]5598.37676867562[/C][C]19782.1401524765[/C][/ROW]
[ROW][C]65[/C][C]12690.2584605760[/C][C]4941.69296545624[/C][C]20438.8239556958[/C][/ROW]
[ROW][C]66[/C][C]12690.2584605760[/C][C]4336.4719818342[/C][C]21044.0449393179[/C][/ROW]
[ROW][C]67[/C][C]12690.2584605760[/C][C]3772.23010041376[/C][C]21608.2868207383[/C][/ROW]
[ROW][C]68[/C][C]12690.2584605760[/C][C]3241.62304942235[/C][C]22138.8938717297[/C][/ROW]
[ROW][C]69[/C][C]12690.2584605760[/C][C]2739.26894027423[/C][C]22641.2479808778[/C][/ROW]
[ROW][C]70[/C][C]12690.2584605760[/C][C]2261.08429703820[/C][C]23119.4326241139[/C][/ROW]
[ROW][C]71[/C][C]12690.2584605760[/C][C]1803.88371809845[/C][C]23576.6332030536[/C][/ROW]
[ROW][C]72[/C][C]12690.2584605760[/C][C]1365.12551063224[/C][C]24015.3914105198[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=102955&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=102955&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
6112690.25846057608101.3215432534717279.1953778986
6212690.25846057607140.139242810118240.3776783420
6312690.25846057606322.424870440119058.0920507120
6412690.25846057605598.3767686756219782.1401524765
6512690.25846057604941.6929654562420438.8239556958
6612690.25846057604336.471981834221044.0449393179
6712690.25846057603772.2301004137621608.2868207383
6812690.25846057603241.6230494223522138.8938717297
6912690.25846057602739.2689402742322641.2479808778
7012690.25846057602261.0842970382023119.4326241139
7112690.25846057601803.8837180984523576.6332030536
7212690.25846057601365.1255106322424015.3914105198



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=0, beta=0)
if (par2 == 'Double') fit <- HoltWinters(x, gamma=0)
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')