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of Irreproducible Research!

Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationWed, 20 Jan 2010 06:30:12 -0700
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/Jan/20/t1263994301g65qspdvh9qeiln.htm/, Retrieved Mon, 06 May 2024 06:08:56 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=72306, Retrieved Mon, 06 May 2024 06:08:56 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywordsKDGP2W62
Estimated Impact178
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [] [2010-01-20 13:30:12] [9b42eb3f67be7a3fb50ab98e0efd6cc3] [Current]
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Dataseries X:
10.846
10.413
10.709
10.662
10.570
10.297
10.635
10.872
10.296
10.383
10.431
10.574
10.653
10.805
10.872
10.625
10.407
10.463
10.556
10.646
10.702
11.353
11.346
11.451
11.964
12.574
13.031
13.812
14.544
14.931
14.886
16.005
17.064
15.168
16.050
15.839
15.137
14.954
15.648
15.305
15.579
16.348
15.928
16.171
15.937
15.713
15.594
15.683
16.438
17.032
17.696
17.745
19.394
20.148
20.108
18.584
18.441
18.391
19.178
18.079
18.483
19.644
19.195
19.650
20.830
23.595
22.937
21.814
21.928
21.777
21.383
21.467




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time1 seconds
R Server'Gwilym Jenkins' @ 72.249.127.135

\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 & 1 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ 72.249.127.135 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=72306&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]1 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Gwilym Jenkins' @ 72.249.127.135[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=72306&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=72306&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 time1 seconds
R Server'Gwilym Jenkins' @ 72.249.127.135







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.824846748999328
beta0.0184321753657881
gamma1

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.824846748999328 \tabularnewline
beta & 0.0184321753657881 \tabularnewline
gamma & 1 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=72306&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]0.824846748999328[/C][/ROW]
[ROW][C]beta[/C][C]0.0184321753657881[/C][/ROW]
[ROW][C]gamma[/C][C]1[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=72306&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=72306&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
alpha0.824846748999328
beta0.0184321753657881
gamma1







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
1310.65310.61884695512820.0341530448717915
1410.80510.8272771840405-0.0222771840404850
1510.87210.8836140926889-0.011614092688923
1610.62510.58473650682720.0402634931728088
1710.40710.33705380054960.0699461994503903
1810.46310.39279322047300.0702067795269752
1910.55610.8778983165717-0.321898316571737
2010.64610.8539744137037-0.207974413703745
2110.70210.09302495367840.608975046321627
2211.35310.69606728589880.656932714101233
2311.34611.32323849880650.0227615011935320
2411.45111.5142033745942-0.0632033745942362
2511.96411.57178149249540.392218507504602
2612.57412.08444342805120.489556571948823
2713.03112.59138071045750.439619289542481
2813.81212.70719675573851.10480324426148
2914.54413.39238890400861.15161109599137
3014.93114.40642074811910.524579251880875
3114.88615.2705821796915-0.384582179691529
3216.00515.28690197130300.718098028696959
3317.06415.51898558783781.54501441216219
3415.16817.0028220489699-1.83482204896988
3516.0515.5260215147180.523978485282003
3615.83916.1853981436523-0.3463981436523
3715.13716.1548885669791-1.01788856697908
3814.95415.5657744386017-0.611774438601712
3915.64815.1830885055540.464911494445989
4015.30515.4642131771372-0.159213177137227
4115.57915.12370358641310.455296413586936
4216.34815.45168883854760.89631116145242
4315.92816.467014230709-0.539014230708997
4416.17116.5505260126632-0.379526012663245
4515.93716.0068238736702-0.0698238736701615
4615.71315.52687410527190.186125894728088
4715.59416.1211206455525-0.527120645552506
4815.68315.7359948118279-0.0529948118278867
4916.43815.80928764541570.628712354584263
5017.03216.65393695971720.378063040282843
5117.69617.29578732221310.400212677786904
5217.74517.43273128483330.312268715166656
5319.39417.61442699629591.77957300370412
5420.14819.15778822929630.990211770703663
5520.10820.04639853751490.0616014624851289
5618.58420.7096259065367-2.12562590653671
5718.44118.8097218746401-0.368721874640141
5818.39118.15333072589320.237669274106786
5919.17818.69122208590180.486777914098187
6018.07919.2669237749264-1.18792377492640
6118.48318.5476941381383-0.064694138138254
6219.64418.79016172956370.853838270436285
6319.19519.8492412889133-0.654241288913337
6419.6519.10589499537640.544105004623589
6520.8319.74422434805981.08577565194016
6623.59520.57490271941463.02009728058540
6722.93723.0039230022748-0.0669230022748337
6821.81423.2047979754168-1.3907979754168
6921.92822.2566745199270-0.328674519926960
7021.77721.7780692448329-0.00106924483286619
7121.38322.1975819504328-0.814581950432768
7221.46721.42165807837940.0453419216206044

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 10.653 & 10.6188469551282 & 0.0341530448717915 \tabularnewline
14 & 10.805 & 10.8272771840405 & -0.0222771840404850 \tabularnewline
15 & 10.872 & 10.8836140926889 & -0.011614092688923 \tabularnewline
16 & 10.625 & 10.5847365068272 & 0.0402634931728088 \tabularnewline
17 & 10.407 & 10.3370538005496 & 0.0699461994503903 \tabularnewline
18 & 10.463 & 10.3927932204730 & 0.0702067795269752 \tabularnewline
19 & 10.556 & 10.8778983165717 & -0.321898316571737 \tabularnewline
20 & 10.646 & 10.8539744137037 & -0.207974413703745 \tabularnewline
21 & 10.702 & 10.0930249536784 & 0.608975046321627 \tabularnewline
22 & 11.353 & 10.6960672858988 & 0.656932714101233 \tabularnewline
23 & 11.346 & 11.3232384988065 & 0.0227615011935320 \tabularnewline
24 & 11.451 & 11.5142033745942 & -0.0632033745942362 \tabularnewline
25 & 11.964 & 11.5717814924954 & 0.392218507504602 \tabularnewline
26 & 12.574 & 12.0844434280512 & 0.489556571948823 \tabularnewline
27 & 13.031 & 12.5913807104575 & 0.439619289542481 \tabularnewline
28 & 13.812 & 12.7071967557385 & 1.10480324426148 \tabularnewline
29 & 14.544 & 13.3923889040086 & 1.15161109599137 \tabularnewline
30 & 14.931 & 14.4064207481191 & 0.524579251880875 \tabularnewline
31 & 14.886 & 15.2705821796915 & -0.384582179691529 \tabularnewline
32 & 16.005 & 15.2869019713030 & 0.718098028696959 \tabularnewline
33 & 17.064 & 15.5189855878378 & 1.54501441216219 \tabularnewline
34 & 15.168 & 17.0028220489699 & -1.83482204896988 \tabularnewline
35 & 16.05 & 15.526021514718 & 0.523978485282003 \tabularnewline
36 & 15.839 & 16.1853981436523 & -0.3463981436523 \tabularnewline
37 & 15.137 & 16.1548885669791 & -1.01788856697908 \tabularnewline
38 & 14.954 & 15.5657744386017 & -0.611774438601712 \tabularnewline
39 & 15.648 & 15.183088505554 & 0.464911494445989 \tabularnewline
40 & 15.305 & 15.4642131771372 & -0.159213177137227 \tabularnewline
41 & 15.579 & 15.1237035864131 & 0.455296413586936 \tabularnewline
42 & 16.348 & 15.4516888385476 & 0.89631116145242 \tabularnewline
43 & 15.928 & 16.467014230709 & -0.539014230708997 \tabularnewline
44 & 16.171 & 16.5505260126632 & -0.379526012663245 \tabularnewline
45 & 15.937 & 16.0068238736702 & -0.0698238736701615 \tabularnewline
46 & 15.713 & 15.5268741052719 & 0.186125894728088 \tabularnewline
47 & 15.594 & 16.1211206455525 & -0.527120645552506 \tabularnewline
48 & 15.683 & 15.7359948118279 & -0.0529948118278867 \tabularnewline
49 & 16.438 & 15.8092876454157 & 0.628712354584263 \tabularnewline
50 & 17.032 & 16.6539369597172 & 0.378063040282843 \tabularnewline
51 & 17.696 & 17.2957873222131 & 0.400212677786904 \tabularnewline
52 & 17.745 & 17.4327312848333 & 0.312268715166656 \tabularnewline
53 & 19.394 & 17.6144269962959 & 1.77957300370412 \tabularnewline
54 & 20.148 & 19.1577882292963 & 0.990211770703663 \tabularnewline
55 & 20.108 & 20.0463985375149 & 0.0616014624851289 \tabularnewline
56 & 18.584 & 20.7096259065367 & -2.12562590653671 \tabularnewline
57 & 18.441 & 18.8097218746401 & -0.368721874640141 \tabularnewline
58 & 18.391 & 18.1533307258932 & 0.237669274106786 \tabularnewline
59 & 19.178 & 18.6912220859018 & 0.486777914098187 \tabularnewline
60 & 18.079 & 19.2669237749264 & -1.18792377492640 \tabularnewline
61 & 18.483 & 18.5476941381383 & -0.064694138138254 \tabularnewline
62 & 19.644 & 18.7901617295637 & 0.853838270436285 \tabularnewline
63 & 19.195 & 19.8492412889133 & -0.654241288913337 \tabularnewline
64 & 19.65 & 19.1058949953764 & 0.544105004623589 \tabularnewline
65 & 20.83 & 19.7442243480598 & 1.08577565194016 \tabularnewline
66 & 23.595 & 20.5749027194146 & 3.02009728058540 \tabularnewline
67 & 22.937 & 23.0039230022748 & -0.0669230022748337 \tabularnewline
68 & 21.814 & 23.2047979754168 & -1.3907979754168 \tabularnewline
69 & 21.928 & 22.2566745199270 & -0.328674519926960 \tabularnewline
70 & 21.777 & 21.7780692448329 & -0.00106924483286619 \tabularnewline
71 & 21.383 & 22.1975819504328 & -0.814581950432768 \tabularnewline
72 & 21.467 & 21.4216580783794 & 0.0453419216206044 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=72306&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]10.653[/C][C]10.6188469551282[/C][C]0.0341530448717915[/C][/ROW]
[ROW][C]14[/C][C]10.805[/C][C]10.8272771840405[/C][C]-0.0222771840404850[/C][/ROW]
[ROW][C]15[/C][C]10.872[/C][C]10.8836140926889[/C][C]-0.011614092688923[/C][/ROW]
[ROW][C]16[/C][C]10.625[/C][C]10.5847365068272[/C][C]0.0402634931728088[/C][/ROW]
[ROW][C]17[/C][C]10.407[/C][C]10.3370538005496[/C][C]0.0699461994503903[/C][/ROW]
[ROW][C]18[/C][C]10.463[/C][C]10.3927932204730[/C][C]0.0702067795269752[/C][/ROW]
[ROW][C]19[/C][C]10.556[/C][C]10.8778983165717[/C][C]-0.321898316571737[/C][/ROW]
[ROW][C]20[/C][C]10.646[/C][C]10.8539744137037[/C][C]-0.207974413703745[/C][/ROW]
[ROW][C]21[/C][C]10.702[/C][C]10.0930249536784[/C][C]0.608975046321627[/C][/ROW]
[ROW][C]22[/C][C]11.353[/C][C]10.6960672858988[/C][C]0.656932714101233[/C][/ROW]
[ROW][C]23[/C][C]11.346[/C][C]11.3232384988065[/C][C]0.0227615011935320[/C][/ROW]
[ROW][C]24[/C][C]11.451[/C][C]11.5142033745942[/C][C]-0.0632033745942362[/C][/ROW]
[ROW][C]25[/C][C]11.964[/C][C]11.5717814924954[/C][C]0.392218507504602[/C][/ROW]
[ROW][C]26[/C][C]12.574[/C][C]12.0844434280512[/C][C]0.489556571948823[/C][/ROW]
[ROW][C]27[/C][C]13.031[/C][C]12.5913807104575[/C][C]0.439619289542481[/C][/ROW]
[ROW][C]28[/C][C]13.812[/C][C]12.7071967557385[/C][C]1.10480324426148[/C][/ROW]
[ROW][C]29[/C][C]14.544[/C][C]13.3923889040086[/C][C]1.15161109599137[/C][/ROW]
[ROW][C]30[/C][C]14.931[/C][C]14.4064207481191[/C][C]0.524579251880875[/C][/ROW]
[ROW][C]31[/C][C]14.886[/C][C]15.2705821796915[/C][C]-0.384582179691529[/C][/ROW]
[ROW][C]32[/C][C]16.005[/C][C]15.2869019713030[/C][C]0.718098028696959[/C][/ROW]
[ROW][C]33[/C][C]17.064[/C][C]15.5189855878378[/C][C]1.54501441216219[/C][/ROW]
[ROW][C]34[/C][C]15.168[/C][C]17.0028220489699[/C][C]-1.83482204896988[/C][/ROW]
[ROW][C]35[/C][C]16.05[/C][C]15.526021514718[/C][C]0.523978485282003[/C][/ROW]
[ROW][C]36[/C][C]15.839[/C][C]16.1853981436523[/C][C]-0.3463981436523[/C][/ROW]
[ROW][C]37[/C][C]15.137[/C][C]16.1548885669791[/C][C]-1.01788856697908[/C][/ROW]
[ROW][C]38[/C][C]14.954[/C][C]15.5657744386017[/C][C]-0.611774438601712[/C][/ROW]
[ROW][C]39[/C][C]15.648[/C][C]15.183088505554[/C][C]0.464911494445989[/C][/ROW]
[ROW][C]40[/C][C]15.305[/C][C]15.4642131771372[/C][C]-0.159213177137227[/C][/ROW]
[ROW][C]41[/C][C]15.579[/C][C]15.1237035864131[/C][C]0.455296413586936[/C][/ROW]
[ROW][C]42[/C][C]16.348[/C][C]15.4516888385476[/C][C]0.89631116145242[/C][/ROW]
[ROW][C]43[/C][C]15.928[/C][C]16.467014230709[/C][C]-0.539014230708997[/C][/ROW]
[ROW][C]44[/C][C]16.171[/C][C]16.5505260126632[/C][C]-0.379526012663245[/C][/ROW]
[ROW][C]45[/C][C]15.937[/C][C]16.0068238736702[/C][C]-0.0698238736701615[/C][/ROW]
[ROW][C]46[/C][C]15.713[/C][C]15.5268741052719[/C][C]0.186125894728088[/C][/ROW]
[ROW][C]47[/C][C]15.594[/C][C]16.1211206455525[/C][C]-0.527120645552506[/C][/ROW]
[ROW][C]48[/C][C]15.683[/C][C]15.7359948118279[/C][C]-0.0529948118278867[/C][/ROW]
[ROW][C]49[/C][C]16.438[/C][C]15.8092876454157[/C][C]0.628712354584263[/C][/ROW]
[ROW][C]50[/C][C]17.032[/C][C]16.6539369597172[/C][C]0.378063040282843[/C][/ROW]
[ROW][C]51[/C][C]17.696[/C][C]17.2957873222131[/C][C]0.400212677786904[/C][/ROW]
[ROW][C]52[/C][C]17.745[/C][C]17.4327312848333[/C][C]0.312268715166656[/C][/ROW]
[ROW][C]53[/C][C]19.394[/C][C]17.6144269962959[/C][C]1.77957300370412[/C][/ROW]
[ROW][C]54[/C][C]20.148[/C][C]19.1577882292963[/C][C]0.990211770703663[/C][/ROW]
[ROW][C]55[/C][C]20.108[/C][C]20.0463985375149[/C][C]0.0616014624851289[/C][/ROW]
[ROW][C]56[/C][C]18.584[/C][C]20.7096259065367[/C][C]-2.12562590653671[/C][/ROW]
[ROW][C]57[/C][C]18.441[/C][C]18.8097218746401[/C][C]-0.368721874640141[/C][/ROW]
[ROW][C]58[/C][C]18.391[/C][C]18.1533307258932[/C][C]0.237669274106786[/C][/ROW]
[ROW][C]59[/C][C]19.178[/C][C]18.6912220859018[/C][C]0.486777914098187[/C][/ROW]
[ROW][C]60[/C][C]18.079[/C][C]19.2669237749264[/C][C]-1.18792377492640[/C][/ROW]
[ROW][C]61[/C][C]18.483[/C][C]18.5476941381383[/C][C]-0.064694138138254[/C][/ROW]
[ROW][C]62[/C][C]19.644[/C][C]18.7901617295637[/C][C]0.853838270436285[/C][/ROW]
[ROW][C]63[/C][C]19.195[/C][C]19.8492412889133[/C][C]-0.654241288913337[/C][/ROW]
[ROW][C]64[/C][C]19.65[/C][C]19.1058949953764[/C][C]0.544105004623589[/C][/ROW]
[ROW][C]65[/C][C]20.83[/C][C]19.7442243480598[/C][C]1.08577565194016[/C][/ROW]
[ROW][C]66[/C][C]23.595[/C][C]20.5749027194146[/C][C]3.02009728058540[/C][/ROW]
[ROW][C]67[/C][C]22.937[/C][C]23.0039230022748[/C][C]-0.0669230022748337[/C][/ROW]
[ROW][C]68[/C][C]21.814[/C][C]23.2047979754168[/C][C]-1.3907979754168[/C][/ROW]
[ROW][C]69[/C][C]21.928[/C][C]22.2566745199270[/C][C]-0.328674519926960[/C][/ROW]
[ROW][C]70[/C][C]21.777[/C][C]21.7780692448329[/C][C]-0.00106924483286619[/C][/ROW]
[ROW][C]71[/C][C]21.383[/C][C]22.1975819504328[/C][C]-0.814581950432768[/C][/ROW]
[ROW][C]72[/C][C]21.467[/C][C]21.4216580783794[/C][C]0.0453419216206044[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=72306&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=72306&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
1310.65310.61884695512820.0341530448717915
1410.80510.8272771840405-0.0222771840404850
1510.87210.8836140926889-0.011614092688923
1610.62510.58473650682720.0402634931728088
1710.40710.33705380054960.0699461994503903
1810.46310.39279322047300.0702067795269752
1910.55610.8778983165717-0.321898316571737
2010.64610.8539744137037-0.207974413703745
2110.70210.09302495367840.608975046321627
2211.35310.69606728589880.656932714101233
2311.34611.32323849880650.0227615011935320
2411.45111.5142033745942-0.0632033745942362
2511.96411.57178149249540.392218507504602
2612.57412.08444342805120.489556571948823
2713.03112.59138071045750.439619289542481
2813.81212.70719675573851.10480324426148
2914.54413.39238890400861.15161109599137
3014.93114.40642074811910.524579251880875
3114.88615.2705821796915-0.384582179691529
3216.00515.28690197130300.718098028696959
3317.06415.51898558783781.54501441216219
3415.16817.0028220489699-1.83482204896988
3516.0515.5260215147180.523978485282003
3615.83916.1853981436523-0.3463981436523
3715.13716.1548885669791-1.01788856697908
3814.95415.5657744386017-0.611774438601712
3915.64815.1830885055540.464911494445989
4015.30515.4642131771372-0.159213177137227
4115.57915.12370358641310.455296413586936
4216.34815.45168883854760.89631116145242
4315.92816.467014230709-0.539014230708997
4416.17116.5505260126632-0.379526012663245
4515.93716.0068238736702-0.0698238736701615
4615.71315.52687410527190.186125894728088
4715.59416.1211206455525-0.527120645552506
4815.68315.7359948118279-0.0529948118278867
4916.43815.80928764541570.628712354584263
5017.03216.65393695971720.378063040282843
5117.69617.29578732221310.400212677786904
5217.74517.43273128483330.312268715166656
5319.39417.61442699629591.77957300370412
5420.14819.15778822929630.990211770703663
5520.10820.04639853751490.0616014624851289
5618.58420.7096259065367-2.12562590653671
5718.44118.8097218746401-0.368721874640141
5818.39118.15333072589320.237669274106786
5919.17818.69122208590180.486777914098187
6018.07919.2669237749264-1.18792377492640
6118.48318.5476941381383-0.064694138138254
6219.64418.79016172956370.853838270436285
6319.19519.8492412889133-0.654241288913337
6419.6519.10589499537640.544105004623589
6520.8319.74422434805981.08577565194016
6623.59520.57490271941463.02009728058540
6722.93723.0039230022748-0.0669230022748337
6821.81423.2047979754168-1.3907979754168
6921.92822.2566745199270-0.328674519926960
7021.77721.7780692448329-0.00106924483286619
7121.38322.1975819504328-0.814581950432768
7221.46721.42165807837940.0453419216206044







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
7321.950297528538220.348620459761323.5519745973151
7422.441871962548820.35005179272624.5336921323717
7522.554399400394320.053964228438725.0548345723500
7622.592421695162119.729564957973925.4552784323502
7722.900376297360919.705346476748726.0954061179732
7823.181304163736619.675571343603326.6870369838699
7922.539633961316818.739242423786826.3400254988468
8022.52597520515818.443348448044026.608601962272
8122.894372672596418.539381881507027.2493634636857
8222.732543069266618.113184620041127.3519015184921
8322.998753032919618.12160116938627.8759048964532
8423.046042262154717.916564293659328.1755202306501

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
73 & 21.9502975285382 & 20.3486204597613 & 23.5519745973151 \tabularnewline
74 & 22.4418719625488 & 20.350051792726 & 24.5336921323717 \tabularnewline
75 & 22.5543994003943 & 20.0539642284387 & 25.0548345723500 \tabularnewline
76 & 22.5924216951621 & 19.7295649579739 & 25.4552784323502 \tabularnewline
77 & 22.9003762973609 & 19.7053464767487 & 26.0954061179732 \tabularnewline
78 & 23.1813041637366 & 19.6755713436033 & 26.6870369838699 \tabularnewline
79 & 22.5396339613168 & 18.7392424237868 & 26.3400254988468 \tabularnewline
80 & 22.525975205158 & 18.4433484480440 & 26.608601962272 \tabularnewline
81 & 22.8943726725964 & 18.5393818815070 & 27.2493634636857 \tabularnewline
82 & 22.7325430692666 & 18.1131846200411 & 27.3519015184921 \tabularnewline
83 & 22.9987530329196 & 18.121601169386 & 27.8759048964532 \tabularnewline
84 & 23.0460422621547 & 17.9165642936593 & 28.1755202306501 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=72306&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]21.9502975285382[/C][C]20.3486204597613[/C][C]23.5519745973151[/C][/ROW]
[ROW][C]74[/C][C]22.4418719625488[/C][C]20.350051792726[/C][C]24.5336921323717[/C][/ROW]
[ROW][C]75[/C][C]22.5543994003943[/C][C]20.0539642284387[/C][C]25.0548345723500[/C][/ROW]
[ROW][C]76[/C][C]22.5924216951621[/C][C]19.7295649579739[/C][C]25.4552784323502[/C][/ROW]
[ROW][C]77[/C][C]22.9003762973609[/C][C]19.7053464767487[/C][C]26.0954061179732[/C][/ROW]
[ROW][C]78[/C][C]23.1813041637366[/C][C]19.6755713436033[/C][C]26.6870369838699[/C][/ROW]
[ROW][C]79[/C][C]22.5396339613168[/C][C]18.7392424237868[/C][C]26.3400254988468[/C][/ROW]
[ROW][C]80[/C][C]22.525975205158[/C][C]18.4433484480440[/C][C]26.608601962272[/C][/ROW]
[ROW][C]81[/C][C]22.8943726725964[/C][C]18.5393818815070[/C][C]27.2493634636857[/C][/ROW]
[ROW][C]82[/C][C]22.7325430692666[/C][C]18.1131846200411[/C][C]27.3519015184921[/C][/ROW]
[ROW][C]83[/C][C]22.9987530329196[/C][C]18.121601169386[/C][C]27.8759048964532[/C][/ROW]
[ROW][C]84[/C][C]23.0460422621547[/C][C]17.9165642936593[/C][C]28.1755202306501[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=72306&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=72306&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
7321.950297528538220.348620459761323.5519745973151
7422.441871962548820.35005179272624.5336921323717
7522.554399400394320.053964228438725.0548345723500
7622.592421695162119.729564957973925.4552784323502
7722.900376297360919.705346476748726.0954061179732
7823.181304163736619.675571343603326.6870369838699
7922.539633961316818.739242423786826.3400254988468
8022.52597520515818.443348448044026.608601962272
8122.894372672596418.539381881507027.2493634636857
8222.732543069266618.113184620041127.3519015184921
8322.998753032919618.12160116938627.8759048964532
8423.046042262154717.916564293659328.1755202306501



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')