Free Statistics

of Irreproducible Research!

Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationMon, 18 Aug 2014 13:24:52 +0100
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2014/Aug/18/t1408364718pc7spxf0f9e39fb.htm/, Retrieved Thu, 16 May 2024 08:21:23 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=235713, Retrieved Thu, 16 May 2024 08:21:23 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywordsVan Reusel Raphael
Estimated Impact77
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [Tijdreeks 2] [2014-08-18 12:24:52] [bf566d88435d8cc6ce5d208f6f8dd684] [Current]
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Dataseries X:
770
710
890
730
790
820
810
810
760
840
830
890
800
710
850
790
800
840
850
810
760
860
860
880
770
740
850
790
860
820
900
800
660
820
850
850
760
730
770
880
890
790
930
770
680
810
870
850
820
740
800
920
970
780
880
750
620
760
930
820
900
700
810
970
820
740
930
720
580
800
910
810
890
710
830
900
830
680
980
690
530
740
930
770
870
660
770
900
830
660
1000
710
460
740
940
870
810
650
760
950
870
670
960
750
480
690
850
890




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 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 & 2 seconds \tabularnewline
R Server & 'George Udny Yule' @ yule.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=235713&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]'George Udny Yule' @ yule.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=235713&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=235713&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'George Udny Yule' @ yule.wessa.net







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.0519459889267136
beta0.0750253924507982
gamma1

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.0519459889267136 \tabularnewline
beta & 0.0750253924507982 \tabularnewline
gamma & 1 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=235713&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]0.0519459889267136[/C][/ROW]
[ROW][C]beta[/C][C]0.0750253924507982[/C][/ROW]
[ROW][C]gamma[/C][C]1[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=235713&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=235713&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
alpha0.0519459889267136
beta0.0750253924507982
gamma1







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
13800791.7948717948728.20512820512806
14710701.8509749769368.1490250230645
15850843.602589426526.39741057348033
16790784.4548136227945.54518637720616
17800794.0343792689665.9656207310336
18840834.9090344174285.09096558257181
19850819.09142893086730.9085710691332
20810820.985403484329-10.9854034843288
21760773.577007702483-13.5770077024835
22860853.4810752361756.51892476382466
23860842.37111852011717.6288814798834
24880903.573650638563-23.5736506385629
25770819.072908346953-49.0729083469533
26740726.05757139163513.9424286083646
27850866.429196224408-16.429196224408
28790805.178445189682-15.1784451896817
29860813.8900602256646.1099397743404
30820855.987249033209-35.9872490332092
31900862.31860431156937.6813956884313
32800824.679369645185-24.6793696451847
33660773.881997738412-113.881997738412
34820867.016088566592-47.0160885665917
35850862.837837178304-12.8378371783042
36850882.456578161393-32.4565781613927
37760772.346169250171-12.346169250171
38730740.150155374442-10.1501553744417
39770849.55200443689-79.5520044368897
40880785.0377278035694.9622721964404
41890856.83433000109733.1656699989026
42790819.635018954846-29.635018954846
43930895.37142975697534.6285702430249
44770797.673570197904-27.6735701979037
45680661.36141386992718.6385861300731
46810824.498040782403-14.4980407824025
47870854.26466132579715.735338674203
48850856.732256895305-6.73225689530454
49820767.08835049491252.9116495050879
50740740.682958905662-0.682958905662076
51800785.1355862680614.8644137319403
52920891.69848670038528.3015132996146
53970901.90968131532168.0903186846789
54780807.586099390088-27.5860993900884
55880944.962260807208-64.9622608072082
56750783.245094675278-33.2450946752775
57620690.748063619036-70.7480636190359
58760817.675854859926-57.6758548599262
59930873.54391659580956.4560834041913
60820856.666475867346-36.6664758673463
61900821.73676832486178.2632316751385
62700745.660024947915-45.6600249479151
63810802.1630541183317.83694588166918
64970920.71964499070649.2803550092945
65820969.443946063552-149.443946063552
66740771.967533573655-31.9675335736551
67930872.51801554906757.4819844509327
68720746.544659700596-26.5446597005961
69580618.180698927142-38.1806989271416
70800758.66016753237641.3398324676243
71910927.727603069701-17.7276030697009
72810818.274951964762-8.27495196476195
73890893.453840237506-3.45384023750637
74710695.00200869674314.9979913032566
75830804.96612329669125.0338767033091
76900963.365764068593-63.3657640685931
77830817.0573162844812.9426837155203
78680739.243222110856-59.2432221108562
79980922.92651532598757.0734846740128
80690717.015249997209-27.0152499972086
81530577.338523736549-47.3385237365494
82740792.439621780532-52.4396217805321
83930899.97857090899130.0214290910087
84770801.496104348165-31.4961043481654
85870879.477112201233-9.4771122012329
86660697.619945433331-37.6199454333309
87770813.574481158246-43.5744811582463
88900883.54432422527116.4556757747292
89830812.97966093561217.0203390643876
90660666.209989620212-6.20998962021179
911000962.39809427637837.6019057236224
92710675.15423767747234.8457623225285
93460519.064011993062-59.0640119930621
94740728.31483442187611.685165578124
95940917.20718350487422.792816495126
96870759.843947768199110.156052231801
97810866.427139831537-56.4271398315367
98650655.635933698087-5.635933698087
99760767.917091514869-7.91709151486918
100950897.10039287659952.8996071234013
101870829.55557757428740.4444224257131
102670662.6617777175297.33822228247072
1039601001.82519233983-41.8251923398253
104750708.2683866612141.7316133387897
105480463.95709399006916.0429060099306
106690744.928951821339-54.928951821339
107850941.377495318284-91.3774953182843
108890860.94956117592429.0504388240759

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 800 & 791.794871794872 & 8.20512820512806 \tabularnewline
14 & 710 & 701.850974976936 & 8.1490250230645 \tabularnewline
15 & 850 & 843.60258942652 & 6.39741057348033 \tabularnewline
16 & 790 & 784.454813622794 & 5.54518637720616 \tabularnewline
17 & 800 & 794.034379268966 & 5.9656207310336 \tabularnewline
18 & 840 & 834.909034417428 & 5.09096558257181 \tabularnewline
19 & 850 & 819.091428930867 & 30.9085710691332 \tabularnewline
20 & 810 & 820.985403484329 & -10.9854034843288 \tabularnewline
21 & 760 & 773.577007702483 & -13.5770077024835 \tabularnewline
22 & 860 & 853.481075236175 & 6.51892476382466 \tabularnewline
23 & 860 & 842.371118520117 & 17.6288814798834 \tabularnewline
24 & 880 & 903.573650638563 & -23.5736506385629 \tabularnewline
25 & 770 & 819.072908346953 & -49.0729083469533 \tabularnewline
26 & 740 & 726.057571391635 & 13.9424286083646 \tabularnewline
27 & 850 & 866.429196224408 & -16.429196224408 \tabularnewline
28 & 790 & 805.178445189682 & -15.1784451896817 \tabularnewline
29 & 860 & 813.89006022566 & 46.1099397743404 \tabularnewline
30 & 820 & 855.987249033209 & -35.9872490332092 \tabularnewline
31 & 900 & 862.318604311569 & 37.6813956884313 \tabularnewline
32 & 800 & 824.679369645185 & -24.6793696451847 \tabularnewline
33 & 660 & 773.881997738412 & -113.881997738412 \tabularnewline
34 & 820 & 867.016088566592 & -47.0160885665917 \tabularnewline
35 & 850 & 862.837837178304 & -12.8378371783042 \tabularnewline
36 & 850 & 882.456578161393 & -32.4565781613927 \tabularnewline
37 & 760 & 772.346169250171 & -12.346169250171 \tabularnewline
38 & 730 & 740.150155374442 & -10.1501553744417 \tabularnewline
39 & 770 & 849.55200443689 & -79.5520044368897 \tabularnewline
40 & 880 & 785.03772780356 & 94.9622721964404 \tabularnewline
41 & 890 & 856.834330001097 & 33.1656699989026 \tabularnewline
42 & 790 & 819.635018954846 & -29.635018954846 \tabularnewline
43 & 930 & 895.371429756975 & 34.6285702430249 \tabularnewline
44 & 770 & 797.673570197904 & -27.6735701979037 \tabularnewline
45 & 680 & 661.361413869927 & 18.6385861300731 \tabularnewline
46 & 810 & 824.498040782403 & -14.4980407824025 \tabularnewline
47 & 870 & 854.264661325797 & 15.735338674203 \tabularnewline
48 & 850 & 856.732256895305 & -6.73225689530454 \tabularnewline
49 & 820 & 767.088350494912 & 52.9116495050879 \tabularnewline
50 & 740 & 740.682958905662 & -0.682958905662076 \tabularnewline
51 & 800 & 785.13558626806 & 14.8644137319403 \tabularnewline
52 & 920 & 891.698486700385 & 28.3015132996146 \tabularnewline
53 & 970 & 901.909681315321 & 68.0903186846789 \tabularnewline
54 & 780 & 807.586099390088 & -27.5860993900884 \tabularnewline
55 & 880 & 944.962260807208 & -64.9622608072082 \tabularnewline
56 & 750 & 783.245094675278 & -33.2450946752775 \tabularnewline
57 & 620 & 690.748063619036 & -70.7480636190359 \tabularnewline
58 & 760 & 817.675854859926 & -57.6758548599262 \tabularnewline
59 & 930 & 873.543916595809 & 56.4560834041913 \tabularnewline
60 & 820 & 856.666475867346 & -36.6664758673463 \tabularnewline
61 & 900 & 821.736768324861 & 78.2632316751385 \tabularnewline
62 & 700 & 745.660024947915 & -45.6600249479151 \tabularnewline
63 & 810 & 802.163054118331 & 7.83694588166918 \tabularnewline
64 & 970 & 920.719644990706 & 49.2803550092945 \tabularnewline
65 & 820 & 969.443946063552 & -149.443946063552 \tabularnewline
66 & 740 & 771.967533573655 & -31.9675335736551 \tabularnewline
67 & 930 & 872.518015549067 & 57.4819844509327 \tabularnewline
68 & 720 & 746.544659700596 & -26.5446597005961 \tabularnewline
69 & 580 & 618.180698927142 & -38.1806989271416 \tabularnewline
70 & 800 & 758.660167532376 & 41.3398324676243 \tabularnewline
71 & 910 & 927.727603069701 & -17.7276030697009 \tabularnewline
72 & 810 & 818.274951964762 & -8.27495196476195 \tabularnewline
73 & 890 & 893.453840237506 & -3.45384023750637 \tabularnewline
74 & 710 & 695.002008696743 & 14.9979913032566 \tabularnewline
75 & 830 & 804.966123296691 & 25.0338767033091 \tabularnewline
76 & 900 & 963.365764068593 & -63.3657640685931 \tabularnewline
77 & 830 & 817.05731628448 & 12.9426837155203 \tabularnewline
78 & 680 & 739.243222110856 & -59.2432221108562 \tabularnewline
79 & 980 & 922.926515325987 & 57.0734846740128 \tabularnewline
80 & 690 & 717.015249997209 & -27.0152499972086 \tabularnewline
81 & 530 & 577.338523736549 & -47.3385237365494 \tabularnewline
82 & 740 & 792.439621780532 & -52.4396217805321 \tabularnewline
83 & 930 & 899.978570908991 & 30.0214290910087 \tabularnewline
84 & 770 & 801.496104348165 & -31.4961043481654 \tabularnewline
85 & 870 & 879.477112201233 & -9.4771122012329 \tabularnewline
86 & 660 & 697.619945433331 & -37.6199454333309 \tabularnewline
87 & 770 & 813.574481158246 & -43.5744811582463 \tabularnewline
88 & 900 & 883.544324225271 & 16.4556757747292 \tabularnewline
89 & 830 & 812.979660935612 & 17.0203390643876 \tabularnewline
90 & 660 & 666.209989620212 & -6.20998962021179 \tabularnewline
91 & 1000 & 962.398094276378 & 37.6019057236224 \tabularnewline
92 & 710 & 675.154237677472 & 34.8457623225285 \tabularnewline
93 & 460 & 519.064011993062 & -59.0640119930621 \tabularnewline
94 & 740 & 728.314834421876 & 11.685165578124 \tabularnewline
95 & 940 & 917.207183504874 & 22.792816495126 \tabularnewline
96 & 870 & 759.843947768199 & 110.156052231801 \tabularnewline
97 & 810 & 866.427139831537 & -56.4271398315367 \tabularnewline
98 & 650 & 655.635933698087 & -5.635933698087 \tabularnewline
99 & 760 & 767.917091514869 & -7.91709151486918 \tabularnewline
100 & 950 & 897.100392876599 & 52.8996071234013 \tabularnewline
101 & 870 & 829.555577574287 & 40.4444224257131 \tabularnewline
102 & 670 & 662.661777717529 & 7.33822228247072 \tabularnewline
103 & 960 & 1001.82519233983 & -41.8251923398253 \tabularnewline
104 & 750 & 708.26838666121 & 41.7316133387897 \tabularnewline
105 & 480 & 463.957093990069 & 16.0429060099306 \tabularnewline
106 & 690 & 744.928951821339 & -54.928951821339 \tabularnewline
107 & 850 & 941.377495318284 & -91.3774953182843 \tabularnewline
108 & 890 & 860.949561175924 & 29.0504388240759 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=235713&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]800[/C][C]791.794871794872[/C][C]8.20512820512806[/C][/ROW]
[ROW][C]14[/C][C]710[/C][C]701.850974976936[/C][C]8.1490250230645[/C][/ROW]
[ROW][C]15[/C][C]850[/C][C]843.60258942652[/C][C]6.39741057348033[/C][/ROW]
[ROW][C]16[/C][C]790[/C][C]784.454813622794[/C][C]5.54518637720616[/C][/ROW]
[ROW][C]17[/C][C]800[/C][C]794.034379268966[/C][C]5.9656207310336[/C][/ROW]
[ROW][C]18[/C][C]840[/C][C]834.909034417428[/C][C]5.09096558257181[/C][/ROW]
[ROW][C]19[/C][C]850[/C][C]819.091428930867[/C][C]30.9085710691332[/C][/ROW]
[ROW][C]20[/C][C]810[/C][C]820.985403484329[/C][C]-10.9854034843288[/C][/ROW]
[ROW][C]21[/C][C]760[/C][C]773.577007702483[/C][C]-13.5770077024835[/C][/ROW]
[ROW][C]22[/C][C]860[/C][C]853.481075236175[/C][C]6.51892476382466[/C][/ROW]
[ROW][C]23[/C][C]860[/C][C]842.371118520117[/C][C]17.6288814798834[/C][/ROW]
[ROW][C]24[/C][C]880[/C][C]903.573650638563[/C][C]-23.5736506385629[/C][/ROW]
[ROW][C]25[/C][C]770[/C][C]819.072908346953[/C][C]-49.0729083469533[/C][/ROW]
[ROW][C]26[/C][C]740[/C][C]726.057571391635[/C][C]13.9424286083646[/C][/ROW]
[ROW][C]27[/C][C]850[/C][C]866.429196224408[/C][C]-16.429196224408[/C][/ROW]
[ROW][C]28[/C][C]790[/C][C]805.178445189682[/C][C]-15.1784451896817[/C][/ROW]
[ROW][C]29[/C][C]860[/C][C]813.89006022566[/C][C]46.1099397743404[/C][/ROW]
[ROW][C]30[/C][C]820[/C][C]855.987249033209[/C][C]-35.9872490332092[/C][/ROW]
[ROW][C]31[/C][C]900[/C][C]862.318604311569[/C][C]37.6813956884313[/C][/ROW]
[ROW][C]32[/C][C]800[/C][C]824.679369645185[/C][C]-24.6793696451847[/C][/ROW]
[ROW][C]33[/C][C]660[/C][C]773.881997738412[/C][C]-113.881997738412[/C][/ROW]
[ROW][C]34[/C][C]820[/C][C]867.016088566592[/C][C]-47.0160885665917[/C][/ROW]
[ROW][C]35[/C][C]850[/C][C]862.837837178304[/C][C]-12.8378371783042[/C][/ROW]
[ROW][C]36[/C][C]850[/C][C]882.456578161393[/C][C]-32.4565781613927[/C][/ROW]
[ROW][C]37[/C][C]760[/C][C]772.346169250171[/C][C]-12.346169250171[/C][/ROW]
[ROW][C]38[/C][C]730[/C][C]740.150155374442[/C][C]-10.1501553744417[/C][/ROW]
[ROW][C]39[/C][C]770[/C][C]849.55200443689[/C][C]-79.5520044368897[/C][/ROW]
[ROW][C]40[/C][C]880[/C][C]785.03772780356[/C][C]94.9622721964404[/C][/ROW]
[ROW][C]41[/C][C]890[/C][C]856.834330001097[/C][C]33.1656699989026[/C][/ROW]
[ROW][C]42[/C][C]790[/C][C]819.635018954846[/C][C]-29.635018954846[/C][/ROW]
[ROW][C]43[/C][C]930[/C][C]895.371429756975[/C][C]34.6285702430249[/C][/ROW]
[ROW][C]44[/C][C]770[/C][C]797.673570197904[/C][C]-27.6735701979037[/C][/ROW]
[ROW][C]45[/C][C]680[/C][C]661.361413869927[/C][C]18.6385861300731[/C][/ROW]
[ROW][C]46[/C][C]810[/C][C]824.498040782403[/C][C]-14.4980407824025[/C][/ROW]
[ROW][C]47[/C][C]870[/C][C]854.264661325797[/C][C]15.735338674203[/C][/ROW]
[ROW][C]48[/C][C]850[/C][C]856.732256895305[/C][C]-6.73225689530454[/C][/ROW]
[ROW][C]49[/C][C]820[/C][C]767.088350494912[/C][C]52.9116495050879[/C][/ROW]
[ROW][C]50[/C][C]740[/C][C]740.682958905662[/C][C]-0.682958905662076[/C][/ROW]
[ROW][C]51[/C][C]800[/C][C]785.13558626806[/C][C]14.8644137319403[/C][/ROW]
[ROW][C]52[/C][C]920[/C][C]891.698486700385[/C][C]28.3015132996146[/C][/ROW]
[ROW][C]53[/C][C]970[/C][C]901.909681315321[/C][C]68.0903186846789[/C][/ROW]
[ROW][C]54[/C][C]780[/C][C]807.586099390088[/C][C]-27.5860993900884[/C][/ROW]
[ROW][C]55[/C][C]880[/C][C]944.962260807208[/C][C]-64.9622608072082[/C][/ROW]
[ROW][C]56[/C][C]750[/C][C]783.245094675278[/C][C]-33.2450946752775[/C][/ROW]
[ROW][C]57[/C][C]620[/C][C]690.748063619036[/C][C]-70.7480636190359[/C][/ROW]
[ROW][C]58[/C][C]760[/C][C]817.675854859926[/C][C]-57.6758548599262[/C][/ROW]
[ROW][C]59[/C][C]930[/C][C]873.543916595809[/C][C]56.4560834041913[/C][/ROW]
[ROW][C]60[/C][C]820[/C][C]856.666475867346[/C][C]-36.6664758673463[/C][/ROW]
[ROW][C]61[/C][C]900[/C][C]821.736768324861[/C][C]78.2632316751385[/C][/ROW]
[ROW][C]62[/C][C]700[/C][C]745.660024947915[/C][C]-45.6600249479151[/C][/ROW]
[ROW][C]63[/C][C]810[/C][C]802.163054118331[/C][C]7.83694588166918[/C][/ROW]
[ROW][C]64[/C][C]970[/C][C]920.719644990706[/C][C]49.2803550092945[/C][/ROW]
[ROW][C]65[/C][C]820[/C][C]969.443946063552[/C][C]-149.443946063552[/C][/ROW]
[ROW][C]66[/C][C]740[/C][C]771.967533573655[/C][C]-31.9675335736551[/C][/ROW]
[ROW][C]67[/C][C]930[/C][C]872.518015549067[/C][C]57.4819844509327[/C][/ROW]
[ROW][C]68[/C][C]720[/C][C]746.544659700596[/C][C]-26.5446597005961[/C][/ROW]
[ROW][C]69[/C][C]580[/C][C]618.180698927142[/C][C]-38.1806989271416[/C][/ROW]
[ROW][C]70[/C][C]800[/C][C]758.660167532376[/C][C]41.3398324676243[/C][/ROW]
[ROW][C]71[/C][C]910[/C][C]927.727603069701[/C][C]-17.7276030697009[/C][/ROW]
[ROW][C]72[/C][C]810[/C][C]818.274951964762[/C][C]-8.27495196476195[/C][/ROW]
[ROW][C]73[/C][C]890[/C][C]893.453840237506[/C][C]-3.45384023750637[/C][/ROW]
[ROW][C]74[/C][C]710[/C][C]695.002008696743[/C][C]14.9979913032566[/C][/ROW]
[ROW][C]75[/C][C]830[/C][C]804.966123296691[/C][C]25.0338767033091[/C][/ROW]
[ROW][C]76[/C][C]900[/C][C]963.365764068593[/C][C]-63.3657640685931[/C][/ROW]
[ROW][C]77[/C][C]830[/C][C]817.05731628448[/C][C]12.9426837155203[/C][/ROW]
[ROW][C]78[/C][C]680[/C][C]739.243222110856[/C][C]-59.2432221108562[/C][/ROW]
[ROW][C]79[/C][C]980[/C][C]922.926515325987[/C][C]57.0734846740128[/C][/ROW]
[ROW][C]80[/C][C]690[/C][C]717.015249997209[/C][C]-27.0152499972086[/C][/ROW]
[ROW][C]81[/C][C]530[/C][C]577.338523736549[/C][C]-47.3385237365494[/C][/ROW]
[ROW][C]82[/C][C]740[/C][C]792.439621780532[/C][C]-52.4396217805321[/C][/ROW]
[ROW][C]83[/C][C]930[/C][C]899.978570908991[/C][C]30.0214290910087[/C][/ROW]
[ROW][C]84[/C][C]770[/C][C]801.496104348165[/C][C]-31.4961043481654[/C][/ROW]
[ROW][C]85[/C][C]870[/C][C]879.477112201233[/C][C]-9.4771122012329[/C][/ROW]
[ROW][C]86[/C][C]660[/C][C]697.619945433331[/C][C]-37.6199454333309[/C][/ROW]
[ROW][C]87[/C][C]770[/C][C]813.574481158246[/C][C]-43.5744811582463[/C][/ROW]
[ROW][C]88[/C][C]900[/C][C]883.544324225271[/C][C]16.4556757747292[/C][/ROW]
[ROW][C]89[/C][C]830[/C][C]812.979660935612[/C][C]17.0203390643876[/C][/ROW]
[ROW][C]90[/C][C]660[/C][C]666.209989620212[/C][C]-6.20998962021179[/C][/ROW]
[ROW][C]91[/C][C]1000[/C][C]962.398094276378[/C][C]37.6019057236224[/C][/ROW]
[ROW][C]92[/C][C]710[/C][C]675.154237677472[/C][C]34.8457623225285[/C][/ROW]
[ROW][C]93[/C][C]460[/C][C]519.064011993062[/C][C]-59.0640119930621[/C][/ROW]
[ROW][C]94[/C][C]740[/C][C]728.314834421876[/C][C]11.685165578124[/C][/ROW]
[ROW][C]95[/C][C]940[/C][C]917.207183504874[/C][C]22.792816495126[/C][/ROW]
[ROW][C]96[/C][C]870[/C][C]759.843947768199[/C][C]110.156052231801[/C][/ROW]
[ROW][C]97[/C][C]810[/C][C]866.427139831537[/C][C]-56.4271398315367[/C][/ROW]
[ROW][C]98[/C][C]650[/C][C]655.635933698087[/C][C]-5.635933698087[/C][/ROW]
[ROW][C]99[/C][C]760[/C][C]767.917091514869[/C][C]-7.91709151486918[/C][/ROW]
[ROW][C]100[/C][C]950[/C][C]897.100392876599[/C][C]52.8996071234013[/C][/ROW]
[ROW][C]101[/C][C]870[/C][C]829.555577574287[/C][C]40.4444224257131[/C][/ROW]
[ROW][C]102[/C][C]670[/C][C]662.661777717529[/C][C]7.33822228247072[/C][/ROW]
[ROW][C]103[/C][C]960[/C][C]1001.82519233983[/C][C]-41.8251923398253[/C][/ROW]
[ROW][C]104[/C][C]750[/C][C]708.26838666121[/C][C]41.7316133387897[/C][/ROW]
[ROW][C]105[/C][C]480[/C][C]463.957093990069[/C][C]16.0429060099306[/C][/ROW]
[ROW][C]106[/C][C]690[/C][C]744.928951821339[/C][C]-54.928951821339[/C][/ROW]
[ROW][C]107[/C][C]850[/C][C]941.377495318284[/C][C]-91.3774953182843[/C][/ROW]
[ROW][C]108[/C][C]890[/C][C]860.949561175924[/C][C]29.0504388240759[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=235713&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=235713&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
13800791.7948717948728.20512820512806
14710701.8509749769368.1490250230645
15850843.602589426526.39741057348033
16790784.4548136227945.54518637720616
17800794.0343792689665.9656207310336
18840834.9090344174285.09096558257181
19850819.09142893086730.9085710691332
20810820.985403484329-10.9854034843288
21760773.577007702483-13.5770077024835
22860853.4810752361756.51892476382466
23860842.37111852011717.6288814798834
24880903.573650638563-23.5736506385629
25770819.072908346953-49.0729083469533
26740726.05757139163513.9424286083646
27850866.429196224408-16.429196224408
28790805.178445189682-15.1784451896817
29860813.8900602256646.1099397743404
30820855.987249033209-35.9872490332092
31900862.31860431156937.6813956884313
32800824.679369645185-24.6793696451847
33660773.881997738412-113.881997738412
34820867.016088566592-47.0160885665917
35850862.837837178304-12.8378371783042
36850882.456578161393-32.4565781613927
37760772.346169250171-12.346169250171
38730740.150155374442-10.1501553744417
39770849.55200443689-79.5520044368897
40880785.0377278035694.9622721964404
41890856.83433000109733.1656699989026
42790819.635018954846-29.635018954846
43930895.37142975697534.6285702430249
44770797.673570197904-27.6735701979037
45680661.36141386992718.6385861300731
46810824.498040782403-14.4980407824025
47870854.26466132579715.735338674203
48850856.732256895305-6.73225689530454
49820767.08835049491252.9116495050879
50740740.682958905662-0.682958905662076
51800785.1355862680614.8644137319403
52920891.69848670038528.3015132996146
53970901.90968131532168.0903186846789
54780807.586099390088-27.5860993900884
55880944.962260807208-64.9622608072082
56750783.245094675278-33.2450946752775
57620690.748063619036-70.7480636190359
58760817.675854859926-57.6758548599262
59930873.54391659580956.4560834041913
60820856.666475867346-36.6664758673463
61900821.73676832486178.2632316751385
62700745.660024947915-45.6600249479151
63810802.1630541183317.83694588166918
64970920.71964499070649.2803550092945
65820969.443946063552-149.443946063552
66740771.967533573655-31.9675335736551
67930872.51801554906757.4819844509327
68720746.544659700596-26.5446597005961
69580618.180698927142-38.1806989271416
70800758.66016753237641.3398324676243
71910927.727603069701-17.7276030697009
72810818.274951964762-8.27495196476195
73890893.453840237506-3.45384023750637
74710695.00200869674314.9979913032566
75830804.96612329669125.0338767033091
76900963.365764068593-63.3657640685931
77830817.0573162844812.9426837155203
78680739.243222110856-59.2432221108562
79980922.92651532598757.0734846740128
80690717.015249997209-27.0152499972086
81530577.338523736549-47.3385237365494
82740792.439621780532-52.4396217805321
83930899.97857090899130.0214290910087
84770801.496104348165-31.4961043481654
85870879.477112201233-9.4771122012329
86660697.619945433331-37.6199454333309
87770813.574481158246-43.5744811582463
88900883.54432422527116.4556757747292
89830812.97966093561217.0203390643876
90660666.209989620212-6.20998962021179
911000962.39809427637837.6019057236224
92710675.15423767747234.8457623225285
93460519.064011993062-59.0640119930621
94740728.31483442187611.685165578124
95940917.20718350487422.792816495126
96870759.843947768199110.156052231801
97810866.427139831537-56.4271398315367
98650655.635933698087-5.635933698087
99760767.917091514869-7.91709151486918
100950897.10039287659952.8996071234013
101870829.55557757428740.4444224257131
102670662.6617777175297.33822228247072
1039601001.82519233983-41.8251923398253
104750708.2683866612141.7316133387897
105480463.95709399006916.0429060099306
106690744.928951821339-54.928951821339
107850941.377495318284-91.3774953182843
108890860.94956117592429.0504388240759







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
109805.11461348887719.647232797384890.581994180355
110645.352124294952559.751583632192730.952664957712
111755.730096844935669.977415069779841.48277862009
112942.979740869935857.0547464337581028.90473530611
113860.670217824398774.551571931622946.788863717174
114659.922806323299573.588028665355746.257583981243
115951.700637993383865.1261350820081038.27514090476
116739.301032753228652.462128852434826.139936654022
117468.073213529691380.944184158098555.202242901284
118680.46957413965593.023682086583767.915466192716
119844.973363243989757.182897014314932.763829473663
120883.577526822101795.413841396592971.74121224761

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
109 & 805.11461348887 & 719.647232797384 & 890.581994180355 \tabularnewline
110 & 645.352124294952 & 559.751583632192 & 730.952664957712 \tabularnewline
111 & 755.730096844935 & 669.977415069779 & 841.48277862009 \tabularnewline
112 & 942.979740869935 & 857.054746433758 & 1028.90473530611 \tabularnewline
113 & 860.670217824398 & 774.551571931622 & 946.788863717174 \tabularnewline
114 & 659.922806323299 & 573.588028665355 & 746.257583981243 \tabularnewline
115 & 951.700637993383 & 865.126135082008 & 1038.27514090476 \tabularnewline
116 & 739.301032753228 & 652.462128852434 & 826.139936654022 \tabularnewline
117 & 468.073213529691 & 380.944184158098 & 555.202242901284 \tabularnewline
118 & 680.46957413965 & 593.023682086583 & 767.915466192716 \tabularnewline
119 & 844.973363243989 & 757.182897014314 & 932.763829473663 \tabularnewline
120 & 883.577526822101 & 795.413841396592 & 971.74121224761 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=235713&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]109[/C][C]805.11461348887[/C][C]719.647232797384[/C][C]890.581994180355[/C][/ROW]
[ROW][C]110[/C][C]645.352124294952[/C][C]559.751583632192[/C][C]730.952664957712[/C][/ROW]
[ROW][C]111[/C][C]755.730096844935[/C][C]669.977415069779[/C][C]841.48277862009[/C][/ROW]
[ROW][C]112[/C][C]942.979740869935[/C][C]857.054746433758[/C][C]1028.90473530611[/C][/ROW]
[ROW][C]113[/C][C]860.670217824398[/C][C]774.551571931622[/C][C]946.788863717174[/C][/ROW]
[ROW][C]114[/C][C]659.922806323299[/C][C]573.588028665355[/C][C]746.257583981243[/C][/ROW]
[ROW][C]115[/C][C]951.700637993383[/C][C]865.126135082008[/C][C]1038.27514090476[/C][/ROW]
[ROW][C]116[/C][C]739.301032753228[/C][C]652.462128852434[/C][C]826.139936654022[/C][/ROW]
[ROW][C]117[/C][C]468.073213529691[/C][C]380.944184158098[/C][C]555.202242901284[/C][/ROW]
[ROW][C]118[/C][C]680.46957413965[/C][C]593.023682086583[/C][C]767.915466192716[/C][/ROW]
[ROW][C]119[/C][C]844.973363243989[/C][C]757.182897014314[/C][C]932.763829473663[/C][/ROW]
[ROW][C]120[/C][C]883.577526822101[/C][C]795.413841396592[/C][C]971.74121224761[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=235713&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=235713&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
109805.11461348887719.647232797384890.581994180355
110645.352124294952559.751583632192730.952664957712
111755.730096844935669.977415069779841.48277862009
112942.979740869935857.0547464337581028.90473530611
113860.670217824398774.551571931622946.788863717174
114659.922806323299573.588028665355746.257583981243
115951.700637993383865.1261350820081038.27514090476
116739.301032753228652.462128852434826.139936654022
117468.073213529691380.944184158098555.202242901284
118680.46957413965593.023682086583767.915466192716
119844.973363243989757.182897014314932.763829473663
120883.577526822101795.413841396592971.74121224761



Parameters (Session):
par1 = 60 ; par2 = 1 ; par3 = 0 ; par4 = 0 ; par5 = 12 ; par6 = White Noise ; par7 = 0.95 ;
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')