Free Statistics

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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 computationWed, 10 Dec 2014 13:46:46 +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/2014/Dec/10/t1418219296ugtqq3c98zwx4uh.htm/, Retrieved Sun, 19 May 2024 16:12:31 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=265183, Retrieved Sun, 19 May 2024 16:12:31 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact85
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [Bivariate Kernel Density Estimation] [Bivariate Kernel ...] [2014-12-10 10:42:27] [9ecaa0fefb0ae88b4782d69916cabb9e]
- RMPD    [Exponential Smoothing] [Exponential smoot...] [2014-12-10 13:46:46] [10320d42b3a1ca1321e6e126fa928a8a] [Current]
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Dataseries X:
9 769
9 321
9 939
9 336
10 195
9 464
10 010
10 213
9 563
9 890
9 305
9 391
9 928
8 686
9 843
9 627
10 074
9 503
10 119
10 000
9 313
9 866
9 172
9 241
9 659
8 904
9 755
9 080
9 435
8 971
10 063
9 793
9 454
9 759
8 820
9 403
9 676
8 642
9 402
9 610
9 294
9 448
10 319
9 548
9 801
9 596
8 923
9 746
9 829
9 125
9 782
9 441
9 162
9 915
10 444
10 209
9 985
9 842
9 429
10 132
9 849
9 172
10 313
9 819
9 955
10 048
10 082
10 541
10 208
10 233
9 439
9 963
10 158
9 225
10 474
9 757
10 490
10 281
10 444
10 640
10 695
10 786
9 832
9 747
10 411
9 511
10 402
9 701
10 540
10 112
10 915
11 183
10 384
10 834
9 886
10 216
10 943
9 867
10 203
10 837
10 573
10 647
11 502
10 656
10 866
10 835
9 945
10 331
10 718
9 462
10 579
10 633
10 346
10 757
11 207
11 013
11 015
10 765
10 042
10 661




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time3 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 & 3 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ jenkins.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=265183&T=0

[TABLE]
[ROW][C]Summary of computational transaction[/C][/ROW]
[ROW][C]Raw Input[/C][C]view raw input (R code) [/C][/ROW]
[ROW][C]Raw Output[/C][C]view raw output of R engine [/C][/ROW]
[ROW][C]Computing time[/C][C]3 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Gwilym Jenkins' @ jenkins.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=265183&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=265183&T=0

As an alternative you can also use a QR Code:  

The GUIDs for individual cells are displayed in the table below:

Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time3 seconds
R Server'Gwilym Jenkins' @ jenkins.wessa.net







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.112367224627713
beta0.11842934805504
gamma0.31394062074009

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.112367224627713 \tabularnewline
beta & 0.11842934805504 \tabularnewline
gamma & 0.31394062074009 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=265183&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]0.112367224627713[/C][/ROW]
[ROW][C]beta[/C][C]0.11842934805504[/C][/ROW]
[ROW][C]gamma[/C][C]0.31394062074009[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=265183&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=265183&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
alpha0.112367224627713
beta0.11842934805504
gamma0.31394062074009







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
1399289938.65918803419-10.6591880341875
1486868694.00024937148-8.00024937147828
1598439863.49195766431-20.4919576643097
1696279650.43230905773-23.4323090577345
171007410094.8554340649-20.8554340649316
1895039526.54058006536-23.5405800653571
19101199938.11073557649180.889264423509
201000010176.6009698535-176.600969853482
2193139530.19588764121-217.195887641208
2298669814.7555828171851.2444171828192
2391729219.20277572656-47.2027757265623
2492419293.45957621639-52.4595762163935
2596599804.87390962436-145.873909624357
2689048539.06158759083364.93841240917
2797559745.240668255069.75933174494094
2890809533.42575361028-453.42575361028
2994359923.19247052288-488.192470522878
3089719288.33955324198-317.339553241978
31100639706.67737200353356.322627996475
3297939850.40930982482-57.4093098248231
3394549192.81967079236261.180329207644
3497599599.03839582282159.961604177181
3588208982.81548971959-162.815489719595
3694039035.62514377803367.37485622197
3796769566.77969025035109.220309749646
3886428473.96707410095168.03292589905
3994029558.41495840299-156.414958402991
4096109196.01326583735413.986734162654
4192949682.26241066132-388.262410661318
4294489116.28066445226331.719335547736
43103199813.94597092906505.054029070938
4495489879.74666193355-331.746661933548
4598019297.10759751637503.892402483634
4695969722.62074427777-126.62074427777
4789239000.6628601459-77.6628601458997
4897469228.33284456711517.667155432886
4998299723.98398278803105.016017211967
5091258666.57898869921458.421011300792
5197829716.6004866655765.3995133344342
5294419564.38114291972-123.381142919723
5391629785.84600689515-623.846006895146
5499159410.04652043779504.953479562215
551044410193.806282443250.193717556971
561020910012.7177187439196.282281256053
5799859744.23600433154240.763995668463
5898429982.94092682309-140.940926823088
5994299291.28624592701137.713754072989
60101329730.19020121656401.809798783437
61984910117.425642976-268.425642976017
6291729131.1635695955940.8364304044098
631031310033.8085513495279.191448650519
6498199864.91833763454-45.9183376345409
6599559968.56908469529-13.5690846952893
66100489996.9649277902651.0350722097355
671008210673.7506565221-591.750656522107
681054110386.8516135853154.148386414714
691020810129.28983108378.7101689169522
701023310244.5202053798-11.5202053797657
7194399647.88387683122-208.883876831223
72996310119.6479810598-156.647981059801
731015810248.1411799657-90.1411799656653
7492259361.24575944079-136.245759440788
751047410301.2100521272172.789947872758
76975710019.1480484788-262.148048478772
771049010094.0193810567395.980618943282
781028110178.3913000421102.60869995794
791044410674.4905624446-230.490562444564
801064010633.4875901536.51240984704236
811069510333.796848462361.203151538
821078610454.8679167553331.13208324466
8398329845.53789676625-13.5378967662491
84974710360.2099001222-613.209900122229
851041110456.258971193-45.2589711930177
8695119562.4818452316-51.4818452315958
871040210600.1386387325-198.138638732486
88970110152.3093968941-451.309396894057
891054010383.9192039668156.080796033231
901011210350.9868258306-238.986825830607
911091510702.7381385974212.261861402603
921118310770.2811412405412.718858759526
931038410613.2307711159-229.230771115919
941083410649.8759944403184.124005559739
9598869916.32295341796-30.3229534179573
961021610250.1214868822-34.1214868821571
971094310565.3344585332377.665541466757
9898679718.80006991544148.199930084558
991020310742.137839023-539.137839023044
1001083710185.0152731895651.984726810539
1011057310724.1125038356-151.112503835604
1021064710556.738104621590.2618953784513
1031150211085.7819974478416.218002552234
1041065611249.3663511694-593.366351169401
1051086610804.251399956961.7486000431436
1061083510996.5271505443-161.527150544292
107994510167.5227187679-222.52271876787
1081033110479.2551847457-148.255184745669
1091071810895.4640418122-177.464041812247
11094629914.29060948086-452.290609480862
1111057910662.3086960655-83.3086960655273
1121063310478.0873818838154.912618116241
1131034610720.6789353159-374.678935315944
1141075710575.6134312833181.386568716685
1151120711187.109709730719.8902902693426
1161101311000.931589472812.068410527243
1171101510790.5680443119224.431955688138
1181076510925.2335226578-160.233522657833
1191004210065.7227601224-23.7227601224222
1201066110409.4806343894251.519365610573

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 9928 & 9938.65918803419 & -10.6591880341875 \tabularnewline
14 & 8686 & 8694.00024937148 & -8.00024937147828 \tabularnewline
15 & 9843 & 9863.49195766431 & -20.4919576643097 \tabularnewline
16 & 9627 & 9650.43230905773 & -23.4323090577345 \tabularnewline
17 & 10074 & 10094.8554340649 & -20.8554340649316 \tabularnewline
18 & 9503 & 9526.54058006536 & -23.5405800653571 \tabularnewline
19 & 10119 & 9938.11073557649 & 180.889264423509 \tabularnewline
20 & 10000 & 10176.6009698535 & -176.600969853482 \tabularnewline
21 & 9313 & 9530.19588764121 & -217.195887641208 \tabularnewline
22 & 9866 & 9814.75558281718 & 51.2444171828192 \tabularnewline
23 & 9172 & 9219.20277572656 & -47.2027757265623 \tabularnewline
24 & 9241 & 9293.45957621639 & -52.4595762163935 \tabularnewline
25 & 9659 & 9804.87390962436 & -145.873909624357 \tabularnewline
26 & 8904 & 8539.06158759083 & 364.93841240917 \tabularnewline
27 & 9755 & 9745.24066825506 & 9.75933174494094 \tabularnewline
28 & 9080 & 9533.42575361028 & -453.42575361028 \tabularnewline
29 & 9435 & 9923.19247052288 & -488.192470522878 \tabularnewline
30 & 8971 & 9288.33955324198 & -317.339553241978 \tabularnewline
31 & 10063 & 9706.67737200353 & 356.322627996475 \tabularnewline
32 & 9793 & 9850.40930982482 & -57.4093098248231 \tabularnewline
33 & 9454 & 9192.81967079236 & 261.180329207644 \tabularnewline
34 & 9759 & 9599.03839582282 & 159.961604177181 \tabularnewline
35 & 8820 & 8982.81548971959 & -162.815489719595 \tabularnewline
36 & 9403 & 9035.62514377803 & 367.37485622197 \tabularnewline
37 & 9676 & 9566.77969025035 & 109.220309749646 \tabularnewline
38 & 8642 & 8473.96707410095 & 168.03292589905 \tabularnewline
39 & 9402 & 9558.41495840299 & -156.414958402991 \tabularnewline
40 & 9610 & 9196.01326583735 & 413.986734162654 \tabularnewline
41 & 9294 & 9682.26241066132 & -388.262410661318 \tabularnewline
42 & 9448 & 9116.28066445226 & 331.719335547736 \tabularnewline
43 & 10319 & 9813.94597092906 & 505.054029070938 \tabularnewline
44 & 9548 & 9879.74666193355 & -331.746661933548 \tabularnewline
45 & 9801 & 9297.10759751637 & 503.892402483634 \tabularnewline
46 & 9596 & 9722.62074427777 & -126.62074427777 \tabularnewline
47 & 8923 & 9000.6628601459 & -77.6628601458997 \tabularnewline
48 & 9746 & 9228.33284456711 & 517.667155432886 \tabularnewline
49 & 9829 & 9723.98398278803 & 105.016017211967 \tabularnewline
50 & 9125 & 8666.57898869921 & 458.421011300792 \tabularnewline
51 & 9782 & 9716.60048666557 & 65.3995133344342 \tabularnewline
52 & 9441 & 9564.38114291972 & -123.381142919723 \tabularnewline
53 & 9162 & 9785.84600689515 & -623.846006895146 \tabularnewline
54 & 9915 & 9410.04652043779 & 504.953479562215 \tabularnewline
55 & 10444 & 10193.806282443 & 250.193717556971 \tabularnewline
56 & 10209 & 10012.7177187439 & 196.282281256053 \tabularnewline
57 & 9985 & 9744.23600433154 & 240.763995668463 \tabularnewline
58 & 9842 & 9982.94092682309 & -140.940926823088 \tabularnewline
59 & 9429 & 9291.28624592701 & 137.713754072989 \tabularnewline
60 & 10132 & 9730.19020121656 & 401.809798783437 \tabularnewline
61 & 9849 & 10117.425642976 & -268.425642976017 \tabularnewline
62 & 9172 & 9131.16356959559 & 40.8364304044098 \tabularnewline
63 & 10313 & 10033.8085513495 & 279.191448650519 \tabularnewline
64 & 9819 & 9864.91833763454 & -45.9183376345409 \tabularnewline
65 & 9955 & 9968.56908469529 & -13.5690846952893 \tabularnewline
66 & 10048 & 9996.96492779026 & 51.0350722097355 \tabularnewline
67 & 10082 & 10673.7506565221 & -591.750656522107 \tabularnewline
68 & 10541 & 10386.8516135853 & 154.148386414714 \tabularnewline
69 & 10208 & 10129.289831083 & 78.7101689169522 \tabularnewline
70 & 10233 & 10244.5202053798 & -11.5202053797657 \tabularnewline
71 & 9439 & 9647.88387683122 & -208.883876831223 \tabularnewline
72 & 9963 & 10119.6479810598 & -156.647981059801 \tabularnewline
73 & 10158 & 10248.1411799657 & -90.1411799656653 \tabularnewline
74 & 9225 & 9361.24575944079 & -136.245759440788 \tabularnewline
75 & 10474 & 10301.2100521272 & 172.789947872758 \tabularnewline
76 & 9757 & 10019.1480484788 & -262.148048478772 \tabularnewline
77 & 10490 & 10094.0193810567 & 395.980618943282 \tabularnewline
78 & 10281 & 10178.3913000421 & 102.60869995794 \tabularnewline
79 & 10444 & 10674.4905624446 & -230.490562444564 \tabularnewline
80 & 10640 & 10633.487590153 & 6.51240984704236 \tabularnewline
81 & 10695 & 10333.796848462 & 361.203151538 \tabularnewline
82 & 10786 & 10454.8679167553 & 331.13208324466 \tabularnewline
83 & 9832 & 9845.53789676625 & -13.5378967662491 \tabularnewline
84 & 9747 & 10360.2099001222 & -613.209900122229 \tabularnewline
85 & 10411 & 10456.258971193 & -45.2589711930177 \tabularnewline
86 & 9511 & 9562.4818452316 & -51.4818452315958 \tabularnewline
87 & 10402 & 10600.1386387325 & -198.138638732486 \tabularnewline
88 & 9701 & 10152.3093968941 & -451.309396894057 \tabularnewline
89 & 10540 & 10383.9192039668 & 156.080796033231 \tabularnewline
90 & 10112 & 10350.9868258306 & -238.986825830607 \tabularnewline
91 & 10915 & 10702.7381385974 & 212.261861402603 \tabularnewline
92 & 11183 & 10770.2811412405 & 412.718858759526 \tabularnewline
93 & 10384 & 10613.2307711159 & -229.230771115919 \tabularnewline
94 & 10834 & 10649.8759944403 & 184.124005559739 \tabularnewline
95 & 9886 & 9916.32295341796 & -30.3229534179573 \tabularnewline
96 & 10216 & 10250.1214868822 & -34.1214868821571 \tabularnewline
97 & 10943 & 10565.3344585332 & 377.665541466757 \tabularnewline
98 & 9867 & 9718.80006991544 & 148.199930084558 \tabularnewline
99 & 10203 & 10742.137839023 & -539.137839023044 \tabularnewline
100 & 10837 & 10185.0152731895 & 651.984726810539 \tabularnewline
101 & 10573 & 10724.1125038356 & -151.112503835604 \tabularnewline
102 & 10647 & 10556.7381046215 & 90.2618953784513 \tabularnewline
103 & 11502 & 11085.7819974478 & 416.218002552234 \tabularnewline
104 & 10656 & 11249.3663511694 & -593.366351169401 \tabularnewline
105 & 10866 & 10804.2513999569 & 61.7486000431436 \tabularnewline
106 & 10835 & 10996.5271505443 & -161.527150544292 \tabularnewline
107 & 9945 & 10167.5227187679 & -222.52271876787 \tabularnewline
108 & 10331 & 10479.2551847457 & -148.255184745669 \tabularnewline
109 & 10718 & 10895.4640418122 & -177.464041812247 \tabularnewline
110 & 9462 & 9914.29060948086 & -452.290609480862 \tabularnewline
111 & 10579 & 10662.3086960655 & -83.3086960655273 \tabularnewline
112 & 10633 & 10478.0873818838 & 154.912618116241 \tabularnewline
113 & 10346 & 10720.6789353159 & -374.678935315944 \tabularnewline
114 & 10757 & 10575.6134312833 & 181.386568716685 \tabularnewline
115 & 11207 & 11187.1097097307 & 19.8902902693426 \tabularnewline
116 & 11013 & 11000.9315894728 & 12.068410527243 \tabularnewline
117 & 11015 & 10790.5680443119 & 224.431955688138 \tabularnewline
118 & 10765 & 10925.2335226578 & -160.233522657833 \tabularnewline
119 & 10042 & 10065.7227601224 & -23.7227601224222 \tabularnewline
120 & 10661 & 10409.4806343894 & 251.519365610573 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=265183&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]9928[/C][C]9938.65918803419[/C][C]-10.6591880341875[/C][/ROW]
[ROW][C]14[/C][C]8686[/C][C]8694.00024937148[/C][C]-8.00024937147828[/C][/ROW]
[ROW][C]15[/C][C]9843[/C][C]9863.49195766431[/C][C]-20.4919576643097[/C][/ROW]
[ROW][C]16[/C][C]9627[/C][C]9650.43230905773[/C][C]-23.4323090577345[/C][/ROW]
[ROW][C]17[/C][C]10074[/C][C]10094.8554340649[/C][C]-20.8554340649316[/C][/ROW]
[ROW][C]18[/C][C]9503[/C][C]9526.54058006536[/C][C]-23.5405800653571[/C][/ROW]
[ROW][C]19[/C][C]10119[/C][C]9938.11073557649[/C][C]180.889264423509[/C][/ROW]
[ROW][C]20[/C][C]10000[/C][C]10176.6009698535[/C][C]-176.600969853482[/C][/ROW]
[ROW][C]21[/C][C]9313[/C][C]9530.19588764121[/C][C]-217.195887641208[/C][/ROW]
[ROW][C]22[/C][C]9866[/C][C]9814.75558281718[/C][C]51.2444171828192[/C][/ROW]
[ROW][C]23[/C][C]9172[/C][C]9219.20277572656[/C][C]-47.2027757265623[/C][/ROW]
[ROW][C]24[/C][C]9241[/C][C]9293.45957621639[/C][C]-52.4595762163935[/C][/ROW]
[ROW][C]25[/C][C]9659[/C][C]9804.87390962436[/C][C]-145.873909624357[/C][/ROW]
[ROW][C]26[/C][C]8904[/C][C]8539.06158759083[/C][C]364.93841240917[/C][/ROW]
[ROW][C]27[/C][C]9755[/C][C]9745.24066825506[/C][C]9.75933174494094[/C][/ROW]
[ROW][C]28[/C][C]9080[/C][C]9533.42575361028[/C][C]-453.42575361028[/C][/ROW]
[ROW][C]29[/C][C]9435[/C][C]9923.19247052288[/C][C]-488.192470522878[/C][/ROW]
[ROW][C]30[/C][C]8971[/C][C]9288.33955324198[/C][C]-317.339553241978[/C][/ROW]
[ROW][C]31[/C][C]10063[/C][C]9706.67737200353[/C][C]356.322627996475[/C][/ROW]
[ROW][C]32[/C][C]9793[/C][C]9850.40930982482[/C][C]-57.4093098248231[/C][/ROW]
[ROW][C]33[/C][C]9454[/C][C]9192.81967079236[/C][C]261.180329207644[/C][/ROW]
[ROW][C]34[/C][C]9759[/C][C]9599.03839582282[/C][C]159.961604177181[/C][/ROW]
[ROW][C]35[/C][C]8820[/C][C]8982.81548971959[/C][C]-162.815489719595[/C][/ROW]
[ROW][C]36[/C][C]9403[/C][C]9035.62514377803[/C][C]367.37485622197[/C][/ROW]
[ROW][C]37[/C][C]9676[/C][C]9566.77969025035[/C][C]109.220309749646[/C][/ROW]
[ROW][C]38[/C][C]8642[/C][C]8473.96707410095[/C][C]168.03292589905[/C][/ROW]
[ROW][C]39[/C][C]9402[/C][C]9558.41495840299[/C][C]-156.414958402991[/C][/ROW]
[ROW][C]40[/C][C]9610[/C][C]9196.01326583735[/C][C]413.986734162654[/C][/ROW]
[ROW][C]41[/C][C]9294[/C][C]9682.26241066132[/C][C]-388.262410661318[/C][/ROW]
[ROW][C]42[/C][C]9448[/C][C]9116.28066445226[/C][C]331.719335547736[/C][/ROW]
[ROW][C]43[/C][C]10319[/C][C]9813.94597092906[/C][C]505.054029070938[/C][/ROW]
[ROW][C]44[/C][C]9548[/C][C]9879.74666193355[/C][C]-331.746661933548[/C][/ROW]
[ROW][C]45[/C][C]9801[/C][C]9297.10759751637[/C][C]503.892402483634[/C][/ROW]
[ROW][C]46[/C][C]9596[/C][C]9722.62074427777[/C][C]-126.62074427777[/C][/ROW]
[ROW][C]47[/C][C]8923[/C][C]9000.6628601459[/C][C]-77.6628601458997[/C][/ROW]
[ROW][C]48[/C][C]9746[/C][C]9228.33284456711[/C][C]517.667155432886[/C][/ROW]
[ROW][C]49[/C][C]9829[/C][C]9723.98398278803[/C][C]105.016017211967[/C][/ROW]
[ROW][C]50[/C][C]9125[/C][C]8666.57898869921[/C][C]458.421011300792[/C][/ROW]
[ROW][C]51[/C][C]9782[/C][C]9716.60048666557[/C][C]65.3995133344342[/C][/ROW]
[ROW][C]52[/C][C]9441[/C][C]9564.38114291972[/C][C]-123.381142919723[/C][/ROW]
[ROW][C]53[/C][C]9162[/C][C]9785.84600689515[/C][C]-623.846006895146[/C][/ROW]
[ROW][C]54[/C][C]9915[/C][C]9410.04652043779[/C][C]504.953479562215[/C][/ROW]
[ROW][C]55[/C][C]10444[/C][C]10193.806282443[/C][C]250.193717556971[/C][/ROW]
[ROW][C]56[/C][C]10209[/C][C]10012.7177187439[/C][C]196.282281256053[/C][/ROW]
[ROW][C]57[/C][C]9985[/C][C]9744.23600433154[/C][C]240.763995668463[/C][/ROW]
[ROW][C]58[/C][C]9842[/C][C]9982.94092682309[/C][C]-140.940926823088[/C][/ROW]
[ROW][C]59[/C][C]9429[/C][C]9291.28624592701[/C][C]137.713754072989[/C][/ROW]
[ROW][C]60[/C][C]10132[/C][C]9730.19020121656[/C][C]401.809798783437[/C][/ROW]
[ROW][C]61[/C][C]9849[/C][C]10117.425642976[/C][C]-268.425642976017[/C][/ROW]
[ROW][C]62[/C][C]9172[/C][C]9131.16356959559[/C][C]40.8364304044098[/C][/ROW]
[ROW][C]63[/C][C]10313[/C][C]10033.8085513495[/C][C]279.191448650519[/C][/ROW]
[ROW][C]64[/C][C]9819[/C][C]9864.91833763454[/C][C]-45.9183376345409[/C][/ROW]
[ROW][C]65[/C][C]9955[/C][C]9968.56908469529[/C][C]-13.5690846952893[/C][/ROW]
[ROW][C]66[/C][C]10048[/C][C]9996.96492779026[/C][C]51.0350722097355[/C][/ROW]
[ROW][C]67[/C][C]10082[/C][C]10673.7506565221[/C][C]-591.750656522107[/C][/ROW]
[ROW][C]68[/C][C]10541[/C][C]10386.8516135853[/C][C]154.148386414714[/C][/ROW]
[ROW][C]69[/C][C]10208[/C][C]10129.289831083[/C][C]78.7101689169522[/C][/ROW]
[ROW][C]70[/C][C]10233[/C][C]10244.5202053798[/C][C]-11.5202053797657[/C][/ROW]
[ROW][C]71[/C][C]9439[/C][C]9647.88387683122[/C][C]-208.883876831223[/C][/ROW]
[ROW][C]72[/C][C]9963[/C][C]10119.6479810598[/C][C]-156.647981059801[/C][/ROW]
[ROW][C]73[/C][C]10158[/C][C]10248.1411799657[/C][C]-90.1411799656653[/C][/ROW]
[ROW][C]74[/C][C]9225[/C][C]9361.24575944079[/C][C]-136.245759440788[/C][/ROW]
[ROW][C]75[/C][C]10474[/C][C]10301.2100521272[/C][C]172.789947872758[/C][/ROW]
[ROW][C]76[/C][C]9757[/C][C]10019.1480484788[/C][C]-262.148048478772[/C][/ROW]
[ROW][C]77[/C][C]10490[/C][C]10094.0193810567[/C][C]395.980618943282[/C][/ROW]
[ROW][C]78[/C][C]10281[/C][C]10178.3913000421[/C][C]102.60869995794[/C][/ROW]
[ROW][C]79[/C][C]10444[/C][C]10674.4905624446[/C][C]-230.490562444564[/C][/ROW]
[ROW][C]80[/C][C]10640[/C][C]10633.487590153[/C][C]6.51240984704236[/C][/ROW]
[ROW][C]81[/C][C]10695[/C][C]10333.796848462[/C][C]361.203151538[/C][/ROW]
[ROW][C]82[/C][C]10786[/C][C]10454.8679167553[/C][C]331.13208324466[/C][/ROW]
[ROW][C]83[/C][C]9832[/C][C]9845.53789676625[/C][C]-13.5378967662491[/C][/ROW]
[ROW][C]84[/C][C]9747[/C][C]10360.2099001222[/C][C]-613.209900122229[/C][/ROW]
[ROW][C]85[/C][C]10411[/C][C]10456.258971193[/C][C]-45.2589711930177[/C][/ROW]
[ROW][C]86[/C][C]9511[/C][C]9562.4818452316[/C][C]-51.4818452315958[/C][/ROW]
[ROW][C]87[/C][C]10402[/C][C]10600.1386387325[/C][C]-198.138638732486[/C][/ROW]
[ROW][C]88[/C][C]9701[/C][C]10152.3093968941[/C][C]-451.309396894057[/C][/ROW]
[ROW][C]89[/C][C]10540[/C][C]10383.9192039668[/C][C]156.080796033231[/C][/ROW]
[ROW][C]90[/C][C]10112[/C][C]10350.9868258306[/C][C]-238.986825830607[/C][/ROW]
[ROW][C]91[/C][C]10915[/C][C]10702.7381385974[/C][C]212.261861402603[/C][/ROW]
[ROW][C]92[/C][C]11183[/C][C]10770.2811412405[/C][C]412.718858759526[/C][/ROW]
[ROW][C]93[/C][C]10384[/C][C]10613.2307711159[/C][C]-229.230771115919[/C][/ROW]
[ROW][C]94[/C][C]10834[/C][C]10649.8759944403[/C][C]184.124005559739[/C][/ROW]
[ROW][C]95[/C][C]9886[/C][C]9916.32295341796[/C][C]-30.3229534179573[/C][/ROW]
[ROW][C]96[/C][C]10216[/C][C]10250.1214868822[/C][C]-34.1214868821571[/C][/ROW]
[ROW][C]97[/C][C]10943[/C][C]10565.3344585332[/C][C]377.665541466757[/C][/ROW]
[ROW][C]98[/C][C]9867[/C][C]9718.80006991544[/C][C]148.199930084558[/C][/ROW]
[ROW][C]99[/C][C]10203[/C][C]10742.137839023[/C][C]-539.137839023044[/C][/ROW]
[ROW][C]100[/C][C]10837[/C][C]10185.0152731895[/C][C]651.984726810539[/C][/ROW]
[ROW][C]101[/C][C]10573[/C][C]10724.1125038356[/C][C]-151.112503835604[/C][/ROW]
[ROW][C]102[/C][C]10647[/C][C]10556.7381046215[/C][C]90.2618953784513[/C][/ROW]
[ROW][C]103[/C][C]11502[/C][C]11085.7819974478[/C][C]416.218002552234[/C][/ROW]
[ROW][C]104[/C][C]10656[/C][C]11249.3663511694[/C][C]-593.366351169401[/C][/ROW]
[ROW][C]105[/C][C]10866[/C][C]10804.2513999569[/C][C]61.7486000431436[/C][/ROW]
[ROW][C]106[/C][C]10835[/C][C]10996.5271505443[/C][C]-161.527150544292[/C][/ROW]
[ROW][C]107[/C][C]9945[/C][C]10167.5227187679[/C][C]-222.52271876787[/C][/ROW]
[ROW][C]108[/C][C]10331[/C][C]10479.2551847457[/C][C]-148.255184745669[/C][/ROW]
[ROW][C]109[/C][C]10718[/C][C]10895.4640418122[/C][C]-177.464041812247[/C][/ROW]
[ROW][C]110[/C][C]9462[/C][C]9914.29060948086[/C][C]-452.290609480862[/C][/ROW]
[ROW][C]111[/C][C]10579[/C][C]10662.3086960655[/C][C]-83.3086960655273[/C][/ROW]
[ROW][C]112[/C][C]10633[/C][C]10478.0873818838[/C][C]154.912618116241[/C][/ROW]
[ROW][C]113[/C][C]10346[/C][C]10720.6789353159[/C][C]-374.678935315944[/C][/ROW]
[ROW][C]114[/C][C]10757[/C][C]10575.6134312833[/C][C]181.386568716685[/C][/ROW]
[ROW][C]115[/C][C]11207[/C][C]11187.1097097307[/C][C]19.8902902693426[/C][/ROW]
[ROW][C]116[/C][C]11013[/C][C]11000.9315894728[/C][C]12.068410527243[/C][/ROW]
[ROW][C]117[/C][C]11015[/C][C]10790.5680443119[/C][C]224.431955688138[/C][/ROW]
[ROW][C]118[/C][C]10765[/C][C]10925.2335226578[/C][C]-160.233522657833[/C][/ROW]
[ROW][C]119[/C][C]10042[/C][C]10065.7227601224[/C][C]-23.7227601224222[/C][/ROW]
[ROW][C]120[/C][C]10661[/C][C]10409.4806343894[/C][C]251.519365610573[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=265183&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=265183&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
1399289938.65918803419-10.6591880341875
1486868694.00024937148-8.00024937147828
1598439863.49195766431-20.4919576643097
1696279650.43230905773-23.4323090577345
171007410094.8554340649-20.8554340649316
1895039526.54058006536-23.5405800653571
19101199938.11073557649180.889264423509
201000010176.6009698535-176.600969853482
2193139530.19588764121-217.195887641208
2298669814.7555828171851.2444171828192
2391729219.20277572656-47.2027757265623
2492419293.45957621639-52.4595762163935
2596599804.87390962436-145.873909624357
2689048539.06158759083364.93841240917
2797559745.240668255069.75933174494094
2890809533.42575361028-453.42575361028
2994359923.19247052288-488.192470522878
3089719288.33955324198-317.339553241978
31100639706.67737200353356.322627996475
3297939850.40930982482-57.4093098248231
3394549192.81967079236261.180329207644
3497599599.03839582282159.961604177181
3588208982.81548971959-162.815489719595
3694039035.62514377803367.37485622197
3796769566.77969025035109.220309749646
3886428473.96707410095168.03292589905
3994029558.41495840299-156.414958402991
4096109196.01326583735413.986734162654
4192949682.26241066132-388.262410661318
4294489116.28066445226331.719335547736
43103199813.94597092906505.054029070938
4495489879.74666193355-331.746661933548
4598019297.10759751637503.892402483634
4695969722.62074427777-126.62074427777
4789239000.6628601459-77.6628601458997
4897469228.33284456711517.667155432886
4998299723.98398278803105.016017211967
5091258666.57898869921458.421011300792
5197829716.6004866655765.3995133344342
5294419564.38114291972-123.381142919723
5391629785.84600689515-623.846006895146
5499159410.04652043779504.953479562215
551044410193.806282443250.193717556971
561020910012.7177187439196.282281256053
5799859744.23600433154240.763995668463
5898429982.94092682309-140.940926823088
5994299291.28624592701137.713754072989
60101329730.19020121656401.809798783437
61984910117.425642976-268.425642976017
6291729131.1635695955940.8364304044098
631031310033.8085513495279.191448650519
6498199864.91833763454-45.9183376345409
6599559968.56908469529-13.5690846952893
66100489996.9649277902651.0350722097355
671008210673.7506565221-591.750656522107
681054110386.8516135853154.148386414714
691020810129.28983108378.7101689169522
701023310244.5202053798-11.5202053797657
7194399647.88387683122-208.883876831223
72996310119.6479810598-156.647981059801
731015810248.1411799657-90.1411799656653
7492259361.24575944079-136.245759440788
751047410301.2100521272172.789947872758
76975710019.1480484788-262.148048478772
771049010094.0193810567395.980618943282
781028110178.3913000421102.60869995794
791044410674.4905624446-230.490562444564
801064010633.4875901536.51240984704236
811069510333.796848462361.203151538
821078610454.8679167553331.13208324466
8398329845.53789676625-13.5378967662491
84974710360.2099001222-613.209900122229
851041110456.258971193-45.2589711930177
8695119562.4818452316-51.4818452315958
871040210600.1386387325-198.138638732486
88970110152.3093968941-451.309396894057
891054010383.9192039668156.080796033231
901011210350.9868258306-238.986825830607
911091510702.7381385974212.261861402603
921118310770.2811412405412.718858759526
931038410613.2307711159-229.230771115919
941083410649.8759944403184.124005559739
9598869916.32295341796-30.3229534179573
961021610250.1214868822-34.1214868821571
971094310565.3344585332377.665541466757
9898679718.80006991544148.199930084558
991020310742.137839023-539.137839023044
1001083710185.0152731895651.984726810539
1011057310724.1125038356-151.112503835604
1021064710556.738104621590.2618953784513
1031150211085.7819974478416.218002552234
1041065611249.3663511694-593.366351169401
1051086610804.251399956961.7486000431436
1061083510996.5271505443-161.527150544292
107994510167.5227187679-222.52271876787
1081033110479.2551847457-148.255184745669
1091071810895.4640418122-177.464041812247
11094629914.29060948086-452.290609480862
1111057910662.3086960655-83.3086960655273
1121063310478.0873818838154.912618116241
1131034610720.6789353159-374.678935315944
1141075710575.6134312833181.386568716685
1151120711187.109709730719.8902902693426
1161101311000.931589472812.068410527243
1171101510790.5680443119224.431955688138
1181076510925.2335226578-160.233522657833
1191004210065.7227601224-23.7227601224222
1201066110409.4806343894251.519365610573







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
12110856.782744068710315.347015893911398.2184722434
1229815.638956030439269.944218712310361.3336933486
12310719.993314340510169.134609515911270.8520191652
12410615.317165639810058.321495525711172.3128357539
12510694.662311981710130.496407641911258.8282163214
12610753.378724166810180.957449482911325.7999988507
12711303.80094025110721.996118555611885.6057619464
12811117.254474911710524.903901450311709.6050483731
12910968.598654113210364.515051078511572.6822571478
13010971.752022526810354.731704366711588.7723406869
13110171.31831014199540.1493531026610802.4872671811
13210597.78902594459951.2587736541611244.3192782347

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
121 & 10856.7827440687 & 10315.3470158939 & 11398.2184722434 \tabularnewline
122 & 9815.63895603043 & 9269.9442187123 & 10361.3336933486 \tabularnewline
123 & 10719.9933143405 & 10169.1346095159 & 11270.8520191652 \tabularnewline
124 & 10615.3171656398 & 10058.3214955257 & 11172.3128357539 \tabularnewline
125 & 10694.6623119817 & 10130.4964076419 & 11258.8282163214 \tabularnewline
126 & 10753.3787241668 & 10180.9574494829 & 11325.7999988507 \tabularnewline
127 & 11303.800940251 & 10721.9961185556 & 11885.6057619464 \tabularnewline
128 & 11117.2544749117 & 10524.9039014503 & 11709.6050483731 \tabularnewline
129 & 10968.5986541132 & 10364.5150510785 & 11572.6822571478 \tabularnewline
130 & 10971.7520225268 & 10354.7317043667 & 11588.7723406869 \tabularnewline
131 & 10171.3183101419 & 9540.14935310266 & 10802.4872671811 \tabularnewline
132 & 10597.7890259445 & 9951.25877365416 & 11244.3192782347 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=265183&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]121[/C][C]10856.7827440687[/C][C]10315.3470158939[/C][C]11398.2184722434[/C][/ROW]
[ROW][C]122[/C][C]9815.63895603043[/C][C]9269.9442187123[/C][C]10361.3336933486[/C][/ROW]
[ROW][C]123[/C][C]10719.9933143405[/C][C]10169.1346095159[/C][C]11270.8520191652[/C][/ROW]
[ROW][C]124[/C][C]10615.3171656398[/C][C]10058.3214955257[/C][C]11172.3128357539[/C][/ROW]
[ROW][C]125[/C][C]10694.6623119817[/C][C]10130.4964076419[/C][C]11258.8282163214[/C][/ROW]
[ROW][C]126[/C][C]10753.3787241668[/C][C]10180.9574494829[/C][C]11325.7999988507[/C][/ROW]
[ROW][C]127[/C][C]11303.800940251[/C][C]10721.9961185556[/C][C]11885.6057619464[/C][/ROW]
[ROW][C]128[/C][C]11117.2544749117[/C][C]10524.9039014503[/C][C]11709.6050483731[/C][/ROW]
[ROW][C]129[/C][C]10968.5986541132[/C][C]10364.5150510785[/C][C]11572.6822571478[/C][/ROW]
[ROW][C]130[/C][C]10971.7520225268[/C][C]10354.7317043667[/C][C]11588.7723406869[/C][/ROW]
[ROW][C]131[/C][C]10171.3183101419[/C][C]9540.14935310266[/C][C]10802.4872671811[/C][/ROW]
[ROW][C]132[/C][C]10597.7890259445[/C][C]9951.25877365416[/C][C]11244.3192782347[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=265183&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=265183&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
12110856.782744068710315.347015893911398.2184722434
1229815.638956030439269.944218712310361.3336933486
12310719.993314340510169.134609515911270.8520191652
12410615.317165639810058.321495525711172.3128357539
12510694.662311981710130.496407641911258.8282163214
12610753.378724166810180.957449482911325.7999988507
12711303.80094025110721.996118555611885.6057619464
12811117.254474911710524.903901450311709.6050483731
12910968.598654113210364.515051078511572.6822571478
13010971.752022526810354.731704366711588.7723406869
13110171.31831014199540.1493531026610802.4872671811
13210597.78902594459951.2587736541611244.3192782347



Parameters (Session):
par2 = grey ; par3 = FALSE ; par4 = Interval/Ratio ;
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')