Free Statistics

of Irreproducible Research!

Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationMon, 15 Aug 2016 11:02:34 +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/2016/Aug/15/t1471255600w0jsehdl8rkb0kd.htm/, Retrieved Sat, 27 Apr 2024 17:49:43 +0200
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=, Retrieved Sat, 27 Apr 2024 17:49:43 +0200
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact0
Dataseries X:
19064
18993
18921
18772
20246
20168
19064
18330
18401
18401
18480
18622
18843
18843
18701
18330
20246
20538
20097
19064
19506
18843
19142
19285
19434
19064
19142
18622
20246
20759
20318
19506
20389
19434
20318
20246
20467
19655
20538
20467
21792
21493
20318
19726
20538
19434
20246
20389
20688
20026
20389
20610
21422
20759
19876
18921
19805
17375
18551
19213
19876
18921
18921
18921
19434
18701
17739
16934
17518
15238
16635
17447
17596
16784
16855
16635
17375
16855
15830
15089
16342
13621
15388
16193
16193
15238
14355
14284
15089
14355
12959
11997
13030
10601
12809
13984
14355
13543
12517
13251
13543
13322
11113
10088
10821
8613
10893
11705
12367
11263
10230
10821
11113
10529
8321
7359
8242
5813
8463
10088




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time1 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 & 1 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ jenkins.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=&T=0

[TABLE]
[ROW][C]Summary of computational transaction[/C][/ROW]
[ROW][C]Raw Input[/C][C]view raw input (R code) [/C][/ROW]
[ROW][C]Raw Output[/C][C]view raw output of R engine [/C][/ROW]
[ROW][C]Computing time[/C][C]1 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Gwilym Jenkins' @ jenkins.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=&T=0

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

As an alternative you can also use a QR Code:  

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

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







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.405343002238435
beta0.0645195510983809
gamma1

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.405343002238435 \tabularnewline
beta & 0.0645195510983809 \tabularnewline
gamma & 1 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=&T=1

[TABLE]
[ROW][C]Estimated Parameters of Exponential Smoothing[/C][/ROW]
[ROW][C]Parameter[/C][C]Value[/C][/ROW]
[ROW][C]alpha[/C][C]0.405343002238435[/C][/ROW]
[ROW][C]beta[/C][C]0.0645195510983809[/C][/ROW]
[ROW][C]gamma[/C][C]1[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=&T=1

As an alternative you can also use a QR Code:  

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

Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.405343002238435
beta0.0645195510983809
gamma1







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
131884318842.18055555560.819444444445253
141884318800.825808854142.1741911458885
151870118632.336881918768.6631180812547
161833018259.54743834970.4525616510073
172024620194.784180580251.2158194198055
182053820490.354534832447.6454651675595
192009719387.8487213138709.151278686215
201906419014.567440153449.432559846573
211950619180.1249136202325.875086379849
221884319407.4255614212-564.425561421165
231914219328.9212381858-186.921238185758
241928519427.7138505994-142.713850599444
251943419577.1389090191-143.138909019101
261906419510.5861601928-446.586160192797
271914219155.5137615693-13.5137615692947
281862218744.1097559272-122.109755927173
292024620578.4486073918-332.448607391791
302075920694.941492880764.0585071192763
312031819971.4482530011346.551746998943
321950619028.3911353587477.608864641315
332038919512.6009611919876.3990388081
341943419428.73233535085.26766464922548
352031819815.6368969765502.36310302349
362024620248.1430029815-2.14300298152375
372046720485.9996697032-18.9996697031747
381965520324.2703818225-669.270381822476
392053820165.5917850625372.408214937477
402046719885.2617876901581.73821230985
412179221937.4490396091-145.449039609131
422149322428.0451587153-935.045158715329
432031821503.9482512598-1185.94825125979
441972620013.9476648714-287.947664871379
452053820401.2772714193136.72272858068
461943419456.5066361455-22.506636145521
472024620083.9729659896162.027034010418
482038920025.8360917978363.16390820215
492068820358.6150806772329.384919322805
502002619917.3958203867108.604179613299
512038920679.7909046778-290.79090467783
522061020224.0991896587385.900810341296
532142221728.3383427157-306.338342715699
542075921643.83279537-884.832795369988
551987620551.85356388-675.853563879955
561892119776.9246238634-855.924623863411
571980520146.0139225406-341.013922540635
581737518859.867148559-1484.86714855905
591855118913.0235876563-362.023587656342
601921318657.082123005555.91787699503
611987618947.9548918056928.045108194383
621892118533.8152472372387.184752762842
631892119094.6192369152-173.619236915241
641892119014.8773401235-93.877340123483
651943419826.5051383776-392.50513837759
661870119274.3214452462-573.321445246162
671773918352.2836740438-613.283674043832
681693417416.6743991959-482.674399195879
691751818174.0526749963-656.05267499627
701523816002.567114448-764.567114447986
711663516956.796886815-321.796886814987
721744717205.4713541382241.528645861817
731759617524.424635375871.5753646241938
741678416353.3236370724430.676362927628
751685516511.2371048176343.762895182372
761663516615.128848088519.8711519115386
771737517224.7548409977150.245159002276
781685516728.713953535126.286046465029
791583016028.456336152-198.45633615202
801508915311.4739029501-222.473902950085
811634216050.8386940612291.161305938807
821362114203.1595510915-582.159551091456
831538815503.7825193008-115.782519300783
841619316185.49589184597.50410815414398
851619316316.9516712733-123.951671273302
861523815283.4501633487-45.4501633486707
871435515187.5465361851-832.546536185131
881428414582.1226643146-298.122664314593
891508915092.161228972-3.1612289719742
901435514467.4600379739-112.460037973851
911295913418.8435733546-459.843573354592
921199712516.3170337982-519.317033798232
931303013367.7217012159-337.721701215905
941060110656.2823706672-55.2823706671534
951280912372.0643611106436.935638889379
961398413289.8450940591694.154905940939
971435513578.1302055652776.869794434753
981354312936.6819585135606.318041486511
991251712634.1911583184-117.191158318408
1001325112652.5143564822598.485643517823
1011354313740.820176685-197.820176685014
1021332213006.561684829315.438315171043
1031111311970.3490485987-857.349048598711
1041008810906.4666311221-818.466631122124
1051082111771.9130078121-950.91300781206
10686138991.15185093074-378.151850930741
1071089310871.594435439421.4055645606059
1081170511765.8656219288-60.8656219287805
1091236711769.5151464491597.484853550866
1101126310921.4630154278341.536984572183
1111023010042.0088985294187.991101470623
1121082110578.2027427688242.797257231205
1131111311008.086712797104.913287203048
1141052910668.9518940507-139.951894050657
11583218706.03422405533-385.034224055335
11673597824.36566716361-465.365667163611
11782428731.05602401265-489.056024012647
11858136467.05767078636-654.05767078636
11984638455.003611972937.99638802706613
120100889276.30589859216811.694101407837

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 18843 & 18842.1805555556 & 0.819444444445253 \tabularnewline
14 & 18843 & 18800.8258088541 & 42.1741911458885 \tabularnewline
15 & 18701 & 18632.3368819187 & 68.6631180812547 \tabularnewline
16 & 18330 & 18259.547438349 & 70.4525616510073 \tabularnewline
17 & 20246 & 20194.7841805802 & 51.2158194198055 \tabularnewline
18 & 20538 & 20490.3545348324 & 47.6454651675595 \tabularnewline
19 & 20097 & 19387.8487213138 & 709.151278686215 \tabularnewline
20 & 19064 & 19014.5674401534 & 49.432559846573 \tabularnewline
21 & 19506 & 19180.1249136202 & 325.875086379849 \tabularnewline
22 & 18843 & 19407.4255614212 & -564.425561421165 \tabularnewline
23 & 19142 & 19328.9212381858 & -186.921238185758 \tabularnewline
24 & 19285 & 19427.7138505994 & -142.713850599444 \tabularnewline
25 & 19434 & 19577.1389090191 & -143.138909019101 \tabularnewline
26 & 19064 & 19510.5861601928 & -446.586160192797 \tabularnewline
27 & 19142 & 19155.5137615693 & -13.5137615692947 \tabularnewline
28 & 18622 & 18744.1097559272 & -122.109755927173 \tabularnewline
29 & 20246 & 20578.4486073918 & -332.448607391791 \tabularnewline
30 & 20759 & 20694.9414928807 & 64.0585071192763 \tabularnewline
31 & 20318 & 19971.4482530011 & 346.551746998943 \tabularnewline
32 & 19506 & 19028.3911353587 & 477.608864641315 \tabularnewline
33 & 20389 & 19512.6009611919 & 876.3990388081 \tabularnewline
34 & 19434 & 19428.7323353508 & 5.26766464922548 \tabularnewline
35 & 20318 & 19815.6368969765 & 502.36310302349 \tabularnewline
36 & 20246 & 20248.1430029815 & -2.14300298152375 \tabularnewline
37 & 20467 & 20485.9996697032 & -18.9996697031747 \tabularnewline
38 & 19655 & 20324.2703818225 & -669.270381822476 \tabularnewline
39 & 20538 & 20165.5917850625 & 372.408214937477 \tabularnewline
40 & 20467 & 19885.2617876901 & 581.73821230985 \tabularnewline
41 & 21792 & 21937.4490396091 & -145.449039609131 \tabularnewline
42 & 21493 & 22428.0451587153 & -935.045158715329 \tabularnewline
43 & 20318 & 21503.9482512598 & -1185.94825125979 \tabularnewline
44 & 19726 & 20013.9476648714 & -287.947664871379 \tabularnewline
45 & 20538 & 20401.2772714193 & 136.72272858068 \tabularnewline
46 & 19434 & 19456.5066361455 & -22.506636145521 \tabularnewline
47 & 20246 & 20083.9729659896 & 162.027034010418 \tabularnewline
48 & 20389 & 20025.8360917978 & 363.16390820215 \tabularnewline
49 & 20688 & 20358.6150806772 & 329.384919322805 \tabularnewline
50 & 20026 & 19917.3958203867 & 108.604179613299 \tabularnewline
51 & 20389 & 20679.7909046778 & -290.79090467783 \tabularnewline
52 & 20610 & 20224.0991896587 & 385.900810341296 \tabularnewline
53 & 21422 & 21728.3383427157 & -306.338342715699 \tabularnewline
54 & 20759 & 21643.83279537 & -884.832795369988 \tabularnewline
55 & 19876 & 20551.85356388 & -675.853563879955 \tabularnewline
56 & 18921 & 19776.9246238634 & -855.924623863411 \tabularnewline
57 & 19805 & 20146.0139225406 & -341.013922540635 \tabularnewline
58 & 17375 & 18859.867148559 & -1484.86714855905 \tabularnewline
59 & 18551 & 18913.0235876563 & -362.023587656342 \tabularnewline
60 & 19213 & 18657.082123005 & 555.91787699503 \tabularnewline
61 & 19876 & 18947.9548918056 & 928.045108194383 \tabularnewline
62 & 18921 & 18533.8152472372 & 387.184752762842 \tabularnewline
63 & 18921 & 19094.6192369152 & -173.619236915241 \tabularnewline
64 & 18921 & 19014.8773401235 & -93.877340123483 \tabularnewline
65 & 19434 & 19826.5051383776 & -392.50513837759 \tabularnewline
66 & 18701 & 19274.3214452462 & -573.321445246162 \tabularnewline
67 & 17739 & 18352.2836740438 & -613.283674043832 \tabularnewline
68 & 16934 & 17416.6743991959 & -482.674399195879 \tabularnewline
69 & 17518 & 18174.0526749963 & -656.05267499627 \tabularnewline
70 & 15238 & 16002.567114448 & -764.567114447986 \tabularnewline
71 & 16635 & 16956.796886815 & -321.796886814987 \tabularnewline
72 & 17447 & 17205.4713541382 & 241.528645861817 \tabularnewline
73 & 17596 & 17524.4246353758 & 71.5753646241938 \tabularnewline
74 & 16784 & 16353.3236370724 & 430.676362927628 \tabularnewline
75 & 16855 & 16511.2371048176 & 343.762895182372 \tabularnewline
76 & 16635 & 16615.1288480885 & 19.8711519115386 \tabularnewline
77 & 17375 & 17224.7548409977 & 150.245159002276 \tabularnewline
78 & 16855 & 16728.713953535 & 126.286046465029 \tabularnewline
79 & 15830 & 16028.456336152 & -198.45633615202 \tabularnewline
80 & 15089 & 15311.4739029501 & -222.473902950085 \tabularnewline
81 & 16342 & 16050.8386940612 & 291.161305938807 \tabularnewline
82 & 13621 & 14203.1595510915 & -582.159551091456 \tabularnewline
83 & 15388 & 15503.7825193008 & -115.782519300783 \tabularnewline
84 & 16193 & 16185.4958918459 & 7.50410815414398 \tabularnewline
85 & 16193 & 16316.9516712733 & -123.951671273302 \tabularnewline
86 & 15238 & 15283.4501633487 & -45.4501633486707 \tabularnewline
87 & 14355 & 15187.5465361851 & -832.546536185131 \tabularnewline
88 & 14284 & 14582.1226643146 & -298.122664314593 \tabularnewline
89 & 15089 & 15092.161228972 & -3.1612289719742 \tabularnewline
90 & 14355 & 14467.4600379739 & -112.460037973851 \tabularnewline
91 & 12959 & 13418.8435733546 & -459.843573354592 \tabularnewline
92 & 11997 & 12516.3170337982 & -519.317033798232 \tabularnewline
93 & 13030 & 13367.7217012159 & -337.721701215905 \tabularnewline
94 & 10601 & 10656.2823706672 & -55.2823706671534 \tabularnewline
95 & 12809 & 12372.0643611106 & 436.935638889379 \tabularnewline
96 & 13984 & 13289.8450940591 & 694.154905940939 \tabularnewline
97 & 14355 & 13578.1302055652 & 776.869794434753 \tabularnewline
98 & 13543 & 12936.6819585135 & 606.318041486511 \tabularnewline
99 & 12517 & 12634.1911583184 & -117.191158318408 \tabularnewline
100 & 13251 & 12652.5143564822 & 598.485643517823 \tabularnewline
101 & 13543 & 13740.820176685 & -197.820176685014 \tabularnewline
102 & 13322 & 13006.561684829 & 315.438315171043 \tabularnewline
103 & 11113 & 11970.3490485987 & -857.349048598711 \tabularnewline
104 & 10088 & 10906.4666311221 & -818.466631122124 \tabularnewline
105 & 10821 & 11771.9130078121 & -950.91300781206 \tabularnewline
106 & 8613 & 8991.15185093074 & -378.151850930741 \tabularnewline
107 & 10893 & 10871.5944354394 & 21.4055645606059 \tabularnewline
108 & 11705 & 11765.8656219288 & -60.8656219287805 \tabularnewline
109 & 12367 & 11769.5151464491 & 597.484853550866 \tabularnewline
110 & 11263 & 10921.4630154278 & 341.536984572183 \tabularnewline
111 & 10230 & 10042.0088985294 & 187.991101470623 \tabularnewline
112 & 10821 & 10578.2027427688 & 242.797257231205 \tabularnewline
113 & 11113 & 11008.086712797 & 104.913287203048 \tabularnewline
114 & 10529 & 10668.9518940507 & -139.951894050657 \tabularnewline
115 & 8321 & 8706.03422405533 & -385.034224055335 \tabularnewline
116 & 7359 & 7824.36566716361 & -465.365667163611 \tabularnewline
117 & 8242 & 8731.05602401265 & -489.056024012647 \tabularnewline
118 & 5813 & 6467.05767078636 & -654.05767078636 \tabularnewline
119 & 8463 & 8455.00361197293 & 7.99638802706613 \tabularnewline
120 & 10088 & 9276.30589859216 & 811.694101407837 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=&T=2

[TABLE]
[ROW][C]Interpolation Forecasts of Exponential Smoothing[/C][/ROW]
[ROW][C]t[/C][C]Observed[/C][C]Fitted[/C][C]Residuals[/C][/ROW]
[ROW][C]13[/C][C]18843[/C][C]18842.1805555556[/C][C]0.819444444445253[/C][/ROW]
[ROW][C]14[/C][C]18843[/C][C]18800.8258088541[/C][C]42.1741911458885[/C][/ROW]
[ROW][C]15[/C][C]18701[/C][C]18632.3368819187[/C][C]68.6631180812547[/C][/ROW]
[ROW][C]16[/C][C]18330[/C][C]18259.547438349[/C][C]70.4525616510073[/C][/ROW]
[ROW][C]17[/C][C]20246[/C][C]20194.7841805802[/C][C]51.2158194198055[/C][/ROW]
[ROW][C]18[/C][C]20538[/C][C]20490.3545348324[/C][C]47.6454651675595[/C][/ROW]
[ROW][C]19[/C][C]20097[/C][C]19387.8487213138[/C][C]709.151278686215[/C][/ROW]
[ROW][C]20[/C][C]19064[/C][C]19014.5674401534[/C][C]49.432559846573[/C][/ROW]
[ROW][C]21[/C][C]19506[/C][C]19180.1249136202[/C][C]325.875086379849[/C][/ROW]
[ROW][C]22[/C][C]18843[/C][C]19407.4255614212[/C][C]-564.425561421165[/C][/ROW]
[ROW][C]23[/C][C]19142[/C][C]19328.9212381858[/C][C]-186.921238185758[/C][/ROW]
[ROW][C]24[/C][C]19285[/C][C]19427.7138505994[/C][C]-142.713850599444[/C][/ROW]
[ROW][C]25[/C][C]19434[/C][C]19577.1389090191[/C][C]-143.138909019101[/C][/ROW]
[ROW][C]26[/C][C]19064[/C][C]19510.5861601928[/C][C]-446.586160192797[/C][/ROW]
[ROW][C]27[/C][C]19142[/C][C]19155.5137615693[/C][C]-13.5137615692947[/C][/ROW]
[ROW][C]28[/C][C]18622[/C][C]18744.1097559272[/C][C]-122.109755927173[/C][/ROW]
[ROW][C]29[/C][C]20246[/C][C]20578.4486073918[/C][C]-332.448607391791[/C][/ROW]
[ROW][C]30[/C][C]20759[/C][C]20694.9414928807[/C][C]64.0585071192763[/C][/ROW]
[ROW][C]31[/C][C]20318[/C][C]19971.4482530011[/C][C]346.551746998943[/C][/ROW]
[ROW][C]32[/C][C]19506[/C][C]19028.3911353587[/C][C]477.608864641315[/C][/ROW]
[ROW][C]33[/C][C]20389[/C][C]19512.6009611919[/C][C]876.3990388081[/C][/ROW]
[ROW][C]34[/C][C]19434[/C][C]19428.7323353508[/C][C]5.26766464922548[/C][/ROW]
[ROW][C]35[/C][C]20318[/C][C]19815.6368969765[/C][C]502.36310302349[/C][/ROW]
[ROW][C]36[/C][C]20246[/C][C]20248.1430029815[/C][C]-2.14300298152375[/C][/ROW]
[ROW][C]37[/C][C]20467[/C][C]20485.9996697032[/C][C]-18.9996697031747[/C][/ROW]
[ROW][C]38[/C][C]19655[/C][C]20324.2703818225[/C][C]-669.270381822476[/C][/ROW]
[ROW][C]39[/C][C]20538[/C][C]20165.5917850625[/C][C]372.408214937477[/C][/ROW]
[ROW][C]40[/C][C]20467[/C][C]19885.2617876901[/C][C]581.73821230985[/C][/ROW]
[ROW][C]41[/C][C]21792[/C][C]21937.4490396091[/C][C]-145.449039609131[/C][/ROW]
[ROW][C]42[/C][C]21493[/C][C]22428.0451587153[/C][C]-935.045158715329[/C][/ROW]
[ROW][C]43[/C][C]20318[/C][C]21503.9482512598[/C][C]-1185.94825125979[/C][/ROW]
[ROW][C]44[/C][C]19726[/C][C]20013.9476648714[/C][C]-287.947664871379[/C][/ROW]
[ROW][C]45[/C][C]20538[/C][C]20401.2772714193[/C][C]136.72272858068[/C][/ROW]
[ROW][C]46[/C][C]19434[/C][C]19456.5066361455[/C][C]-22.506636145521[/C][/ROW]
[ROW][C]47[/C][C]20246[/C][C]20083.9729659896[/C][C]162.027034010418[/C][/ROW]
[ROW][C]48[/C][C]20389[/C][C]20025.8360917978[/C][C]363.16390820215[/C][/ROW]
[ROW][C]49[/C][C]20688[/C][C]20358.6150806772[/C][C]329.384919322805[/C][/ROW]
[ROW][C]50[/C][C]20026[/C][C]19917.3958203867[/C][C]108.604179613299[/C][/ROW]
[ROW][C]51[/C][C]20389[/C][C]20679.7909046778[/C][C]-290.79090467783[/C][/ROW]
[ROW][C]52[/C][C]20610[/C][C]20224.0991896587[/C][C]385.900810341296[/C][/ROW]
[ROW][C]53[/C][C]21422[/C][C]21728.3383427157[/C][C]-306.338342715699[/C][/ROW]
[ROW][C]54[/C][C]20759[/C][C]21643.83279537[/C][C]-884.832795369988[/C][/ROW]
[ROW][C]55[/C][C]19876[/C][C]20551.85356388[/C][C]-675.853563879955[/C][/ROW]
[ROW][C]56[/C][C]18921[/C][C]19776.9246238634[/C][C]-855.924623863411[/C][/ROW]
[ROW][C]57[/C][C]19805[/C][C]20146.0139225406[/C][C]-341.013922540635[/C][/ROW]
[ROW][C]58[/C][C]17375[/C][C]18859.867148559[/C][C]-1484.86714855905[/C][/ROW]
[ROW][C]59[/C][C]18551[/C][C]18913.0235876563[/C][C]-362.023587656342[/C][/ROW]
[ROW][C]60[/C][C]19213[/C][C]18657.082123005[/C][C]555.91787699503[/C][/ROW]
[ROW][C]61[/C][C]19876[/C][C]18947.9548918056[/C][C]928.045108194383[/C][/ROW]
[ROW][C]62[/C][C]18921[/C][C]18533.8152472372[/C][C]387.184752762842[/C][/ROW]
[ROW][C]63[/C][C]18921[/C][C]19094.6192369152[/C][C]-173.619236915241[/C][/ROW]
[ROW][C]64[/C][C]18921[/C][C]19014.8773401235[/C][C]-93.877340123483[/C][/ROW]
[ROW][C]65[/C][C]19434[/C][C]19826.5051383776[/C][C]-392.50513837759[/C][/ROW]
[ROW][C]66[/C][C]18701[/C][C]19274.3214452462[/C][C]-573.321445246162[/C][/ROW]
[ROW][C]67[/C][C]17739[/C][C]18352.2836740438[/C][C]-613.283674043832[/C][/ROW]
[ROW][C]68[/C][C]16934[/C][C]17416.6743991959[/C][C]-482.674399195879[/C][/ROW]
[ROW][C]69[/C][C]17518[/C][C]18174.0526749963[/C][C]-656.05267499627[/C][/ROW]
[ROW][C]70[/C][C]15238[/C][C]16002.567114448[/C][C]-764.567114447986[/C][/ROW]
[ROW][C]71[/C][C]16635[/C][C]16956.796886815[/C][C]-321.796886814987[/C][/ROW]
[ROW][C]72[/C][C]17447[/C][C]17205.4713541382[/C][C]241.528645861817[/C][/ROW]
[ROW][C]73[/C][C]17596[/C][C]17524.4246353758[/C][C]71.5753646241938[/C][/ROW]
[ROW][C]74[/C][C]16784[/C][C]16353.3236370724[/C][C]430.676362927628[/C][/ROW]
[ROW][C]75[/C][C]16855[/C][C]16511.2371048176[/C][C]343.762895182372[/C][/ROW]
[ROW][C]76[/C][C]16635[/C][C]16615.1288480885[/C][C]19.8711519115386[/C][/ROW]
[ROW][C]77[/C][C]17375[/C][C]17224.7548409977[/C][C]150.245159002276[/C][/ROW]
[ROW][C]78[/C][C]16855[/C][C]16728.713953535[/C][C]126.286046465029[/C][/ROW]
[ROW][C]79[/C][C]15830[/C][C]16028.456336152[/C][C]-198.45633615202[/C][/ROW]
[ROW][C]80[/C][C]15089[/C][C]15311.4739029501[/C][C]-222.473902950085[/C][/ROW]
[ROW][C]81[/C][C]16342[/C][C]16050.8386940612[/C][C]291.161305938807[/C][/ROW]
[ROW][C]82[/C][C]13621[/C][C]14203.1595510915[/C][C]-582.159551091456[/C][/ROW]
[ROW][C]83[/C][C]15388[/C][C]15503.7825193008[/C][C]-115.782519300783[/C][/ROW]
[ROW][C]84[/C][C]16193[/C][C]16185.4958918459[/C][C]7.50410815414398[/C][/ROW]
[ROW][C]85[/C][C]16193[/C][C]16316.9516712733[/C][C]-123.951671273302[/C][/ROW]
[ROW][C]86[/C][C]15238[/C][C]15283.4501633487[/C][C]-45.4501633486707[/C][/ROW]
[ROW][C]87[/C][C]14355[/C][C]15187.5465361851[/C][C]-832.546536185131[/C][/ROW]
[ROW][C]88[/C][C]14284[/C][C]14582.1226643146[/C][C]-298.122664314593[/C][/ROW]
[ROW][C]89[/C][C]15089[/C][C]15092.161228972[/C][C]-3.1612289719742[/C][/ROW]
[ROW][C]90[/C][C]14355[/C][C]14467.4600379739[/C][C]-112.460037973851[/C][/ROW]
[ROW][C]91[/C][C]12959[/C][C]13418.8435733546[/C][C]-459.843573354592[/C][/ROW]
[ROW][C]92[/C][C]11997[/C][C]12516.3170337982[/C][C]-519.317033798232[/C][/ROW]
[ROW][C]93[/C][C]13030[/C][C]13367.7217012159[/C][C]-337.721701215905[/C][/ROW]
[ROW][C]94[/C][C]10601[/C][C]10656.2823706672[/C][C]-55.2823706671534[/C][/ROW]
[ROW][C]95[/C][C]12809[/C][C]12372.0643611106[/C][C]436.935638889379[/C][/ROW]
[ROW][C]96[/C][C]13984[/C][C]13289.8450940591[/C][C]694.154905940939[/C][/ROW]
[ROW][C]97[/C][C]14355[/C][C]13578.1302055652[/C][C]776.869794434753[/C][/ROW]
[ROW][C]98[/C][C]13543[/C][C]12936.6819585135[/C][C]606.318041486511[/C][/ROW]
[ROW][C]99[/C][C]12517[/C][C]12634.1911583184[/C][C]-117.191158318408[/C][/ROW]
[ROW][C]100[/C][C]13251[/C][C]12652.5143564822[/C][C]598.485643517823[/C][/ROW]
[ROW][C]101[/C][C]13543[/C][C]13740.820176685[/C][C]-197.820176685014[/C][/ROW]
[ROW][C]102[/C][C]13322[/C][C]13006.561684829[/C][C]315.438315171043[/C][/ROW]
[ROW][C]103[/C][C]11113[/C][C]11970.3490485987[/C][C]-857.349048598711[/C][/ROW]
[ROW][C]104[/C][C]10088[/C][C]10906.4666311221[/C][C]-818.466631122124[/C][/ROW]
[ROW][C]105[/C][C]10821[/C][C]11771.9130078121[/C][C]-950.91300781206[/C][/ROW]
[ROW][C]106[/C][C]8613[/C][C]8991.15185093074[/C][C]-378.151850930741[/C][/ROW]
[ROW][C]107[/C][C]10893[/C][C]10871.5944354394[/C][C]21.4055645606059[/C][/ROW]
[ROW][C]108[/C][C]11705[/C][C]11765.8656219288[/C][C]-60.8656219287805[/C][/ROW]
[ROW][C]109[/C][C]12367[/C][C]11769.5151464491[/C][C]597.484853550866[/C][/ROW]
[ROW][C]110[/C][C]11263[/C][C]10921.4630154278[/C][C]341.536984572183[/C][/ROW]
[ROW][C]111[/C][C]10230[/C][C]10042.0088985294[/C][C]187.991101470623[/C][/ROW]
[ROW][C]112[/C][C]10821[/C][C]10578.2027427688[/C][C]242.797257231205[/C][/ROW]
[ROW][C]113[/C][C]11113[/C][C]11008.086712797[/C][C]104.913287203048[/C][/ROW]
[ROW][C]114[/C][C]10529[/C][C]10668.9518940507[/C][C]-139.951894050657[/C][/ROW]
[ROW][C]115[/C][C]8321[/C][C]8706.03422405533[/C][C]-385.034224055335[/C][/ROW]
[ROW][C]116[/C][C]7359[/C][C]7824.36566716361[/C][C]-465.365667163611[/C][/ROW]
[ROW][C]117[/C][C]8242[/C][C]8731.05602401265[/C][C]-489.056024012647[/C][/ROW]
[ROW][C]118[/C][C]5813[/C][C]6467.05767078636[/C][C]-654.05767078636[/C][/ROW]
[ROW][C]119[/C][C]8463[/C][C]8455.00361197293[/C][C]7.99638802706613[/C][/ROW]
[ROW][C]120[/C][C]10088[/C][C]9276.30589859216[/C][C]811.694101407837[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=&T=2

As an alternative you can also use a QR Code:  

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

Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
131884318842.18055555560.819444444445253
141884318800.825808854142.1741911458885
151870118632.336881918768.6631180812547
161833018259.54743834970.4525616510073
172024620194.784180580251.2158194198055
182053820490.354534832447.6454651675595
192009719387.8487213138709.151278686215
201906419014.567440153449.432559846573
211950619180.1249136202325.875086379849
221884319407.4255614212-564.425561421165
231914219328.9212381858-186.921238185758
241928519427.7138505994-142.713850599444
251943419577.1389090191-143.138909019101
261906419510.5861601928-446.586160192797
271914219155.5137615693-13.5137615692947
281862218744.1097559272-122.109755927173
292024620578.4486073918-332.448607391791
302075920694.941492880764.0585071192763
312031819971.4482530011346.551746998943
321950619028.3911353587477.608864641315
332038919512.6009611919876.3990388081
341943419428.73233535085.26766464922548
352031819815.6368969765502.36310302349
362024620248.1430029815-2.14300298152375
372046720485.9996697032-18.9996697031747
381965520324.2703818225-669.270381822476
392053820165.5917850625372.408214937477
402046719885.2617876901581.73821230985
412179221937.4490396091-145.449039609131
422149322428.0451587153-935.045158715329
432031821503.9482512598-1185.94825125979
441972620013.9476648714-287.947664871379
452053820401.2772714193136.72272858068
461943419456.5066361455-22.506636145521
472024620083.9729659896162.027034010418
482038920025.8360917978363.16390820215
492068820358.6150806772329.384919322805
502002619917.3958203867108.604179613299
512038920679.7909046778-290.79090467783
522061020224.0991896587385.900810341296
532142221728.3383427157-306.338342715699
542075921643.83279537-884.832795369988
551987620551.85356388-675.853563879955
561892119776.9246238634-855.924623863411
571980520146.0139225406-341.013922540635
581737518859.867148559-1484.86714855905
591855118913.0235876563-362.023587656342
601921318657.082123005555.91787699503
611987618947.9548918056928.045108194383
621892118533.8152472372387.184752762842
631892119094.6192369152-173.619236915241
641892119014.8773401235-93.877340123483
651943419826.5051383776-392.50513837759
661870119274.3214452462-573.321445246162
671773918352.2836740438-613.283674043832
681693417416.6743991959-482.674399195879
691751818174.0526749963-656.05267499627
701523816002.567114448-764.567114447986
711663516956.796886815-321.796886814987
721744717205.4713541382241.528645861817
731759617524.424635375871.5753646241938
741678416353.3236370724430.676362927628
751685516511.2371048176343.762895182372
761663516615.128848088519.8711519115386
771737517224.7548409977150.245159002276
781685516728.713953535126.286046465029
791583016028.456336152-198.45633615202
801508915311.4739029501-222.473902950085
811634216050.8386940612291.161305938807
821362114203.1595510915-582.159551091456
831538815503.7825193008-115.782519300783
841619316185.49589184597.50410815414398
851619316316.9516712733-123.951671273302
861523815283.4501633487-45.4501633486707
871435515187.5465361851-832.546536185131
881428414582.1226643146-298.122664314593
891508915092.161228972-3.1612289719742
901435514467.4600379739-112.460037973851
911295913418.8435733546-459.843573354592
921199712516.3170337982-519.317033798232
931303013367.7217012159-337.721701215905
941060110656.2823706672-55.2823706671534
951280912372.0643611106436.935638889379
961398413289.8450940591694.154905940939
971435513578.1302055652776.869794434753
981354312936.6819585135606.318041486511
991251712634.1911583184-117.191158318408
1001325112652.5143564822598.485643517823
1011354313740.820176685-197.820176685014
1021332213006.561684829315.438315171043
1031111311970.3490485987-857.349048598711
1041008810906.4666311221-818.466631122124
1051082111771.9130078121-950.91300781206
10686138991.15185093074-378.151850930741
1071089310871.594435439421.4055645606059
1081170511765.8656219288-60.8656219287805
1091236711769.5151464491597.484853550866
1101126310921.4630154278341.536984572183
1111023010042.0088985294187.991101470623
1121082110578.2027427688242.797257231205
1131111311008.086712797104.913287203048
1141052910668.9518940507-139.951894050657
11583218706.03422405533-385.034224055335
11673597824.36566716361-465.365667163611
11782428731.05602401265-489.056024012647
11858136467.05767078636-654.05767078636
11984638455.003611972937.99638802706613
120100889276.30589859216811.694101407837







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
12110029.34333151259116.371845262510942.3148177626
1228775.487166459797781.149131496339769.82520142326
1237645.937688075766567.382450459278724.49292569225
1248113.256471567296947.762185598219278.75075753637
1258331.115790374197076.072008125559586.15957262284
1267769.48574705756422.379414109249116.59208000576
1275686.858209883664245.262275223847128.45414454348
1284892.862087269683354.426137185216431.29803735415
1295965.63918322684328.081657275657603.19670917795
1303806.088603470822067.190259356185544.98694758546
1316474.284318857934631.882692967248316.68594474861
1327791.497664285055843.48233374089739.51299482929

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
121 & 10029.3433315125 & 9116.3718452625 & 10942.3148177626 \tabularnewline
122 & 8775.48716645979 & 7781.14913149633 & 9769.82520142326 \tabularnewline
123 & 7645.93768807576 & 6567.38245045927 & 8724.49292569225 \tabularnewline
124 & 8113.25647156729 & 6947.76218559821 & 9278.75075753637 \tabularnewline
125 & 8331.11579037419 & 7076.07200812555 & 9586.15957262284 \tabularnewline
126 & 7769.4857470575 & 6422.37941410924 & 9116.59208000576 \tabularnewline
127 & 5686.85820988366 & 4245.26227522384 & 7128.45414454348 \tabularnewline
128 & 4892.86208726968 & 3354.42613718521 & 6431.29803735415 \tabularnewline
129 & 5965.6391832268 & 4328.08165727565 & 7603.19670917795 \tabularnewline
130 & 3806.08860347082 & 2067.19025935618 & 5544.98694758546 \tabularnewline
131 & 6474.28431885793 & 4631.88269296724 & 8316.68594474861 \tabularnewline
132 & 7791.49766428505 & 5843.4823337408 & 9739.51299482929 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=&T=3

[TABLE]
[ROW][C]Extrapolation Forecasts of Exponential Smoothing[/C][/ROW]
[ROW][C]t[/C][C]Forecast[/C][C]95% Lower Bound[/C][C]95% Upper Bound[/C][/ROW]
[ROW][C]121[/C][C]10029.3433315125[/C][C]9116.3718452625[/C][C]10942.3148177626[/C][/ROW]
[ROW][C]122[/C][C]8775.48716645979[/C][C]7781.14913149633[/C][C]9769.82520142326[/C][/ROW]
[ROW][C]123[/C][C]7645.93768807576[/C][C]6567.38245045927[/C][C]8724.49292569225[/C][/ROW]
[ROW][C]124[/C][C]8113.25647156729[/C][C]6947.76218559821[/C][C]9278.75075753637[/C][/ROW]
[ROW][C]125[/C][C]8331.11579037419[/C][C]7076.07200812555[/C][C]9586.15957262284[/C][/ROW]
[ROW][C]126[/C][C]7769.4857470575[/C][C]6422.37941410924[/C][C]9116.59208000576[/C][/ROW]
[ROW][C]127[/C][C]5686.85820988366[/C][C]4245.26227522384[/C][C]7128.45414454348[/C][/ROW]
[ROW][C]128[/C][C]4892.86208726968[/C][C]3354.42613718521[/C][C]6431.29803735415[/C][/ROW]
[ROW][C]129[/C][C]5965.6391832268[/C][C]4328.08165727565[/C][C]7603.19670917795[/C][/ROW]
[ROW][C]130[/C][C]3806.08860347082[/C][C]2067.19025935618[/C][C]5544.98694758546[/C][/ROW]
[ROW][C]131[/C][C]6474.28431885793[/C][C]4631.88269296724[/C][C]8316.68594474861[/C][/ROW]
[ROW][C]132[/C][C]7791.49766428505[/C][C]5843.4823337408[/C][C]9739.51299482929[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=&T=3

As an alternative you can also use a QR Code:  

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

Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
12110029.34333151259116.371845262510942.3148177626
1228775.487166459797781.149131496339769.82520142326
1237645.937688075766567.382450459278724.49292569225
1248113.256471567296947.762185598219278.75075753637
1258331.115790374197076.072008125559586.15957262284
1267769.48574705756422.379414109249116.59208000576
1275686.858209883664245.262275223847128.45414454348
1284892.862087269683354.426137185216431.29803735415
1295965.63918322684328.081657275657603.19670917795
1303806.088603470822067.190259356185544.98694758546
1316474.284318857934631.882692967248316.68594474861
1327791.497664285055843.48233374089739.51299482929



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')