Free Statistics

of Irreproducible Research!

Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationMon, 26 May 2008 12:59:43 -0600
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2008/May/26/t1211828426low7uv6dl673mnt.htm/, Retrieved Tue, 14 May 2024 12:35:06 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=13294, Retrieved Tue, 14 May 2024 12:35:06 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact174
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [Exponential Smoot...] [2008-05-26 18:59:43] [dd867cfc9ddc7089fae26da93ef9f864] [Current]
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Dataseries X:
36409
33163
34122
35225
28249
30374
26311
22069
23651
28628
23187
14727
43080
32519
39657
33614
28671
34243
27336
22916
24537
26128
22602
15744
41086
39690
43129
37863
35953
29133
24693
22205
21725
27192
21790
13253
37702
30364
32609
30212
29965
28352
25814
22414
20506
28806
22228
13971
36845
35338
35022
34777
26887
23970
22780
17351
21382
24561
17409
11514
31514
27071
29462
26105
22397
23843
21705
18089
20764
25316
17704
15548
28029
29383
36438
32034
22679
24319
18004
17537
20366
22782
19169
13807
29743
25591
29096
26482
22405
27044
17970
18730
19684
19785
18479
10698
31956
29506
34506
27165
26736
23691
18157
17328
18205
20995
17382
9367




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time3 seconds
R Server'Sir Ronald Aylmer Fisher' @ 193.190.124.24

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input & view raw input (R code)  \tabularnewline
Raw Output & view raw output of R engine  \tabularnewline
Computing time & 3 seconds \tabularnewline
R Server & 'Sir Ronald Aylmer Fisher' @ 193.190.124.24 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=13294&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]'Sir Ronald Aylmer Fisher' @ 193.190.124.24[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=13294&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=13294&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'Sir Ronald Aylmer Fisher' @ 193.190.124.24







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.51705592571119
beta0
gamma0

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.51705592571119 \tabularnewline
beta & 0 \tabularnewline
gamma & 0 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=13294&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]0.51705592571119[/C][/ROW]
[ROW][C]beta[/C][C]0[/C][/ROW]
[ROW][C]gamma[/C][C]0[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=13294&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=13294&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
alpha0.51705592571119
beta0
gamma0







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
33412233163959
43522533658.8566327571566.14336724297
52824934468.6403413033-6219.64034130328
63037431252.7384470401-878.73844704005
72631130798.3815258477-4487.38152584774
82206928478.1543169812-6409.15431698124
92365125164.2630985886-1513.26309858864
102862824381.82144630334246.1785536967
112318726577.3332291200-3390.33322911995
121472724824.3413428679-10097.3413428679
134308019603.451167609523476.5488323905
143251931742.1398566451776.860143354876
153965732143.81999721567513.1800027844
163361436028.5542385901-2414.5542385901
172867134780.094661576-6109.09466157602
183424331621.35106607752621.64893392246
192733632976.8901824966-5640.89018249657
202291630060.2344873506-7144.23448735064
212453726366.2657109957-1829.26571099574
222612825420.4330354251707.5669645749
232260225786.2847272960-3184.28472729603
241574424139.831439896-8395.83143989598
254108619798.717042625421287.2829573746
263969030805.43283802688884.5671619732
274312935399.25093650417729.7490634959
283786339395.9634940452-1532.96349404518
293595338603.3356355502-2650.33563555019
302913337232.9638900654-8099.96389006543
312469333044.8295626604-8351.82956266044
322220528726.4665967570-6521.46659675696
332172525354.5036485762-3629.50364857618
342719223477.84727968953714.15272031052
352179025398.2719527224-3608.27195272237
361325323532.5935579898-10279.5935579898
373770218217.468794928619484.5312050714
383036428292.06111421542071.93888578464
393260929363.36939282183245.63060717825
403021231041.5419309329-829.541930932872
412996530612.6223599181-647.622359918128
422835230277.7653810994-1925.76538109939
432581429282.0369792725-3468.03697927249
442241427488.8679085541-5074.86790855411
452050624864.8773842346-4358.87738423465
462880622611.09400326766194.90599673237
472222825814.2068581019-3586.20685810189
481397123959.9373512942-9988.9373512942
493684518795.098102249718049.9018977503
503533828127.90683698717210.09316301285
513502231855.92823185273166.07176814732
523477733492.96440080021284.03559919984
532688734156.8826161906-7269.88261619055
542397030397.9467302645-6427.94673026446
552278027074.3387832253-4294.33878322535
561735124853.9254683473-7502.9254683473
572138220974.4933947689407.506605231083
582456121185.19709977013375.8029002299
591740922930.675993367-5521.67599336699
601151420075.6607011394-8561.66070113936
613151415648.803301686615865.1966983134
622707123851.99726712323219.00273287683
632946225516.40170503763945.59829496235
642610527556.4966839239-1451.49668392390
652239726805.9917223509-4408.99172235091
662384324526.2964258978-683.296425897785
672170524172.9939598701-2467.99395987006
681808922896.9030582998-4807.90305829982
692076420410.9482917609353.051708239058
702531620593.49576958844722.5042304116
711770423035.2945661189-5331.29456611889
721554820278.7171189952-4730.71711899525
732802917832.671799755410196.3282002446
742938323104.7437161886278.25628381202
753643826350.953330866510087.0466691335
763203431566.5205840673467.479415932699
772267931808.2335862233-9129.2335862233
782431927087.9092632649-2768.90926326493
791800425656.2283209372-7652.22832093719
801753721699.5983227016-4162.59832270162
812036619547.3021935933818.697806406715
822278219970.61474576262811.38525423737
831916921424.2581509231-2255.25815092312
841380720258.1635599799-6451.16355997986
852974316922.551213560212820.4487864398
862559123551.44022886572039.55977113427
872909624606.00669437294489.99330562714
882648226927.5843394510-445.58433945095
892240526697.1923163337-4292.19231633373
902704424477.88884488132566.11115511867
911797025804.7118236690-7834.71182366903
921873021753.7276490014-3023.72764900143
931968420190.2913503485-506.291350348474
941978519928.5104075145-143.510407514474
951847919854.3075009079-1375.30750090789
961069819143.1966078884-8445.19660788841
973195614776.557657983717179.4423420163
982950623659.29012133695846.70987866306
993450626682.36611001387823.63388998617
1002716530727.6223734261-3562.62237342607
1012673628885.5473641749-2149.54736417485
1022369127774.1111619314-4083.11116193137
1031815725662.9143403173-7505.91434031725
1041732821781.9368527756-4453.93685277562
1051820519479.0024103045-1274.00241030453
1062099518820.27191468622174.72808531376
1071738219944.7279580083-2562.72795800827
108936718619.6542813344-9252.65428133435

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
3 & 34122 & 33163 & 959 \tabularnewline
4 & 35225 & 33658.856632757 & 1566.14336724297 \tabularnewline
5 & 28249 & 34468.6403413033 & -6219.64034130328 \tabularnewline
6 & 30374 & 31252.7384470401 & -878.73844704005 \tabularnewline
7 & 26311 & 30798.3815258477 & -4487.38152584774 \tabularnewline
8 & 22069 & 28478.1543169812 & -6409.15431698124 \tabularnewline
9 & 23651 & 25164.2630985886 & -1513.26309858864 \tabularnewline
10 & 28628 & 24381.8214463033 & 4246.1785536967 \tabularnewline
11 & 23187 & 26577.3332291200 & -3390.33322911995 \tabularnewline
12 & 14727 & 24824.3413428679 & -10097.3413428679 \tabularnewline
13 & 43080 & 19603.4511676095 & 23476.5488323905 \tabularnewline
14 & 32519 & 31742.1398566451 & 776.860143354876 \tabularnewline
15 & 39657 & 32143.8199972156 & 7513.1800027844 \tabularnewline
16 & 33614 & 36028.5542385901 & -2414.5542385901 \tabularnewline
17 & 28671 & 34780.094661576 & -6109.09466157602 \tabularnewline
18 & 34243 & 31621.3510660775 & 2621.64893392246 \tabularnewline
19 & 27336 & 32976.8901824966 & -5640.89018249657 \tabularnewline
20 & 22916 & 30060.2344873506 & -7144.23448735064 \tabularnewline
21 & 24537 & 26366.2657109957 & -1829.26571099574 \tabularnewline
22 & 26128 & 25420.4330354251 & 707.5669645749 \tabularnewline
23 & 22602 & 25786.2847272960 & -3184.28472729603 \tabularnewline
24 & 15744 & 24139.831439896 & -8395.83143989598 \tabularnewline
25 & 41086 & 19798.7170426254 & 21287.2829573746 \tabularnewline
26 & 39690 & 30805.4328380268 & 8884.5671619732 \tabularnewline
27 & 43129 & 35399.2509365041 & 7729.7490634959 \tabularnewline
28 & 37863 & 39395.9634940452 & -1532.96349404518 \tabularnewline
29 & 35953 & 38603.3356355502 & -2650.33563555019 \tabularnewline
30 & 29133 & 37232.9638900654 & -8099.96389006543 \tabularnewline
31 & 24693 & 33044.8295626604 & -8351.82956266044 \tabularnewline
32 & 22205 & 28726.4665967570 & -6521.46659675696 \tabularnewline
33 & 21725 & 25354.5036485762 & -3629.50364857618 \tabularnewline
34 & 27192 & 23477.8472796895 & 3714.15272031052 \tabularnewline
35 & 21790 & 25398.2719527224 & -3608.27195272237 \tabularnewline
36 & 13253 & 23532.5935579898 & -10279.5935579898 \tabularnewline
37 & 37702 & 18217.4687949286 & 19484.5312050714 \tabularnewline
38 & 30364 & 28292.0611142154 & 2071.93888578464 \tabularnewline
39 & 32609 & 29363.3693928218 & 3245.63060717825 \tabularnewline
40 & 30212 & 31041.5419309329 & -829.541930932872 \tabularnewline
41 & 29965 & 30612.6223599181 & -647.622359918128 \tabularnewline
42 & 28352 & 30277.7653810994 & -1925.76538109939 \tabularnewline
43 & 25814 & 29282.0369792725 & -3468.03697927249 \tabularnewline
44 & 22414 & 27488.8679085541 & -5074.86790855411 \tabularnewline
45 & 20506 & 24864.8773842346 & -4358.87738423465 \tabularnewline
46 & 28806 & 22611.0940032676 & 6194.90599673237 \tabularnewline
47 & 22228 & 25814.2068581019 & -3586.20685810189 \tabularnewline
48 & 13971 & 23959.9373512942 & -9988.9373512942 \tabularnewline
49 & 36845 & 18795.0981022497 & 18049.9018977503 \tabularnewline
50 & 35338 & 28127.9068369871 & 7210.09316301285 \tabularnewline
51 & 35022 & 31855.9282318527 & 3166.07176814732 \tabularnewline
52 & 34777 & 33492.9644008002 & 1284.03559919984 \tabularnewline
53 & 26887 & 34156.8826161906 & -7269.88261619055 \tabularnewline
54 & 23970 & 30397.9467302645 & -6427.94673026446 \tabularnewline
55 & 22780 & 27074.3387832253 & -4294.33878322535 \tabularnewline
56 & 17351 & 24853.9254683473 & -7502.9254683473 \tabularnewline
57 & 21382 & 20974.4933947689 & 407.506605231083 \tabularnewline
58 & 24561 & 21185.1970997701 & 3375.8029002299 \tabularnewline
59 & 17409 & 22930.675993367 & -5521.67599336699 \tabularnewline
60 & 11514 & 20075.6607011394 & -8561.66070113936 \tabularnewline
61 & 31514 & 15648.8033016866 & 15865.1966983134 \tabularnewline
62 & 27071 & 23851.9972671232 & 3219.00273287683 \tabularnewline
63 & 29462 & 25516.4017050376 & 3945.59829496235 \tabularnewline
64 & 26105 & 27556.4966839239 & -1451.49668392390 \tabularnewline
65 & 22397 & 26805.9917223509 & -4408.99172235091 \tabularnewline
66 & 23843 & 24526.2964258978 & -683.296425897785 \tabularnewline
67 & 21705 & 24172.9939598701 & -2467.99395987006 \tabularnewline
68 & 18089 & 22896.9030582998 & -4807.90305829982 \tabularnewline
69 & 20764 & 20410.9482917609 & 353.051708239058 \tabularnewline
70 & 25316 & 20593.4957695884 & 4722.5042304116 \tabularnewline
71 & 17704 & 23035.2945661189 & -5331.29456611889 \tabularnewline
72 & 15548 & 20278.7171189952 & -4730.71711899525 \tabularnewline
73 & 28029 & 17832.6717997554 & 10196.3282002446 \tabularnewline
74 & 29383 & 23104.743716188 & 6278.25628381202 \tabularnewline
75 & 36438 & 26350.9533308665 & 10087.0466691335 \tabularnewline
76 & 32034 & 31566.5205840673 & 467.479415932699 \tabularnewline
77 & 22679 & 31808.2335862233 & -9129.2335862233 \tabularnewline
78 & 24319 & 27087.9092632649 & -2768.90926326493 \tabularnewline
79 & 18004 & 25656.2283209372 & -7652.22832093719 \tabularnewline
80 & 17537 & 21699.5983227016 & -4162.59832270162 \tabularnewline
81 & 20366 & 19547.3021935933 & 818.697806406715 \tabularnewline
82 & 22782 & 19970.6147457626 & 2811.38525423737 \tabularnewline
83 & 19169 & 21424.2581509231 & -2255.25815092312 \tabularnewline
84 & 13807 & 20258.1635599799 & -6451.16355997986 \tabularnewline
85 & 29743 & 16922.5512135602 & 12820.4487864398 \tabularnewline
86 & 25591 & 23551.4402288657 & 2039.55977113427 \tabularnewline
87 & 29096 & 24606.0066943729 & 4489.99330562714 \tabularnewline
88 & 26482 & 26927.5843394510 & -445.58433945095 \tabularnewline
89 & 22405 & 26697.1923163337 & -4292.19231633373 \tabularnewline
90 & 27044 & 24477.8888448813 & 2566.11115511867 \tabularnewline
91 & 17970 & 25804.7118236690 & -7834.71182366903 \tabularnewline
92 & 18730 & 21753.7276490014 & -3023.72764900143 \tabularnewline
93 & 19684 & 20190.2913503485 & -506.291350348474 \tabularnewline
94 & 19785 & 19928.5104075145 & -143.510407514474 \tabularnewline
95 & 18479 & 19854.3075009079 & -1375.30750090789 \tabularnewline
96 & 10698 & 19143.1966078884 & -8445.19660788841 \tabularnewline
97 & 31956 & 14776.5576579837 & 17179.4423420163 \tabularnewline
98 & 29506 & 23659.2901213369 & 5846.70987866306 \tabularnewline
99 & 34506 & 26682.3661100138 & 7823.63388998617 \tabularnewline
100 & 27165 & 30727.6223734261 & -3562.62237342607 \tabularnewline
101 & 26736 & 28885.5473641749 & -2149.54736417485 \tabularnewline
102 & 23691 & 27774.1111619314 & -4083.11116193137 \tabularnewline
103 & 18157 & 25662.9143403173 & -7505.91434031725 \tabularnewline
104 & 17328 & 21781.9368527756 & -4453.93685277562 \tabularnewline
105 & 18205 & 19479.0024103045 & -1274.00241030453 \tabularnewline
106 & 20995 & 18820.2719146862 & 2174.72808531376 \tabularnewline
107 & 17382 & 19944.7279580083 & -2562.72795800827 \tabularnewline
108 & 9367 & 18619.6542813344 & -9252.65428133435 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=13294&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]3[/C][C]34122[/C][C]33163[/C][C]959[/C][/ROW]
[ROW][C]4[/C][C]35225[/C][C]33658.856632757[/C][C]1566.14336724297[/C][/ROW]
[ROW][C]5[/C][C]28249[/C][C]34468.6403413033[/C][C]-6219.64034130328[/C][/ROW]
[ROW][C]6[/C][C]30374[/C][C]31252.7384470401[/C][C]-878.73844704005[/C][/ROW]
[ROW][C]7[/C][C]26311[/C][C]30798.3815258477[/C][C]-4487.38152584774[/C][/ROW]
[ROW][C]8[/C][C]22069[/C][C]28478.1543169812[/C][C]-6409.15431698124[/C][/ROW]
[ROW][C]9[/C][C]23651[/C][C]25164.2630985886[/C][C]-1513.26309858864[/C][/ROW]
[ROW][C]10[/C][C]28628[/C][C]24381.8214463033[/C][C]4246.1785536967[/C][/ROW]
[ROW][C]11[/C][C]23187[/C][C]26577.3332291200[/C][C]-3390.33322911995[/C][/ROW]
[ROW][C]12[/C][C]14727[/C][C]24824.3413428679[/C][C]-10097.3413428679[/C][/ROW]
[ROW][C]13[/C][C]43080[/C][C]19603.4511676095[/C][C]23476.5488323905[/C][/ROW]
[ROW][C]14[/C][C]32519[/C][C]31742.1398566451[/C][C]776.860143354876[/C][/ROW]
[ROW][C]15[/C][C]39657[/C][C]32143.8199972156[/C][C]7513.1800027844[/C][/ROW]
[ROW][C]16[/C][C]33614[/C][C]36028.5542385901[/C][C]-2414.5542385901[/C][/ROW]
[ROW][C]17[/C][C]28671[/C][C]34780.094661576[/C][C]-6109.09466157602[/C][/ROW]
[ROW][C]18[/C][C]34243[/C][C]31621.3510660775[/C][C]2621.64893392246[/C][/ROW]
[ROW][C]19[/C][C]27336[/C][C]32976.8901824966[/C][C]-5640.89018249657[/C][/ROW]
[ROW][C]20[/C][C]22916[/C][C]30060.2344873506[/C][C]-7144.23448735064[/C][/ROW]
[ROW][C]21[/C][C]24537[/C][C]26366.2657109957[/C][C]-1829.26571099574[/C][/ROW]
[ROW][C]22[/C][C]26128[/C][C]25420.4330354251[/C][C]707.5669645749[/C][/ROW]
[ROW][C]23[/C][C]22602[/C][C]25786.2847272960[/C][C]-3184.28472729603[/C][/ROW]
[ROW][C]24[/C][C]15744[/C][C]24139.831439896[/C][C]-8395.83143989598[/C][/ROW]
[ROW][C]25[/C][C]41086[/C][C]19798.7170426254[/C][C]21287.2829573746[/C][/ROW]
[ROW][C]26[/C][C]39690[/C][C]30805.4328380268[/C][C]8884.5671619732[/C][/ROW]
[ROW][C]27[/C][C]43129[/C][C]35399.2509365041[/C][C]7729.7490634959[/C][/ROW]
[ROW][C]28[/C][C]37863[/C][C]39395.9634940452[/C][C]-1532.96349404518[/C][/ROW]
[ROW][C]29[/C][C]35953[/C][C]38603.3356355502[/C][C]-2650.33563555019[/C][/ROW]
[ROW][C]30[/C][C]29133[/C][C]37232.9638900654[/C][C]-8099.96389006543[/C][/ROW]
[ROW][C]31[/C][C]24693[/C][C]33044.8295626604[/C][C]-8351.82956266044[/C][/ROW]
[ROW][C]32[/C][C]22205[/C][C]28726.4665967570[/C][C]-6521.46659675696[/C][/ROW]
[ROW][C]33[/C][C]21725[/C][C]25354.5036485762[/C][C]-3629.50364857618[/C][/ROW]
[ROW][C]34[/C][C]27192[/C][C]23477.8472796895[/C][C]3714.15272031052[/C][/ROW]
[ROW][C]35[/C][C]21790[/C][C]25398.2719527224[/C][C]-3608.27195272237[/C][/ROW]
[ROW][C]36[/C][C]13253[/C][C]23532.5935579898[/C][C]-10279.5935579898[/C][/ROW]
[ROW][C]37[/C][C]37702[/C][C]18217.4687949286[/C][C]19484.5312050714[/C][/ROW]
[ROW][C]38[/C][C]30364[/C][C]28292.0611142154[/C][C]2071.93888578464[/C][/ROW]
[ROW][C]39[/C][C]32609[/C][C]29363.3693928218[/C][C]3245.63060717825[/C][/ROW]
[ROW][C]40[/C][C]30212[/C][C]31041.5419309329[/C][C]-829.541930932872[/C][/ROW]
[ROW][C]41[/C][C]29965[/C][C]30612.6223599181[/C][C]-647.622359918128[/C][/ROW]
[ROW][C]42[/C][C]28352[/C][C]30277.7653810994[/C][C]-1925.76538109939[/C][/ROW]
[ROW][C]43[/C][C]25814[/C][C]29282.0369792725[/C][C]-3468.03697927249[/C][/ROW]
[ROW][C]44[/C][C]22414[/C][C]27488.8679085541[/C][C]-5074.86790855411[/C][/ROW]
[ROW][C]45[/C][C]20506[/C][C]24864.8773842346[/C][C]-4358.87738423465[/C][/ROW]
[ROW][C]46[/C][C]28806[/C][C]22611.0940032676[/C][C]6194.90599673237[/C][/ROW]
[ROW][C]47[/C][C]22228[/C][C]25814.2068581019[/C][C]-3586.20685810189[/C][/ROW]
[ROW][C]48[/C][C]13971[/C][C]23959.9373512942[/C][C]-9988.9373512942[/C][/ROW]
[ROW][C]49[/C][C]36845[/C][C]18795.0981022497[/C][C]18049.9018977503[/C][/ROW]
[ROW][C]50[/C][C]35338[/C][C]28127.9068369871[/C][C]7210.09316301285[/C][/ROW]
[ROW][C]51[/C][C]35022[/C][C]31855.9282318527[/C][C]3166.07176814732[/C][/ROW]
[ROW][C]52[/C][C]34777[/C][C]33492.9644008002[/C][C]1284.03559919984[/C][/ROW]
[ROW][C]53[/C][C]26887[/C][C]34156.8826161906[/C][C]-7269.88261619055[/C][/ROW]
[ROW][C]54[/C][C]23970[/C][C]30397.9467302645[/C][C]-6427.94673026446[/C][/ROW]
[ROW][C]55[/C][C]22780[/C][C]27074.3387832253[/C][C]-4294.33878322535[/C][/ROW]
[ROW][C]56[/C][C]17351[/C][C]24853.9254683473[/C][C]-7502.9254683473[/C][/ROW]
[ROW][C]57[/C][C]21382[/C][C]20974.4933947689[/C][C]407.506605231083[/C][/ROW]
[ROW][C]58[/C][C]24561[/C][C]21185.1970997701[/C][C]3375.8029002299[/C][/ROW]
[ROW][C]59[/C][C]17409[/C][C]22930.675993367[/C][C]-5521.67599336699[/C][/ROW]
[ROW][C]60[/C][C]11514[/C][C]20075.6607011394[/C][C]-8561.66070113936[/C][/ROW]
[ROW][C]61[/C][C]31514[/C][C]15648.8033016866[/C][C]15865.1966983134[/C][/ROW]
[ROW][C]62[/C][C]27071[/C][C]23851.9972671232[/C][C]3219.00273287683[/C][/ROW]
[ROW][C]63[/C][C]29462[/C][C]25516.4017050376[/C][C]3945.59829496235[/C][/ROW]
[ROW][C]64[/C][C]26105[/C][C]27556.4966839239[/C][C]-1451.49668392390[/C][/ROW]
[ROW][C]65[/C][C]22397[/C][C]26805.9917223509[/C][C]-4408.99172235091[/C][/ROW]
[ROW][C]66[/C][C]23843[/C][C]24526.2964258978[/C][C]-683.296425897785[/C][/ROW]
[ROW][C]67[/C][C]21705[/C][C]24172.9939598701[/C][C]-2467.99395987006[/C][/ROW]
[ROW][C]68[/C][C]18089[/C][C]22896.9030582998[/C][C]-4807.90305829982[/C][/ROW]
[ROW][C]69[/C][C]20764[/C][C]20410.9482917609[/C][C]353.051708239058[/C][/ROW]
[ROW][C]70[/C][C]25316[/C][C]20593.4957695884[/C][C]4722.5042304116[/C][/ROW]
[ROW][C]71[/C][C]17704[/C][C]23035.2945661189[/C][C]-5331.29456611889[/C][/ROW]
[ROW][C]72[/C][C]15548[/C][C]20278.7171189952[/C][C]-4730.71711899525[/C][/ROW]
[ROW][C]73[/C][C]28029[/C][C]17832.6717997554[/C][C]10196.3282002446[/C][/ROW]
[ROW][C]74[/C][C]29383[/C][C]23104.743716188[/C][C]6278.25628381202[/C][/ROW]
[ROW][C]75[/C][C]36438[/C][C]26350.9533308665[/C][C]10087.0466691335[/C][/ROW]
[ROW][C]76[/C][C]32034[/C][C]31566.5205840673[/C][C]467.479415932699[/C][/ROW]
[ROW][C]77[/C][C]22679[/C][C]31808.2335862233[/C][C]-9129.2335862233[/C][/ROW]
[ROW][C]78[/C][C]24319[/C][C]27087.9092632649[/C][C]-2768.90926326493[/C][/ROW]
[ROW][C]79[/C][C]18004[/C][C]25656.2283209372[/C][C]-7652.22832093719[/C][/ROW]
[ROW][C]80[/C][C]17537[/C][C]21699.5983227016[/C][C]-4162.59832270162[/C][/ROW]
[ROW][C]81[/C][C]20366[/C][C]19547.3021935933[/C][C]818.697806406715[/C][/ROW]
[ROW][C]82[/C][C]22782[/C][C]19970.6147457626[/C][C]2811.38525423737[/C][/ROW]
[ROW][C]83[/C][C]19169[/C][C]21424.2581509231[/C][C]-2255.25815092312[/C][/ROW]
[ROW][C]84[/C][C]13807[/C][C]20258.1635599799[/C][C]-6451.16355997986[/C][/ROW]
[ROW][C]85[/C][C]29743[/C][C]16922.5512135602[/C][C]12820.4487864398[/C][/ROW]
[ROW][C]86[/C][C]25591[/C][C]23551.4402288657[/C][C]2039.55977113427[/C][/ROW]
[ROW][C]87[/C][C]29096[/C][C]24606.0066943729[/C][C]4489.99330562714[/C][/ROW]
[ROW][C]88[/C][C]26482[/C][C]26927.5843394510[/C][C]-445.58433945095[/C][/ROW]
[ROW][C]89[/C][C]22405[/C][C]26697.1923163337[/C][C]-4292.19231633373[/C][/ROW]
[ROW][C]90[/C][C]27044[/C][C]24477.8888448813[/C][C]2566.11115511867[/C][/ROW]
[ROW][C]91[/C][C]17970[/C][C]25804.7118236690[/C][C]-7834.71182366903[/C][/ROW]
[ROW][C]92[/C][C]18730[/C][C]21753.7276490014[/C][C]-3023.72764900143[/C][/ROW]
[ROW][C]93[/C][C]19684[/C][C]20190.2913503485[/C][C]-506.291350348474[/C][/ROW]
[ROW][C]94[/C][C]19785[/C][C]19928.5104075145[/C][C]-143.510407514474[/C][/ROW]
[ROW][C]95[/C][C]18479[/C][C]19854.3075009079[/C][C]-1375.30750090789[/C][/ROW]
[ROW][C]96[/C][C]10698[/C][C]19143.1966078884[/C][C]-8445.19660788841[/C][/ROW]
[ROW][C]97[/C][C]31956[/C][C]14776.5576579837[/C][C]17179.4423420163[/C][/ROW]
[ROW][C]98[/C][C]29506[/C][C]23659.2901213369[/C][C]5846.70987866306[/C][/ROW]
[ROW][C]99[/C][C]34506[/C][C]26682.3661100138[/C][C]7823.63388998617[/C][/ROW]
[ROW][C]100[/C][C]27165[/C][C]30727.6223734261[/C][C]-3562.62237342607[/C][/ROW]
[ROW][C]101[/C][C]26736[/C][C]28885.5473641749[/C][C]-2149.54736417485[/C][/ROW]
[ROW][C]102[/C][C]23691[/C][C]27774.1111619314[/C][C]-4083.11116193137[/C][/ROW]
[ROW][C]103[/C][C]18157[/C][C]25662.9143403173[/C][C]-7505.91434031725[/C][/ROW]
[ROW][C]104[/C][C]17328[/C][C]21781.9368527756[/C][C]-4453.93685277562[/C][/ROW]
[ROW][C]105[/C][C]18205[/C][C]19479.0024103045[/C][C]-1274.00241030453[/C][/ROW]
[ROW][C]106[/C][C]20995[/C][C]18820.2719146862[/C][C]2174.72808531376[/C][/ROW]
[ROW][C]107[/C][C]17382[/C][C]19944.7279580083[/C][C]-2562.72795800827[/C][/ROW]
[ROW][C]108[/C][C]9367[/C][C]18619.6542813344[/C][C]-9252.65428133435[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=13294&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=13294&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
33412233163959
43522533658.8566327571566.14336724297
52824934468.6403413033-6219.64034130328
63037431252.7384470401-878.73844704005
72631130798.3815258477-4487.38152584774
82206928478.1543169812-6409.15431698124
92365125164.2630985886-1513.26309858864
102862824381.82144630334246.1785536967
112318726577.3332291200-3390.33322911995
121472724824.3413428679-10097.3413428679
134308019603.451167609523476.5488323905
143251931742.1398566451776.860143354876
153965732143.81999721567513.1800027844
163361436028.5542385901-2414.5542385901
172867134780.094661576-6109.09466157602
183424331621.35106607752621.64893392246
192733632976.8901824966-5640.89018249657
202291630060.2344873506-7144.23448735064
212453726366.2657109957-1829.26571099574
222612825420.4330354251707.5669645749
232260225786.2847272960-3184.28472729603
241574424139.831439896-8395.83143989598
254108619798.717042625421287.2829573746
263969030805.43283802688884.5671619732
274312935399.25093650417729.7490634959
283786339395.9634940452-1532.96349404518
293595338603.3356355502-2650.33563555019
302913337232.9638900654-8099.96389006543
312469333044.8295626604-8351.82956266044
322220528726.4665967570-6521.46659675696
332172525354.5036485762-3629.50364857618
342719223477.84727968953714.15272031052
352179025398.2719527224-3608.27195272237
361325323532.5935579898-10279.5935579898
373770218217.468794928619484.5312050714
383036428292.06111421542071.93888578464
393260929363.36939282183245.63060717825
403021231041.5419309329-829.541930932872
412996530612.6223599181-647.622359918128
422835230277.7653810994-1925.76538109939
432581429282.0369792725-3468.03697927249
442241427488.8679085541-5074.86790855411
452050624864.8773842346-4358.87738423465
462880622611.09400326766194.90599673237
472222825814.2068581019-3586.20685810189
481397123959.9373512942-9988.9373512942
493684518795.098102249718049.9018977503
503533828127.90683698717210.09316301285
513502231855.92823185273166.07176814732
523477733492.96440080021284.03559919984
532688734156.8826161906-7269.88261619055
542397030397.9467302645-6427.94673026446
552278027074.3387832253-4294.33878322535
561735124853.9254683473-7502.9254683473
572138220974.4933947689407.506605231083
582456121185.19709977013375.8029002299
591740922930.675993367-5521.67599336699
601151420075.6607011394-8561.66070113936
613151415648.803301686615865.1966983134
622707123851.99726712323219.00273287683
632946225516.40170503763945.59829496235
642610527556.4966839239-1451.49668392390
652239726805.9917223509-4408.99172235091
662384324526.2964258978-683.296425897785
672170524172.9939598701-2467.99395987006
681808922896.9030582998-4807.90305829982
692076420410.9482917609353.051708239058
702531620593.49576958844722.5042304116
711770423035.2945661189-5331.29456611889
721554820278.7171189952-4730.71711899525
732802917832.671799755410196.3282002446
742938323104.7437161886278.25628381202
753643826350.953330866510087.0466691335
763203431566.5205840673467.479415932699
772267931808.2335862233-9129.2335862233
782431927087.9092632649-2768.90926326493
791800425656.2283209372-7652.22832093719
801753721699.5983227016-4162.59832270162
812036619547.3021935933818.697806406715
822278219970.61474576262811.38525423737
831916921424.2581509231-2255.25815092312
841380720258.1635599799-6451.16355997986
852974316922.551213560212820.4487864398
862559123551.44022886572039.55977113427
872909624606.00669437294489.99330562714
882648226927.5843394510-445.58433945095
892240526697.1923163337-4292.19231633373
902704424477.88884488132566.11115511867
911797025804.7118236690-7834.71182366903
921873021753.7276490014-3023.72764900143
931968420190.2913503485-506.291350348474
941978519928.5104075145-143.510407514474
951847919854.3075009079-1375.30750090789
961069819143.1966078884-8445.19660788841
973195614776.557657983717179.4423420163
982950623659.29012133695846.70987866306
993450626682.36611001387823.63388998617
1002716530727.6223734261-3562.62237342607
1012673628885.5473641749-2149.54736417485
1022369127774.1111619314-4083.11116193137
1031815725662.9143403173-7505.91434031725
1041732821781.9368527756-4453.93685277562
1051820519479.0024103045-1274.00241030453
1062099518820.27191468622174.72808531376
1071738219944.7279580083-2562.72795800827
108936718619.6542813344-9252.65428133435







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
10913835.5145566134199.38010308887927471.6490101379
11013835.5145566134-1515.5683167100029186.5974299368
11113835.5145566134-3057.3042707075130728.3333839343
11213835.5145566134-4469.6462042685632140.6753174954
11313835.5145566134-5780.5628553152533451.5919685421
11413835.5145566134-7009.1988158420234680.2279290688
11513835.5145566134-8169.3407741736435840.3698874005
11613835.5145566134-9271.3078272175636942.3369404444
11713835.5145566134-10323.062041087037994.0911543138
11813835.5145566134-11330.899684911039001.9287981378
11913835.5145566134-12299.901803663839970.9309168906
12013835.5145566134-13234.239244891540905.2683581183

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
109 & 13835.5145566134 & 199.380103088879 & 27471.6490101379 \tabularnewline
110 & 13835.5145566134 & -1515.56831671000 & 29186.5974299368 \tabularnewline
111 & 13835.5145566134 & -3057.30427070751 & 30728.3333839343 \tabularnewline
112 & 13835.5145566134 & -4469.64620426856 & 32140.6753174954 \tabularnewline
113 & 13835.5145566134 & -5780.56285531525 & 33451.5919685421 \tabularnewline
114 & 13835.5145566134 & -7009.19881584202 & 34680.2279290688 \tabularnewline
115 & 13835.5145566134 & -8169.34077417364 & 35840.3698874005 \tabularnewline
116 & 13835.5145566134 & -9271.30782721756 & 36942.3369404444 \tabularnewline
117 & 13835.5145566134 & -10323.0620410870 & 37994.0911543138 \tabularnewline
118 & 13835.5145566134 & -11330.8996849110 & 39001.9287981378 \tabularnewline
119 & 13835.5145566134 & -12299.9018036638 & 39970.9309168906 \tabularnewline
120 & 13835.5145566134 & -13234.2392448915 & 40905.2683581183 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=13294&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]13835.5145566134[/C][C]199.380103088879[/C][C]27471.6490101379[/C][/ROW]
[ROW][C]110[/C][C]13835.5145566134[/C][C]-1515.56831671000[/C][C]29186.5974299368[/C][/ROW]
[ROW][C]111[/C][C]13835.5145566134[/C][C]-3057.30427070751[/C][C]30728.3333839343[/C][/ROW]
[ROW][C]112[/C][C]13835.5145566134[/C][C]-4469.64620426856[/C][C]32140.6753174954[/C][/ROW]
[ROW][C]113[/C][C]13835.5145566134[/C][C]-5780.56285531525[/C][C]33451.5919685421[/C][/ROW]
[ROW][C]114[/C][C]13835.5145566134[/C][C]-7009.19881584202[/C][C]34680.2279290688[/C][/ROW]
[ROW][C]115[/C][C]13835.5145566134[/C][C]-8169.34077417364[/C][C]35840.3698874005[/C][/ROW]
[ROW][C]116[/C][C]13835.5145566134[/C][C]-9271.30782721756[/C][C]36942.3369404444[/C][/ROW]
[ROW][C]117[/C][C]13835.5145566134[/C][C]-10323.0620410870[/C][C]37994.0911543138[/C][/ROW]
[ROW][C]118[/C][C]13835.5145566134[/C][C]-11330.8996849110[/C][C]39001.9287981378[/C][/ROW]
[ROW][C]119[/C][C]13835.5145566134[/C][C]-12299.9018036638[/C][C]39970.9309168906[/C][/ROW]
[ROW][C]120[/C][C]13835.5145566134[/C][C]-13234.2392448915[/C][C]40905.2683581183[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=13294&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=13294&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
10913835.5145566134199.38010308887927471.6490101379
11013835.5145566134-1515.5683167100029186.5974299368
11113835.5145566134-3057.3042707075130728.3333839343
11213835.5145566134-4469.6462042685632140.6753174954
11313835.5145566134-5780.5628553152533451.5919685421
11413835.5145566134-7009.1988158420234680.2279290688
11513835.5145566134-8169.3407741736435840.3698874005
11613835.5145566134-9271.3078272175636942.3369404444
11713835.5145566134-10323.062041087037994.0911543138
11813835.5145566134-11330.899684911039001.9287981378
11913835.5145566134-12299.901803663839970.9309168906
12013835.5145566134-13234.239244891540905.2683581183



Parameters (Session):
par1 = 12 ; par2 = Double ; par3 = multiplicative ;
Parameters (R input):
par1 = 12 ; par2 = Double ; par3 = multiplicative ;
R code (references can be found in the software module):
par1 <- as.numeric(par1)
if (par2 == 'Single') K <- 1
if (par2 == 'Double') K <- 2
if (par2 == 'Triple') K <- par1
nx <- length(x)
nxmK <- nx - K
x <- ts(x, frequency = par1)
if (par2 == 'Single') fit <- HoltWinters(x, gamma=0, beta=0)
if (par2 == 'Double') fit <- HoltWinters(x, gamma=0)
if (par2 == 'Triple') fit <- HoltWinters(x, seasonal=par3)
fit
myresid <- x - fit$fitted[,'xhat']
bitmap(file='test1.png')
op <- par(mfrow=c(2,1))
plot(fit,ylab='Observed (black) / Fitted (red)',main='Interpolation Fit of Exponential Smoothing')
plot(myresid,ylab='Residuals',main='Interpolation Prediction Errors')
par(op)
dev.off()
bitmap(file='test2.png')
p <- predict(fit, par1, prediction.interval=TRUE)
np <- length(p[,1])
plot(fit,p,ylab='Observed (black) / Fitted (red)',main='Extrapolation Fit of Exponential Smoothing')
dev.off()
bitmap(file='test3.png')
op <- par(mfrow = c(2,2))
acf(as.numeric(myresid),lag.max = nx/2,main='Residual ACF')
spectrum(myresid,main='Residals Periodogram')
cpgram(myresid,main='Residal Cumulative Periodogram')
qqnorm(myresid,main='Residual Normal QQ Plot')
qqline(myresid)
par(op)
dev.off()
load(file='createtable')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Estimated Parameters of Exponential Smoothing',2,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'Parameter',header=TRUE)
a<-table.element(a,'Value',header=TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'alpha',header=TRUE)
a<-table.element(a,fit$alpha)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'beta',header=TRUE)
a<-table.element(a,fit$beta)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'gamma',header=TRUE)
a<-table.element(a,fit$gamma)
a<-table.row.end(a)
a<-table.end(a)
table.save(a,file='mytable.tab')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Interpolation Forecasts of Exponential Smoothing',4,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'t',header=TRUE)
a<-table.element(a,'Observed',header=TRUE)
a<-table.element(a,'Fitted',header=TRUE)
a<-table.element(a,'Residuals',header=TRUE)
a<-table.row.end(a)
for (i in 1:nxmK) {
a<-table.row.start(a)
a<-table.element(a,i+K,header=TRUE)
a<-table.element(a,x[i+K])
a<-table.element(a,fit$fitted[i,'xhat'])
a<-table.element(a,myresid[i])
a<-table.row.end(a)
}
a<-table.end(a)
table.save(a,file='mytable1.tab')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Extrapolation Forecasts of Exponential Smoothing',4,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'t',header=TRUE)
a<-table.element(a,'Forecast',header=TRUE)
a<-table.element(a,'95% Lower Bound',header=TRUE)
a<-table.element(a,'95% Upper Bound',header=TRUE)
a<-table.row.end(a)
for (i in 1:np) {
a<-table.row.start(a)
a<-table.element(a,nx+i,header=TRUE)
a<-table.element(a,p[i,'fit'])
a<-table.element(a,p[i,'lwr'])
a<-table.element(a,p[i,'upr'])
a<-table.row.end(a)
}
a<-table.end(a)
table.save(a,file='mytable2.tab')