Free Statistics

of Irreproducible Research!

Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationWed, 28 May 2008 06:51:18 -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/28/t12119792086veotonx3p4skeb.htm/, Retrieved Tue, 14 May 2024 04:56:20 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=13431, Retrieved Tue, 14 May 2024 04:56:20 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact202
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [evelyne van haeve...] [2008-05-28 12:51:18] [c8f95257d399ca81c3dd1b8178a81b78] [Current]
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Dataseries X:
13328
12873
14000
13477
14237
13674
13529
14058
12975
14326
14008
16193
14483
14011
15057
14884
15414
14440
14900
15074
14442
15307
14938
17193
15528
14765
15838
15723
16150
15486
15986
15983
15692
16490
15686
18897
16316
15636
17163
16534
16518
16375
16290
16352
15943
16362
16393
19051
16747
16320
17910
16961
17480
17049
16879
17473
16998
17307
17418
20169
17871
17226
19062
17804
19100
18522
18060
18869
18127
18871
18890
21263
19547
18450
20254
19240
20216
19420
19415
20018
18652
19978
19514
22148




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time5 seconds
R Server'Gwilym Jenkins' @ 72.249.127.135

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input & view raw input (R code)  \tabularnewline
Raw Output & view raw output of R engine  \tabularnewline
Computing time & 5 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ 72.249.127.135 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=13431&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]5 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Gwilym Jenkins' @ 72.249.127.135[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=13431&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=13431&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 time5 seconds
R Server'Gwilym Jenkins' @ 72.249.127.135







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.257708065841373
beta0.273715620885234
gamma0

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.257708065841373 \tabularnewline
beta & 0.273715620885234 \tabularnewline
gamma & 0 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=13431&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]0.257708065841373[/C][/ROW]
[ROW][C]beta[/C][C]0.273715620885234[/C][/ROW]
[ROW][C]gamma[/C][C]0[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=13431&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=13431&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
alpha0.257708065841373
beta0.273715620885234
gamma0







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
314000124181582
41347712482.2864203408994.713579659181
51423712465.39021910821771.60978089179
61367412773.6735272941900.326472705858
71352912920.9279792195608.072020780533
81405813035.75872559481022.24127440517
91297513329.4318236016-354.431823601633
101432613243.32399190961082.67600809039
111400813603.9410232314404.058976768649
121619313818.17477630272374.82522369733
131448314707.8080263143-224.808026314342
141401114911.6371484163-900.637148416263
151505714877.7698600622179.230139937794
161488415134.8357471942-250.835747194178
171541415263.3765530168150.623446983245
181444015506.0014169266-1066.00141692658
191490015359.8978613722-459.897861372154
201507415337.5514728531-263.551472853147
211444215347.2145479489-905.214547948883
221530715127.6631945612179.336805438779
231493815200.2596620479-262.259662047925
241719315140.55369629572052.4463037043
251552815822.1430697692-294.143069769201
261476515878.2489578869-1113.24895788689
271583815644.737491711193.262508289017
281572315761.5570590694-38.5570590694279
291615015815.9150883808334.084911619244
301548615989.8718823319-503.871882331925
311598615912.337972394673.6620276054164
321598315988.8352347242-5.83523472421257
331569216044.4338013319-352.433801331887
341649015985.85089134504.149108660005
351568616183.5783407668-497.578340766839
361889716088.05400582772808.94599417232
371631617042.7871260072-726.787126007159
381563617035.0666665116-1399.06666651162
391716316755.4059705321407.59402946788
401653416970.0874705877-436.087470587663
411651816936.5843896776-418.58438967765
421637516878.0655854754-503.065585475437
431629016762.2896915943-472.289691594313
441635216621.1302819512-269.130281951151
451594316513.3425843482-570.342584348153
461636216287.698809172474.3011908276039
471639316233.4260455907159.573954409281
481905116212.38490398842838.61509601157
491674717081.9865579657-334.986557965658
501632017110.095943841-790.095943840988
511791016965.1876110135944.81238898655
521696117334.0250086798-373.025008679841
531748017336.932371648143.067628351993
541704917482.9327777428-433.932777742819
551687917449.6264610754-570.626461075422
561747317340.8418176473132.158182352658
571699817422.4927148302-424.492714830190
581730717330.7470118186-23.7470118185993
591741817340.601624929777.3983750702973
602016917381.98180262372787.01819737628
611787118318.2455692040-447.245569204042
621722618389.4653446477-1163.46534464774
631906218194.0401470887867.959852911303
641780418583.3543879497-779.354387949694
651910018493.1677984811606.832201518948
661852218803.0178426011-281.01784260109
671806018864.2391292665-804.239129266534
681886918733.8920687731135.107931226878
691812718855.1526633628-728.152663362791
701887118702.5810805998168.418919400217
711889018792.943281864497.0567181355837
722126318871.76112524702391.23887475303
731954719710.4831521074-163.483152107427
741845019879.3008138410-1429.30081384095
752025419621.0859997143632.914000285673
761924019938.9655221922-698.965522192208
772021619864.3048134681351.695186531859
781942020085.2159732756-665.215973275623
791941519997.1374395170-582.13743951697
802001819889.4056822673128.594317732717
811865219973.9061105004-1321.90611050038
821997819591.3553095818386.644690418172
831951419676.3852537728-162.385253772791
842214819608.47130448172539.52869551828

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
3 & 14000 & 12418 & 1582 \tabularnewline
4 & 13477 & 12482.2864203408 & 994.713579659181 \tabularnewline
5 & 14237 & 12465.3902191082 & 1771.60978089179 \tabularnewline
6 & 13674 & 12773.6735272941 & 900.326472705858 \tabularnewline
7 & 13529 & 12920.9279792195 & 608.072020780533 \tabularnewline
8 & 14058 & 13035.7587255948 & 1022.24127440517 \tabularnewline
9 & 12975 & 13329.4318236016 & -354.431823601633 \tabularnewline
10 & 14326 & 13243.3239919096 & 1082.67600809039 \tabularnewline
11 & 14008 & 13603.9410232314 & 404.058976768649 \tabularnewline
12 & 16193 & 13818.1747763027 & 2374.82522369733 \tabularnewline
13 & 14483 & 14707.8080263143 & -224.808026314342 \tabularnewline
14 & 14011 & 14911.6371484163 & -900.637148416263 \tabularnewline
15 & 15057 & 14877.7698600622 & 179.230139937794 \tabularnewline
16 & 14884 & 15134.8357471942 & -250.835747194178 \tabularnewline
17 & 15414 & 15263.3765530168 & 150.623446983245 \tabularnewline
18 & 14440 & 15506.0014169266 & -1066.00141692658 \tabularnewline
19 & 14900 & 15359.8978613722 & -459.897861372154 \tabularnewline
20 & 15074 & 15337.5514728531 & -263.551472853147 \tabularnewline
21 & 14442 & 15347.2145479489 & -905.214547948883 \tabularnewline
22 & 15307 & 15127.6631945612 & 179.336805438779 \tabularnewline
23 & 14938 & 15200.2596620479 & -262.259662047925 \tabularnewline
24 & 17193 & 15140.5536962957 & 2052.4463037043 \tabularnewline
25 & 15528 & 15822.1430697692 & -294.143069769201 \tabularnewline
26 & 14765 & 15878.2489578869 & -1113.24895788689 \tabularnewline
27 & 15838 & 15644.737491711 & 193.262508289017 \tabularnewline
28 & 15723 & 15761.5570590694 & -38.5570590694279 \tabularnewline
29 & 16150 & 15815.9150883808 & 334.084911619244 \tabularnewline
30 & 15486 & 15989.8718823319 & -503.871882331925 \tabularnewline
31 & 15986 & 15912.3379723946 & 73.6620276054164 \tabularnewline
32 & 15983 & 15988.8352347242 & -5.83523472421257 \tabularnewline
33 & 15692 & 16044.4338013319 & -352.433801331887 \tabularnewline
34 & 16490 & 15985.85089134 & 504.149108660005 \tabularnewline
35 & 15686 & 16183.5783407668 & -497.578340766839 \tabularnewline
36 & 18897 & 16088.0540058277 & 2808.94599417232 \tabularnewline
37 & 16316 & 17042.7871260072 & -726.787126007159 \tabularnewline
38 & 15636 & 17035.0666665116 & -1399.06666651162 \tabularnewline
39 & 17163 & 16755.4059705321 & 407.59402946788 \tabularnewline
40 & 16534 & 16970.0874705877 & -436.087470587663 \tabularnewline
41 & 16518 & 16936.5843896776 & -418.58438967765 \tabularnewline
42 & 16375 & 16878.0655854754 & -503.065585475437 \tabularnewline
43 & 16290 & 16762.2896915943 & -472.289691594313 \tabularnewline
44 & 16352 & 16621.1302819512 & -269.130281951151 \tabularnewline
45 & 15943 & 16513.3425843482 & -570.342584348153 \tabularnewline
46 & 16362 & 16287.6988091724 & 74.3011908276039 \tabularnewline
47 & 16393 & 16233.4260455907 & 159.573954409281 \tabularnewline
48 & 19051 & 16212.3849039884 & 2838.61509601157 \tabularnewline
49 & 16747 & 17081.9865579657 & -334.986557965658 \tabularnewline
50 & 16320 & 17110.095943841 & -790.095943840988 \tabularnewline
51 & 17910 & 16965.1876110135 & 944.81238898655 \tabularnewline
52 & 16961 & 17334.0250086798 & -373.025008679841 \tabularnewline
53 & 17480 & 17336.932371648 & 143.067628351993 \tabularnewline
54 & 17049 & 17482.9327777428 & -433.932777742819 \tabularnewline
55 & 16879 & 17449.6264610754 & -570.626461075422 \tabularnewline
56 & 17473 & 17340.8418176473 & 132.158182352658 \tabularnewline
57 & 16998 & 17422.4927148302 & -424.492714830190 \tabularnewline
58 & 17307 & 17330.7470118186 & -23.7470118185993 \tabularnewline
59 & 17418 & 17340.6016249297 & 77.3983750702973 \tabularnewline
60 & 20169 & 17381.9818026237 & 2787.01819737628 \tabularnewline
61 & 17871 & 18318.2455692040 & -447.245569204042 \tabularnewline
62 & 17226 & 18389.4653446477 & -1163.46534464774 \tabularnewline
63 & 19062 & 18194.0401470887 & 867.959852911303 \tabularnewline
64 & 17804 & 18583.3543879497 & -779.354387949694 \tabularnewline
65 & 19100 & 18493.1677984811 & 606.832201518948 \tabularnewline
66 & 18522 & 18803.0178426011 & -281.01784260109 \tabularnewline
67 & 18060 & 18864.2391292665 & -804.239129266534 \tabularnewline
68 & 18869 & 18733.8920687731 & 135.107931226878 \tabularnewline
69 & 18127 & 18855.1526633628 & -728.152663362791 \tabularnewline
70 & 18871 & 18702.5810805998 & 168.418919400217 \tabularnewline
71 & 18890 & 18792.9432818644 & 97.0567181355837 \tabularnewline
72 & 21263 & 18871.7611252470 & 2391.23887475303 \tabularnewline
73 & 19547 & 19710.4831521074 & -163.483152107427 \tabularnewline
74 & 18450 & 19879.3008138410 & -1429.30081384095 \tabularnewline
75 & 20254 & 19621.0859997143 & 632.914000285673 \tabularnewline
76 & 19240 & 19938.9655221922 & -698.965522192208 \tabularnewline
77 & 20216 & 19864.3048134681 & 351.695186531859 \tabularnewline
78 & 19420 & 20085.2159732756 & -665.215973275623 \tabularnewline
79 & 19415 & 19997.1374395170 & -582.13743951697 \tabularnewline
80 & 20018 & 19889.4056822673 & 128.594317732717 \tabularnewline
81 & 18652 & 19973.9061105004 & -1321.90611050038 \tabularnewline
82 & 19978 & 19591.3553095818 & 386.644690418172 \tabularnewline
83 & 19514 & 19676.3852537728 & -162.385253772791 \tabularnewline
84 & 22148 & 19608.4713044817 & 2539.52869551828 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=13431&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]14000[/C][C]12418[/C][C]1582[/C][/ROW]
[ROW][C]4[/C][C]13477[/C][C]12482.2864203408[/C][C]994.713579659181[/C][/ROW]
[ROW][C]5[/C][C]14237[/C][C]12465.3902191082[/C][C]1771.60978089179[/C][/ROW]
[ROW][C]6[/C][C]13674[/C][C]12773.6735272941[/C][C]900.326472705858[/C][/ROW]
[ROW][C]7[/C][C]13529[/C][C]12920.9279792195[/C][C]608.072020780533[/C][/ROW]
[ROW][C]8[/C][C]14058[/C][C]13035.7587255948[/C][C]1022.24127440517[/C][/ROW]
[ROW][C]9[/C][C]12975[/C][C]13329.4318236016[/C][C]-354.431823601633[/C][/ROW]
[ROW][C]10[/C][C]14326[/C][C]13243.3239919096[/C][C]1082.67600809039[/C][/ROW]
[ROW][C]11[/C][C]14008[/C][C]13603.9410232314[/C][C]404.058976768649[/C][/ROW]
[ROW][C]12[/C][C]16193[/C][C]13818.1747763027[/C][C]2374.82522369733[/C][/ROW]
[ROW][C]13[/C][C]14483[/C][C]14707.8080263143[/C][C]-224.808026314342[/C][/ROW]
[ROW][C]14[/C][C]14011[/C][C]14911.6371484163[/C][C]-900.637148416263[/C][/ROW]
[ROW][C]15[/C][C]15057[/C][C]14877.7698600622[/C][C]179.230139937794[/C][/ROW]
[ROW][C]16[/C][C]14884[/C][C]15134.8357471942[/C][C]-250.835747194178[/C][/ROW]
[ROW][C]17[/C][C]15414[/C][C]15263.3765530168[/C][C]150.623446983245[/C][/ROW]
[ROW][C]18[/C][C]14440[/C][C]15506.0014169266[/C][C]-1066.00141692658[/C][/ROW]
[ROW][C]19[/C][C]14900[/C][C]15359.8978613722[/C][C]-459.897861372154[/C][/ROW]
[ROW][C]20[/C][C]15074[/C][C]15337.5514728531[/C][C]-263.551472853147[/C][/ROW]
[ROW][C]21[/C][C]14442[/C][C]15347.2145479489[/C][C]-905.214547948883[/C][/ROW]
[ROW][C]22[/C][C]15307[/C][C]15127.6631945612[/C][C]179.336805438779[/C][/ROW]
[ROW][C]23[/C][C]14938[/C][C]15200.2596620479[/C][C]-262.259662047925[/C][/ROW]
[ROW][C]24[/C][C]17193[/C][C]15140.5536962957[/C][C]2052.4463037043[/C][/ROW]
[ROW][C]25[/C][C]15528[/C][C]15822.1430697692[/C][C]-294.143069769201[/C][/ROW]
[ROW][C]26[/C][C]14765[/C][C]15878.2489578869[/C][C]-1113.24895788689[/C][/ROW]
[ROW][C]27[/C][C]15838[/C][C]15644.737491711[/C][C]193.262508289017[/C][/ROW]
[ROW][C]28[/C][C]15723[/C][C]15761.5570590694[/C][C]-38.5570590694279[/C][/ROW]
[ROW][C]29[/C][C]16150[/C][C]15815.9150883808[/C][C]334.084911619244[/C][/ROW]
[ROW][C]30[/C][C]15486[/C][C]15989.8718823319[/C][C]-503.871882331925[/C][/ROW]
[ROW][C]31[/C][C]15986[/C][C]15912.3379723946[/C][C]73.6620276054164[/C][/ROW]
[ROW][C]32[/C][C]15983[/C][C]15988.8352347242[/C][C]-5.83523472421257[/C][/ROW]
[ROW][C]33[/C][C]15692[/C][C]16044.4338013319[/C][C]-352.433801331887[/C][/ROW]
[ROW][C]34[/C][C]16490[/C][C]15985.85089134[/C][C]504.149108660005[/C][/ROW]
[ROW][C]35[/C][C]15686[/C][C]16183.5783407668[/C][C]-497.578340766839[/C][/ROW]
[ROW][C]36[/C][C]18897[/C][C]16088.0540058277[/C][C]2808.94599417232[/C][/ROW]
[ROW][C]37[/C][C]16316[/C][C]17042.7871260072[/C][C]-726.787126007159[/C][/ROW]
[ROW][C]38[/C][C]15636[/C][C]17035.0666665116[/C][C]-1399.06666651162[/C][/ROW]
[ROW][C]39[/C][C]17163[/C][C]16755.4059705321[/C][C]407.59402946788[/C][/ROW]
[ROW][C]40[/C][C]16534[/C][C]16970.0874705877[/C][C]-436.087470587663[/C][/ROW]
[ROW][C]41[/C][C]16518[/C][C]16936.5843896776[/C][C]-418.58438967765[/C][/ROW]
[ROW][C]42[/C][C]16375[/C][C]16878.0655854754[/C][C]-503.065585475437[/C][/ROW]
[ROW][C]43[/C][C]16290[/C][C]16762.2896915943[/C][C]-472.289691594313[/C][/ROW]
[ROW][C]44[/C][C]16352[/C][C]16621.1302819512[/C][C]-269.130281951151[/C][/ROW]
[ROW][C]45[/C][C]15943[/C][C]16513.3425843482[/C][C]-570.342584348153[/C][/ROW]
[ROW][C]46[/C][C]16362[/C][C]16287.6988091724[/C][C]74.3011908276039[/C][/ROW]
[ROW][C]47[/C][C]16393[/C][C]16233.4260455907[/C][C]159.573954409281[/C][/ROW]
[ROW][C]48[/C][C]19051[/C][C]16212.3849039884[/C][C]2838.61509601157[/C][/ROW]
[ROW][C]49[/C][C]16747[/C][C]17081.9865579657[/C][C]-334.986557965658[/C][/ROW]
[ROW][C]50[/C][C]16320[/C][C]17110.095943841[/C][C]-790.095943840988[/C][/ROW]
[ROW][C]51[/C][C]17910[/C][C]16965.1876110135[/C][C]944.81238898655[/C][/ROW]
[ROW][C]52[/C][C]16961[/C][C]17334.0250086798[/C][C]-373.025008679841[/C][/ROW]
[ROW][C]53[/C][C]17480[/C][C]17336.932371648[/C][C]143.067628351993[/C][/ROW]
[ROW][C]54[/C][C]17049[/C][C]17482.9327777428[/C][C]-433.932777742819[/C][/ROW]
[ROW][C]55[/C][C]16879[/C][C]17449.6264610754[/C][C]-570.626461075422[/C][/ROW]
[ROW][C]56[/C][C]17473[/C][C]17340.8418176473[/C][C]132.158182352658[/C][/ROW]
[ROW][C]57[/C][C]16998[/C][C]17422.4927148302[/C][C]-424.492714830190[/C][/ROW]
[ROW][C]58[/C][C]17307[/C][C]17330.7470118186[/C][C]-23.7470118185993[/C][/ROW]
[ROW][C]59[/C][C]17418[/C][C]17340.6016249297[/C][C]77.3983750702973[/C][/ROW]
[ROW][C]60[/C][C]20169[/C][C]17381.9818026237[/C][C]2787.01819737628[/C][/ROW]
[ROW][C]61[/C][C]17871[/C][C]18318.2455692040[/C][C]-447.245569204042[/C][/ROW]
[ROW][C]62[/C][C]17226[/C][C]18389.4653446477[/C][C]-1163.46534464774[/C][/ROW]
[ROW][C]63[/C][C]19062[/C][C]18194.0401470887[/C][C]867.959852911303[/C][/ROW]
[ROW][C]64[/C][C]17804[/C][C]18583.3543879497[/C][C]-779.354387949694[/C][/ROW]
[ROW][C]65[/C][C]19100[/C][C]18493.1677984811[/C][C]606.832201518948[/C][/ROW]
[ROW][C]66[/C][C]18522[/C][C]18803.0178426011[/C][C]-281.01784260109[/C][/ROW]
[ROW][C]67[/C][C]18060[/C][C]18864.2391292665[/C][C]-804.239129266534[/C][/ROW]
[ROW][C]68[/C][C]18869[/C][C]18733.8920687731[/C][C]135.107931226878[/C][/ROW]
[ROW][C]69[/C][C]18127[/C][C]18855.1526633628[/C][C]-728.152663362791[/C][/ROW]
[ROW][C]70[/C][C]18871[/C][C]18702.5810805998[/C][C]168.418919400217[/C][/ROW]
[ROW][C]71[/C][C]18890[/C][C]18792.9432818644[/C][C]97.0567181355837[/C][/ROW]
[ROW][C]72[/C][C]21263[/C][C]18871.7611252470[/C][C]2391.23887475303[/C][/ROW]
[ROW][C]73[/C][C]19547[/C][C]19710.4831521074[/C][C]-163.483152107427[/C][/ROW]
[ROW][C]74[/C][C]18450[/C][C]19879.3008138410[/C][C]-1429.30081384095[/C][/ROW]
[ROW][C]75[/C][C]20254[/C][C]19621.0859997143[/C][C]632.914000285673[/C][/ROW]
[ROW][C]76[/C][C]19240[/C][C]19938.9655221922[/C][C]-698.965522192208[/C][/ROW]
[ROW][C]77[/C][C]20216[/C][C]19864.3048134681[/C][C]351.695186531859[/C][/ROW]
[ROW][C]78[/C][C]19420[/C][C]20085.2159732756[/C][C]-665.215973275623[/C][/ROW]
[ROW][C]79[/C][C]19415[/C][C]19997.1374395170[/C][C]-582.13743951697[/C][/ROW]
[ROW][C]80[/C][C]20018[/C][C]19889.4056822673[/C][C]128.594317732717[/C][/ROW]
[ROW][C]81[/C][C]18652[/C][C]19973.9061105004[/C][C]-1321.90611050038[/C][/ROW]
[ROW][C]82[/C][C]19978[/C][C]19591.3553095818[/C][C]386.644690418172[/C][/ROW]
[ROW][C]83[/C][C]19514[/C][C]19676.3852537728[/C][C]-162.385253772791[/C][/ROW]
[ROW][C]84[/C][C]22148[/C][C]19608.4713044817[/C][C]2539.52869551828[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=13431&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=13431&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
314000124181582
41347712482.2864203408994.713579659181
51423712465.39021910821771.60978089179
61367412773.6735272941900.326472705858
71352912920.9279792195608.072020780533
81405813035.75872559481022.24127440517
91297513329.4318236016-354.431823601633
101432613243.32399190961082.67600809039
111400813603.9410232314404.058976768649
121619313818.17477630272374.82522369733
131448314707.8080263143-224.808026314342
141401114911.6371484163-900.637148416263
151505714877.7698600622179.230139937794
161488415134.8357471942-250.835747194178
171541415263.3765530168150.623446983245
181444015506.0014169266-1066.00141692658
191490015359.8978613722-459.897861372154
201507415337.5514728531-263.551472853147
211444215347.2145479489-905.214547948883
221530715127.6631945612179.336805438779
231493815200.2596620479-262.259662047925
241719315140.55369629572052.4463037043
251552815822.1430697692-294.143069769201
261476515878.2489578869-1113.24895788689
271583815644.737491711193.262508289017
281572315761.5570590694-38.5570590694279
291615015815.9150883808334.084911619244
301548615989.8718823319-503.871882331925
311598615912.337972394673.6620276054164
321598315988.8352347242-5.83523472421257
331569216044.4338013319-352.433801331887
341649015985.85089134504.149108660005
351568616183.5783407668-497.578340766839
361889716088.05400582772808.94599417232
371631617042.7871260072-726.787126007159
381563617035.0666665116-1399.06666651162
391716316755.4059705321407.59402946788
401653416970.0874705877-436.087470587663
411651816936.5843896776-418.58438967765
421637516878.0655854754-503.065585475437
431629016762.2896915943-472.289691594313
441635216621.1302819512-269.130281951151
451594316513.3425843482-570.342584348153
461636216287.698809172474.3011908276039
471639316233.4260455907159.573954409281
481905116212.38490398842838.61509601157
491674717081.9865579657-334.986557965658
501632017110.095943841-790.095943840988
511791016965.1876110135944.81238898655
521696117334.0250086798-373.025008679841
531748017336.932371648143.067628351993
541704917482.9327777428-433.932777742819
551687917449.6264610754-570.626461075422
561747317340.8418176473132.158182352658
571699817422.4927148302-424.492714830190
581730717330.7470118186-23.7470118185993
591741817340.601624929777.3983750702973
602016917381.98180262372787.01819737628
611787118318.2455692040-447.245569204042
621722618389.4653446477-1163.46534464774
631906218194.0401470887867.959852911303
641780418583.3543879497-779.354387949694
651910018493.1677984811606.832201518948
661852218803.0178426011-281.01784260109
671806018864.2391292665-804.239129266534
681886918733.8920687731135.107931226878
691812718855.1526633628-728.152663362791
701887118702.5810805998168.418919400217
711889018792.943281864497.0567181355837
722126318871.76112524702391.23887475303
731954719710.4831521074-163.483152107427
741845019879.3008138410-1429.30081384095
752025419621.0859997143632.914000285673
761924019938.9655221922-698.965522192208
772021619864.3048134681351.695186531859
781942020085.2159732756-665.215973275623
791941519997.1374395170-582.13743951697
802001819889.4056822673128.594317732717
811865219973.9061105004-1321.90611050038
821997819591.3553095818386.644690418172
831951419676.3852537728-162.385253772791
842214819608.47130448172539.52869551828







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
8520415.997484968118496.969357589822335.0256123463
8620569.066637183818549.298919012622588.834355355
8720722.135789399518562.247816606622882.0237621923
8820875.204941615218535.059645062723215.3502381676
8921028.274093830818469.055210340723587.492977321
9021181.343246046518366.786850220523995.8996418726
9121334.412398262218231.299921996524437.524874528
9221487.481550477918065.641826705424909.3212742504
9321640.550702693617872.604887512625408.4965178747
9421793.619854909317654.629573502825932.6101363158
9521946.68900712517413.797044827626479.5809694223
9622099.758159340717151.862602707527047.6537159738

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
85 & 20415.9974849681 & 18496.9693575898 & 22335.0256123463 \tabularnewline
86 & 20569.0666371838 & 18549.2989190126 & 22588.834355355 \tabularnewline
87 & 20722.1357893995 & 18562.2478166066 & 22882.0237621923 \tabularnewline
88 & 20875.2049416152 & 18535.0596450627 & 23215.3502381676 \tabularnewline
89 & 21028.2740938308 & 18469.0552103407 & 23587.492977321 \tabularnewline
90 & 21181.3432460465 & 18366.7868502205 & 23995.8996418726 \tabularnewline
91 & 21334.4123982622 & 18231.2999219965 & 24437.524874528 \tabularnewline
92 & 21487.4815504779 & 18065.6418267054 & 24909.3212742504 \tabularnewline
93 & 21640.5507026936 & 17872.6048875126 & 25408.4965178747 \tabularnewline
94 & 21793.6198549093 & 17654.6295735028 & 25932.6101363158 \tabularnewline
95 & 21946.689007125 & 17413.7970448276 & 26479.5809694223 \tabularnewline
96 & 22099.7581593407 & 17151.8626027075 & 27047.6537159738 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=13431&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]85[/C][C]20415.9974849681[/C][C]18496.9693575898[/C][C]22335.0256123463[/C][/ROW]
[ROW][C]86[/C][C]20569.0666371838[/C][C]18549.2989190126[/C][C]22588.834355355[/C][/ROW]
[ROW][C]87[/C][C]20722.1357893995[/C][C]18562.2478166066[/C][C]22882.0237621923[/C][/ROW]
[ROW][C]88[/C][C]20875.2049416152[/C][C]18535.0596450627[/C][C]23215.3502381676[/C][/ROW]
[ROW][C]89[/C][C]21028.2740938308[/C][C]18469.0552103407[/C][C]23587.492977321[/C][/ROW]
[ROW][C]90[/C][C]21181.3432460465[/C][C]18366.7868502205[/C][C]23995.8996418726[/C][/ROW]
[ROW][C]91[/C][C]21334.4123982622[/C][C]18231.2999219965[/C][C]24437.524874528[/C][/ROW]
[ROW][C]92[/C][C]21487.4815504779[/C][C]18065.6418267054[/C][C]24909.3212742504[/C][/ROW]
[ROW][C]93[/C][C]21640.5507026936[/C][C]17872.6048875126[/C][C]25408.4965178747[/C][/ROW]
[ROW][C]94[/C][C]21793.6198549093[/C][C]17654.6295735028[/C][C]25932.6101363158[/C][/ROW]
[ROW][C]95[/C][C]21946.689007125[/C][C]17413.7970448276[/C][C]26479.5809694223[/C][/ROW]
[ROW][C]96[/C][C]22099.7581593407[/C][C]17151.8626027075[/C][C]27047.6537159738[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=13431&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=13431&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
8520415.997484968118496.969357589822335.0256123463
8620569.066637183818549.298919012622588.834355355
8720722.135789399518562.247816606622882.0237621923
8820875.204941615218535.059645062723215.3502381676
8921028.274093830818469.055210340723587.492977321
9021181.343246046518366.786850220523995.8996418726
9121334.412398262218231.299921996524437.524874528
9221487.481550477918065.641826705424909.3212742504
9321640.550702693617872.604887512625408.4965178747
9421793.619854909317654.629573502825932.6101363158
9521946.68900712517413.797044827626479.5809694223
9622099.758159340717151.862602707527047.6537159738



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')