Free Statistics

of Irreproducible Research!

Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationFri, 25 Nov 2016 11:18:55 +0000
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2016/Nov/25/t1480072811vl5wl0pvl8oys4d.htm/, Retrieved Sun, 19 May 2024 02:58:45 +0200
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=, Retrieved Sun, 19 May 2024 02:58:45 +0200
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact0
Dataseries X:
12347
12624
11918
10028
10228
11026
13878
22165
23533
13445
12164
9606
12177
13142
11210
9485
10082
10680
13579
21709
22205
14687
11222
8196
12794
12627
11080
10425
10865
10771
14771
20993
23882
14825
11648
10091
14976
14472
12254
12257
10767
12275
14845
21939
26740
16974
12956
12494
16024
15306
13989
12792
10697
14257
17251
25795
29016
18968
16009
14511




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time1 seconds
R Server'Sir Maurice George Kendall' @ kendall.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 & 'Sir Maurice George Kendall' @ kendall.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]'Sir Maurice George Kendall' @ kendall.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'Sir Maurice George Kendall' @ kendall.wessa.net







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.130595304369704
beta0.0281246545115487
gammaFALSE

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.130595304369704 \tabularnewline
beta & 0.0281246545115487 \tabularnewline
gamma & FALSE \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]0.130595304369704[/C][/ROW]
[ROW][C]beta[/C][C]0.0281246545115487[/C][/ROW]
[ROW][C]gamma[/C][C]FALSE[/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
alpha0.130595304369704
beta0.0281246545115487
gammaFALSE







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
31191812901-983
41002813046.0143081012-3018.01430810122
51022812914.180294177-2686.18029417698
61102612815.8160442559-1789.8160442559
71387812827.93885544821050.06114455181
82216513214.79311227328950.20688772681
92353314666.24294983628866.75705016378
101344516139.3617664075-2694.36176640753
111216416092.7565021083-3928.75650210834
12960615870.514963973-6264.51496397303
131217715320.2251020197-3143.22510201973
141314215166.0161378399-2024.01613783992
151121015150.536503337-3940.53650333698
16948514870.2949234265-5385.29492342651
171008214381.594770675-4299.59477067502
181068014018.8897726027-3338.88977260272
191357913769.3847682643-190.384768264263
202170913930.36045995817778.63954004192
212220515160.62384383657044.37615616345
221468716320.8695036293-1633.86950362934
231122216341.7759126611-5119.77591266108
24819615888.634643443-7692.63464344302
251279415071.2354595636-2277.23545956357
261262714952.6978133781-2325.69781337806
271108014819.2890446408-3739.28904464082
281042514487.5376852717-4062.53768527172
291086514098.6500823729-3233.65008237286
301077113806.1342802544-3035.13428025436
311477113528.39581990911242.6041800909
322099313813.87393611637179.12606388368
332388214901.00249003368980.99750996636
341482516256.433729079-1431.43372907899
351164816246.7927598433-4598.7927598433
361009115806.6184481123-5715.61844811225
371497615199.5987773964-223.598777396435
381447215308.989820541-836.989820541003
391225415335.2006537749-3081.20065377489
401225715057.0110009602-2800.01100096017
411076714805.259102149-4038.25910214901
421227514376.9655007273-2101.96550072728
431484514193.8223419366651.177658063358
442193914372.61849349887566.3815065012
452674015482.298720857311257.7012791427
461697417115.3969267788-141.396926778812
471295617259.3070894244-4303.30708942442
481249416843.8855052433-4349.88550524329
491602416406.4040962039-382.404096203914
501530616485.6525790691-1179.65257906911
511398916456.451351292-2467.45135129204
521279216250.0068308372-3458.0068308372
531069715901.4993373983-5204.49933739826
541425715305.7922690097-1048.79226900971
551725115248.94887081462002.05112918544
562579515597.884724113910197.1152758861
572901617054.510946265311961.4890537347
581896818785.4900240555182.509975944486
591600918978.8600936349-2969.86009363491
601451118749.6372933462-4238.63729334623

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
3 & 11918 & 12901 & -983 \tabularnewline
4 & 10028 & 13046.0143081012 & -3018.01430810122 \tabularnewline
5 & 10228 & 12914.180294177 & -2686.18029417698 \tabularnewline
6 & 11026 & 12815.8160442559 & -1789.8160442559 \tabularnewline
7 & 13878 & 12827.9388554482 & 1050.06114455181 \tabularnewline
8 & 22165 & 13214.7931122732 & 8950.20688772681 \tabularnewline
9 & 23533 & 14666.2429498362 & 8866.75705016378 \tabularnewline
10 & 13445 & 16139.3617664075 & -2694.36176640753 \tabularnewline
11 & 12164 & 16092.7565021083 & -3928.75650210834 \tabularnewline
12 & 9606 & 15870.514963973 & -6264.51496397303 \tabularnewline
13 & 12177 & 15320.2251020197 & -3143.22510201973 \tabularnewline
14 & 13142 & 15166.0161378399 & -2024.01613783992 \tabularnewline
15 & 11210 & 15150.536503337 & -3940.53650333698 \tabularnewline
16 & 9485 & 14870.2949234265 & -5385.29492342651 \tabularnewline
17 & 10082 & 14381.594770675 & -4299.59477067502 \tabularnewline
18 & 10680 & 14018.8897726027 & -3338.88977260272 \tabularnewline
19 & 13579 & 13769.3847682643 & -190.384768264263 \tabularnewline
20 & 21709 & 13930.3604599581 & 7778.63954004192 \tabularnewline
21 & 22205 & 15160.6238438365 & 7044.37615616345 \tabularnewline
22 & 14687 & 16320.8695036293 & -1633.86950362934 \tabularnewline
23 & 11222 & 16341.7759126611 & -5119.77591266108 \tabularnewline
24 & 8196 & 15888.634643443 & -7692.63464344302 \tabularnewline
25 & 12794 & 15071.2354595636 & -2277.23545956357 \tabularnewline
26 & 12627 & 14952.6978133781 & -2325.69781337806 \tabularnewline
27 & 11080 & 14819.2890446408 & -3739.28904464082 \tabularnewline
28 & 10425 & 14487.5376852717 & -4062.53768527172 \tabularnewline
29 & 10865 & 14098.6500823729 & -3233.65008237286 \tabularnewline
30 & 10771 & 13806.1342802544 & -3035.13428025436 \tabularnewline
31 & 14771 & 13528.3958199091 & 1242.6041800909 \tabularnewline
32 & 20993 & 13813.8739361163 & 7179.12606388368 \tabularnewline
33 & 23882 & 14901.0024900336 & 8980.99750996636 \tabularnewline
34 & 14825 & 16256.433729079 & -1431.43372907899 \tabularnewline
35 & 11648 & 16246.7927598433 & -4598.7927598433 \tabularnewline
36 & 10091 & 15806.6184481123 & -5715.61844811225 \tabularnewline
37 & 14976 & 15199.5987773964 & -223.598777396435 \tabularnewline
38 & 14472 & 15308.989820541 & -836.989820541003 \tabularnewline
39 & 12254 & 15335.2006537749 & -3081.20065377489 \tabularnewline
40 & 12257 & 15057.0110009602 & -2800.01100096017 \tabularnewline
41 & 10767 & 14805.259102149 & -4038.25910214901 \tabularnewline
42 & 12275 & 14376.9655007273 & -2101.96550072728 \tabularnewline
43 & 14845 & 14193.8223419366 & 651.177658063358 \tabularnewline
44 & 21939 & 14372.6184934988 & 7566.3815065012 \tabularnewline
45 & 26740 & 15482.2987208573 & 11257.7012791427 \tabularnewline
46 & 16974 & 17115.3969267788 & -141.396926778812 \tabularnewline
47 & 12956 & 17259.3070894244 & -4303.30708942442 \tabularnewline
48 & 12494 & 16843.8855052433 & -4349.88550524329 \tabularnewline
49 & 16024 & 16406.4040962039 & -382.404096203914 \tabularnewline
50 & 15306 & 16485.6525790691 & -1179.65257906911 \tabularnewline
51 & 13989 & 16456.451351292 & -2467.45135129204 \tabularnewline
52 & 12792 & 16250.0068308372 & -3458.0068308372 \tabularnewline
53 & 10697 & 15901.4993373983 & -5204.49933739826 \tabularnewline
54 & 14257 & 15305.7922690097 & -1048.79226900971 \tabularnewline
55 & 17251 & 15248.9488708146 & 2002.05112918544 \tabularnewline
56 & 25795 & 15597.8847241139 & 10197.1152758861 \tabularnewline
57 & 29016 & 17054.5109462653 & 11961.4890537347 \tabularnewline
58 & 18968 & 18785.4900240555 & 182.509975944486 \tabularnewline
59 & 16009 & 18978.8600936349 & -2969.86009363491 \tabularnewline
60 & 14511 & 18749.6372933462 & -4238.63729334623 \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]3[/C][C]11918[/C][C]12901[/C][C]-983[/C][/ROW]
[ROW][C]4[/C][C]10028[/C][C]13046.0143081012[/C][C]-3018.01430810122[/C][/ROW]
[ROW][C]5[/C][C]10228[/C][C]12914.180294177[/C][C]-2686.18029417698[/C][/ROW]
[ROW][C]6[/C][C]11026[/C][C]12815.8160442559[/C][C]-1789.8160442559[/C][/ROW]
[ROW][C]7[/C][C]13878[/C][C]12827.9388554482[/C][C]1050.06114455181[/C][/ROW]
[ROW][C]8[/C][C]22165[/C][C]13214.7931122732[/C][C]8950.20688772681[/C][/ROW]
[ROW][C]9[/C][C]23533[/C][C]14666.2429498362[/C][C]8866.75705016378[/C][/ROW]
[ROW][C]10[/C][C]13445[/C][C]16139.3617664075[/C][C]-2694.36176640753[/C][/ROW]
[ROW][C]11[/C][C]12164[/C][C]16092.7565021083[/C][C]-3928.75650210834[/C][/ROW]
[ROW][C]12[/C][C]9606[/C][C]15870.514963973[/C][C]-6264.51496397303[/C][/ROW]
[ROW][C]13[/C][C]12177[/C][C]15320.2251020197[/C][C]-3143.22510201973[/C][/ROW]
[ROW][C]14[/C][C]13142[/C][C]15166.0161378399[/C][C]-2024.01613783992[/C][/ROW]
[ROW][C]15[/C][C]11210[/C][C]15150.536503337[/C][C]-3940.53650333698[/C][/ROW]
[ROW][C]16[/C][C]9485[/C][C]14870.2949234265[/C][C]-5385.29492342651[/C][/ROW]
[ROW][C]17[/C][C]10082[/C][C]14381.594770675[/C][C]-4299.59477067502[/C][/ROW]
[ROW][C]18[/C][C]10680[/C][C]14018.8897726027[/C][C]-3338.88977260272[/C][/ROW]
[ROW][C]19[/C][C]13579[/C][C]13769.3847682643[/C][C]-190.384768264263[/C][/ROW]
[ROW][C]20[/C][C]21709[/C][C]13930.3604599581[/C][C]7778.63954004192[/C][/ROW]
[ROW][C]21[/C][C]22205[/C][C]15160.6238438365[/C][C]7044.37615616345[/C][/ROW]
[ROW][C]22[/C][C]14687[/C][C]16320.8695036293[/C][C]-1633.86950362934[/C][/ROW]
[ROW][C]23[/C][C]11222[/C][C]16341.7759126611[/C][C]-5119.77591266108[/C][/ROW]
[ROW][C]24[/C][C]8196[/C][C]15888.634643443[/C][C]-7692.63464344302[/C][/ROW]
[ROW][C]25[/C][C]12794[/C][C]15071.2354595636[/C][C]-2277.23545956357[/C][/ROW]
[ROW][C]26[/C][C]12627[/C][C]14952.6978133781[/C][C]-2325.69781337806[/C][/ROW]
[ROW][C]27[/C][C]11080[/C][C]14819.2890446408[/C][C]-3739.28904464082[/C][/ROW]
[ROW][C]28[/C][C]10425[/C][C]14487.5376852717[/C][C]-4062.53768527172[/C][/ROW]
[ROW][C]29[/C][C]10865[/C][C]14098.6500823729[/C][C]-3233.65008237286[/C][/ROW]
[ROW][C]30[/C][C]10771[/C][C]13806.1342802544[/C][C]-3035.13428025436[/C][/ROW]
[ROW][C]31[/C][C]14771[/C][C]13528.3958199091[/C][C]1242.6041800909[/C][/ROW]
[ROW][C]32[/C][C]20993[/C][C]13813.8739361163[/C][C]7179.12606388368[/C][/ROW]
[ROW][C]33[/C][C]23882[/C][C]14901.0024900336[/C][C]8980.99750996636[/C][/ROW]
[ROW][C]34[/C][C]14825[/C][C]16256.433729079[/C][C]-1431.43372907899[/C][/ROW]
[ROW][C]35[/C][C]11648[/C][C]16246.7927598433[/C][C]-4598.7927598433[/C][/ROW]
[ROW][C]36[/C][C]10091[/C][C]15806.6184481123[/C][C]-5715.61844811225[/C][/ROW]
[ROW][C]37[/C][C]14976[/C][C]15199.5987773964[/C][C]-223.598777396435[/C][/ROW]
[ROW][C]38[/C][C]14472[/C][C]15308.989820541[/C][C]-836.989820541003[/C][/ROW]
[ROW][C]39[/C][C]12254[/C][C]15335.2006537749[/C][C]-3081.20065377489[/C][/ROW]
[ROW][C]40[/C][C]12257[/C][C]15057.0110009602[/C][C]-2800.01100096017[/C][/ROW]
[ROW][C]41[/C][C]10767[/C][C]14805.259102149[/C][C]-4038.25910214901[/C][/ROW]
[ROW][C]42[/C][C]12275[/C][C]14376.9655007273[/C][C]-2101.96550072728[/C][/ROW]
[ROW][C]43[/C][C]14845[/C][C]14193.8223419366[/C][C]651.177658063358[/C][/ROW]
[ROW][C]44[/C][C]21939[/C][C]14372.6184934988[/C][C]7566.3815065012[/C][/ROW]
[ROW][C]45[/C][C]26740[/C][C]15482.2987208573[/C][C]11257.7012791427[/C][/ROW]
[ROW][C]46[/C][C]16974[/C][C]17115.3969267788[/C][C]-141.396926778812[/C][/ROW]
[ROW][C]47[/C][C]12956[/C][C]17259.3070894244[/C][C]-4303.30708942442[/C][/ROW]
[ROW][C]48[/C][C]12494[/C][C]16843.8855052433[/C][C]-4349.88550524329[/C][/ROW]
[ROW][C]49[/C][C]16024[/C][C]16406.4040962039[/C][C]-382.404096203914[/C][/ROW]
[ROW][C]50[/C][C]15306[/C][C]16485.6525790691[/C][C]-1179.65257906911[/C][/ROW]
[ROW][C]51[/C][C]13989[/C][C]16456.451351292[/C][C]-2467.45135129204[/C][/ROW]
[ROW][C]52[/C][C]12792[/C][C]16250.0068308372[/C][C]-3458.0068308372[/C][/ROW]
[ROW][C]53[/C][C]10697[/C][C]15901.4993373983[/C][C]-5204.49933739826[/C][/ROW]
[ROW][C]54[/C][C]14257[/C][C]15305.7922690097[/C][C]-1048.79226900971[/C][/ROW]
[ROW][C]55[/C][C]17251[/C][C]15248.9488708146[/C][C]2002.05112918544[/C][/ROW]
[ROW][C]56[/C][C]25795[/C][C]15597.8847241139[/C][C]10197.1152758861[/C][/ROW]
[ROW][C]57[/C][C]29016[/C][C]17054.5109462653[/C][C]11961.4890537347[/C][/ROW]
[ROW][C]58[/C][C]18968[/C][C]18785.4900240555[/C][C]182.509975944486[/C][/ROW]
[ROW][C]59[/C][C]16009[/C][C]18978.8600936349[/C][C]-2969.86009363491[/C][/ROW]
[ROW][C]60[/C][C]14511[/C][C]18749.6372933462[/C][C]-4238.63729334623[/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
31191812901-983
41002813046.0143081012-3018.01430810122
51022812914.180294177-2686.18029417698
61102612815.8160442559-1789.8160442559
71387812827.93885544821050.06114455181
82216513214.79311227328950.20688772681
92353314666.24294983628866.75705016378
101344516139.3617664075-2694.36176640753
111216416092.7565021083-3928.75650210834
12960615870.514963973-6264.51496397303
131217715320.2251020197-3143.22510201973
141314215166.0161378399-2024.01613783992
151121015150.536503337-3940.53650333698
16948514870.2949234265-5385.29492342651
171008214381.594770675-4299.59477067502
181068014018.8897726027-3338.88977260272
191357913769.3847682643-190.384768264263
202170913930.36045995817778.63954004192
212220515160.62384383657044.37615616345
221468716320.8695036293-1633.86950362934
231122216341.7759126611-5119.77591266108
24819615888.634643443-7692.63464344302
251279415071.2354595636-2277.23545956357
261262714952.6978133781-2325.69781337806
271108014819.2890446408-3739.28904464082
281042514487.5376852717-4062.53768527172
291086514098.6500823729-3233.65008237286
301077113806.1342802544-3035.13428025436
311477113528.39581990911242.6041800909
322099313813.87393611637179.12606388368
332388214901.00249003368980.99750996636
341482516256.433729079-1431.43372907899
351164816246.7927598433-4598.7927598433
361009115806.6184481123-5715.61844811225
371497615199.5987773964-223.598777396435
381447215308.989820541-836.989820541003
391225415335.2006537749-3081.20065377489
401225715057.0110009602-2800.01100096017
411076714805.259102149-4038.25910214901
421227514376.9655007273-2101.96550072728
431484514193.8223419366651.177658063358
442193914372.61849349887566.3815065012
452674015482.298720857311257.7012791427
461697417115.3969267788-141.396926778812
471295617259.3070894244-4303.30708942442
481249416843.8855052433-4349.88550524329
491602416406.4040962039-382.404096203914
501530616485.6525790691-1179.65257906911
511398916456.451351292-2467.45135129204
521279216250.0068308372-3458.0068308372
531069715901.4993373983-5204.49933739826
541425715305.7922690097-1048.79226900971
551725115248.94887081462002.05112918544
562579515597.884724113910197.1152758861
572901617054.510946265311961.4890537347
581896818785.4900240555182.509975944486
591600918978.8600936349-2969.86009363491
601451118749.6372933462-4238.63729334623







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
6118339.14985489358827.6175206113627850.6821891757
6218482.20854387818885.3224010086728079.0946867476
6318625.26723286288939.1094759818828311.4249897436
6418768.32592184748988.9612358838628547.6906078109
6518911.3846108329034.8655222115228787.9036994525
6619054.44329981669076.8153256610729032.0712739722
6719197.50198880129114.8085654944429280.195412108
6819340.56067778599148.8478531357329532.273502436
6919483.61936677059178.9402429497329788.2984905912
7019626.67805575519205.0969731301630048.25913838
7119769.73674473979227.3331995504530312.140289929
7219912.79543372439245.6677253104730579.9231421382

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
61 & 18339.1498548935 & 8827.61752061136 & 27850.6821891757 \tabularnewline
62 & 18482.2085438781 & 8885.32240100867 & 28079.0946867476 \tabularnewline
63 & 18625.2672328628 & 8939.10947598188 & 28311.4249897436 \tabularnewline
64 & 18768.3259218474 & 8988.96123588386 & 28547.6906078109 \tabularnewline
65 & 18911.384610832 & 9034.86552221152 & 28787.9036994525 \tabularnewline
66 & 19054.4432998166 & 9076.81532566107 & 29032.0712739722 \tabularnewline
67 & 19197.5019888012 & 9114.80856549444 & 29280.195412108 \tabularnewline
68 & 19340.5606777859 & 9148.84785313573 & 29532.273502436 \tabularnewline
69 & 19483.6193667705 & 9178.94024294973 & 29788.2984905912 \tabularnewline
70 & 19626.6780557551 & 9205.09697313016 & 30048.25913838 \tabularnewline
71 & 19769.7367447397 & 9227.33319955045 & 30312.140289929 \tabularnewline
72 & 19912.7954337243 & 9245.66772531047 & 30579.9231421382 \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]61[/C][C]18339.1498548935[/C][C]8827.61752061136[/C][C]27850.6821891757[/C][/ROW]
[ROW][C]62[/C][C]18482.2085438781[/C][C]8885.32240100867[/C][C]28079.0946867476[/C][/ROW]
[ROW][C]63[/C][C]18625.2672328628[/C][C]8939.10947598188[/C][C]28311.4249897436[/C][/ROW]
[ROW][C]64[/C][C]18768.3259218474[/C][C]8988.96123588386[/C][C]28547.6906078109[/C][/ROW]
[ROW][C]65[/C][C]18911.384610832[/C][C]9034.86552221152[/C][C]28787.9036994525[/C][/ROW]
[ROW][C]66[/C][C]19054.4432998166[/C][C]9076.81532566107[/C][C]29032.0712739722[/C][/ROW]
[ROW][C]67[/C][C]19197.5019888012[/C][C]9114.80856549444[/C][C]29280.195412108[/C][/ROW]
[ROW][C]68[/C][C]19340.5606777859[/C][C]9148.84785313573[/C][C]29532.273502436[/C][/ROW]
[ROW][C]69[/C][C]19483.6193667705[/C][C]9178.94024294973[/C][C]29788.2984905912[/C][/ROW]
[ROW][C]70[/C][C]19626.6780557551[/C][C]9205.09697313016[/C][C]30048.25913838[/C][/ROW]
[ROW][C]71[/C][C]19769.7367447397[/C][C]9227.33319955045[/C][C]30312.140289929[/C][/ROW]
[ROW][C]72[/C][C]19912.7954337243[/C][C]9245.66772531047[/C][C]30579.9231421382[/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
6118339.14985489358827.6175206113627850.6821891757
6218482.20854387818885.3224010086728079.0946867476
6318625.26723286288939.1094759818828311.4249897436
6418768.32592184748988.9612358838628547.6906078109
6518911.3846108329034.8655222115228787.9036994525
6619054.44329981669076.8153256610729032.0712739722
6719197.50198880129114.8085654944429280.195412108
6819340.56067778599148.8478531357329532.273502436
6919483.61936677059178.9402429497329788.2984905912
7019626.67805575519205.0969731301630048.25913838
7119769.73674473979227.3331995504530312.140289929
7219912.79543372439245.6677253104730579.9231421382



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=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')