Free Statistics

of Irreproducible Research!

Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationFri, 28 Dec 2012 08:21:12 -0500
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2012/Dec/28/t1356700949ek1dmsodra6z8e2.htm/, Retrieved Mon, 29 Apr 2024 08:56:33 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=204819, Retrieved Mon, 29 Apr 2024 08:56:33 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact122
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [] [2012-12-28 13:21:12] [6c22bb999934aa737b0ea317b07bbf4f] [Current]
Feedback Forum

Post a new message
Dataseries X:
8,7
8,7
8,6
8,5
8,3
8
8,2
8,1
8,1
8
7,9
7,9
8
8
7,9
8
7,7
7,2
7,5
7,3
7
7
7
7,2
7,3
7,1
6,8
6,4
6,1
6,5
7,7
7,9
7,5
6,9
6,6
6,9
7,7
8
8
7,7
7,3
7,4
8,1
8,3
8,1
7,9
7,9
8,3
8,6
8,7
8,5
8,3
8
8
8,8
8,7
8,5
8,1
7,8
7,7
7,5
7,2
6,9
6,6
6,5
6,6
7,7
8
7,7
7,2
7
7
7,3
7,3
7,1
6,9
6,7
6,8
7,5




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'Herman Ole Andreas Wold' @ wold.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 & 2 seconds \tabularnewline
R Server & 'Herman Ole Andreas Wold' @ wold.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=204819&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]2 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Herman Ole Andreas Wold' @ wold.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=204819&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=204819&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 time2 seconds
R Server'Herman Ole Andreas Wold' @ wold.wessa.net







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.999933893038648
betaFALSE
gammaFALSE

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.999933893038648 \tabularnewline
beta & FALSE \tabularnewline
gamma & FALSE \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=204819&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]0.999933893038648[/C][/ROW]
[ROW][C]beta[/C][C]FALSE[/C][/ROW]
[ROW][C]gamma[/C][C]FALSE[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=204819&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=204819&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
alpha0.999933893038648
betaFALSE
gammaFALSE







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
28.78.70
38.68.7-0.0999999999999996
48.58.60000661069613-0.100006610696134
58.38.50000661113315-0.200006611133148
688.30001322182931-0.300013221829314
78.28.000019832962460.199980167037539
88.18.19998677991883-0.0999867799188259
98.18.1000066098222-6.60982219535811e-06
1088.10000000043696-0.100000000436955
117.98.00000661069616-0.100006610696164
127.97.90000661113315-6.61113314848194e-06
1387.900000000437040.0999999995629581
1487.999993389303896.61069610607967e-06
157.97.99999999956299-0.0999999995629866
1687.900006610696110.0999933893038936
177.77.99999338974088-0.299993389740878
187.27.70001983165142-0.500019831651421
197.57.200033054791690.299966945208314
207.37.49998017009675-0.199980170096747
2177.30001322008138-0.300013220081375
2277.00001983296235-1.9832962345312e-05
2377.0000000013111-1.31109700873822e-09
247.27.000000000000090.199999999999913
257.37.199986778607730.10001322139227
267.17.29999338842984-0.199993388429839
276.87.1000132209552-0.3000132209552
286.46.8000198329624-0.400019832962403
296.16.40002644409564-0.300026444095638
306.56.100019833836540.399980166163456
317.76.499973558526611.20002644147339
327.97.699920669898410.200079330101588
337.57.89998677336346-0.399986773363458
346.97.50002644191017-0.600026441910168
356.66.90003966592481-0.300039665924806
366.96.60001983471060.299980165289401
377.76.899980169222810.800019830777193
3887.699947113119970.300052886880033
3987.99998016441541.98355845961729e-05
407.77.99999999868873-0.29999999868873
417.37.70001983208832-0.400019832088319
427.47.300026444095580.0999735559044206
438.17.3999933910520.700006608947995
448.38.099953724690160.200046275309845
458.18.29998677554861-0.199986775548611
467.98.10001322051804-0.200013220518041
477.97.90001322226624-1.32222662383441e-05
488.37.900000000874080.399999999125916
498.68.299973557215520.300026442784482
508.78.599980166163540.100019833836457
518.58.69999338799271-0.199993387992709
528.38.50001322095517-0.200013220955171
5388.30001322226627-0.300013222266267
5488.00001983296249-1.9832962490085e-05
558.88.00000000131110.799999998688904
568.78.79994711443101-0.0999471144310071
578.58.70000660720003-0.200006607200031
588.18.50001322182905-0.400013221829052
597.88.1000264436586-0.300026443658596
607.77.80001983383652-0.100019833836515
617.57.70000661200729-0.20000661200729
627.27.50001322182937-0.30001322182937
636.97.20001983296246-0.300019832962461
646.66.9000198333995-0.300019833399503
656.56.60001983339953-0.100019833399531
666.66.500006612007260.0999933879927388
677.76.599993389740961.10000661025904
6887.699927281905530.300072718094471
697.77.99998016310442-0.299980163104422
707.27.70001983077705-0.500019830777049
7177.20003305479163-0.200033054791628
7277.00001322357742-1.32235774223943e-05
737.37.000000000874170.299999999125829
747.37.299980167911651.98320883475489e-05
757.17.29999999868896-0.199999998688961
766.97.10001322139218-0.200013221392183
776.76.9000132222663-0.200013222266296
786.86.700013222266350.0999867777336458
797.56.799993390177950.700006609822052

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
2 & 8.7 & 8.7 & 0 \tabularnewline
3 & 8.6 & 8.7 & -0.0999999999999996 \tabularnewline
4 & 8.5 & 8.60000661069613 & -0.100006610696134 \tabularnewline
5 & 8.3 & 8.50000661113315 & -0.200006611133148 \tabularnewline
6 & 8 & 8.30001322182931 & -0.300013221829314 \tabularnewline
7 & 8.2 & 8.00001983296246 & 0.199980167037539 \tabularnewline
8 & 8.1 & 8.19998677991883 & -0.0999867799188259 \tabularnewline
9 & 8.1 & 8.1000066098222 & -6.60982219535811e-06 \tabularnewline
10 & 8 & 8.10000000043696 & -0.100000000436955 \tabularnewline
11 & 7.9 & 8.00000661069616 & -0.100006610696164 \tabularnewline
12 & 7.9 & 7.90000661113315 & -6.61113314848194e-06 \tabularnewline
13 & 8 & 7.90000000043704 & 0.0999999995629581 \tabularnewline
14 & 8 & 7.99999338930389 & 6.61069610607967e-06 \tabularnewline
15 & 7.9 & 7.99999999956299 & -0.0999999995629866 \tabularnewline
16 & 8 & 7.90000661069611 & 0.0999933893038936 \tabularnewline
17 & 7.7 & 7.99999338974088 & -0.299993389740878 \tabularnewline
18 & 7.2 & 7.70001983165142 & -0.500019831651421 \tabularnewline
19 & 7.5 & 7.20003305479169 & 0.299966945208314 \tabularnewline
20 & 7.3 & 7.49998017009675 & -0.199980170096747 \tabularnewline
21 & 7 & 7.30001322008138 & -0.300013220081375 \tabularnewline
22 & 7 & 7.00001983296235 & -1.9832962345312e-05 \tabularnewline
23 & 7 & 7.0000000013111 & -1.31109700873822e-09 \tabularnewline
24 & 7.2 & 7.00000000000009 & 0.199999999999913 \tabularnewline
25 & 7.3 & 7.19998677860773 & 0.10001322139227 \tabularnewline
26 & 7.1 & 7.29999338842984 & -0.199993388429839 \tabularnewline
27 & 6.8 & 7.1000132209552 & -0.3000132209552 \tabularnewline
28 & 6.4 & 6.8000198329624 & -0.400019832962403 \tabularnewline
29 & 6.1 & 6.40002644409564 & -0.300026444095638 \tabularnewline
30 & 6.5 & 6.10001983383654 & 0.399980166163456 \tabularnewline
31 & 7.7 & 6.49997355852661 & 1.20002644147339 \tabularnewline
32 & 7.9 & 7.69992066989841 & 0.200079330101588 \tabularnewline
33 & 7.5 & 7.89998677336346 & -0.399986773363458 \tabularnewline
34 & 6.9 & 7.50002644191017 & -0.600026441910168 \tabularnewline
35 & 6.6 & 6.90003966592481 & -0.300039665924806 \tabularnewline
36 & 6.9 & 6.6000198347106 & 0.299980165289401 \tabularnewline
37 & 7.7 & 6.89998016922281 & 0.800019830777193 \tabularnewline
38 & 8 & 7.69994711311997 & 0.300052886880033 \tabularnewline
39 & 8 & 7.9999801644154 & 1.98355845961729e-05 \tabularnewline
40 & 7.7 & 7.99999999868873 & -0.29999999868873 \tabularnewline
41 & 7.3 & 7.70001983208832 & -0.400019832088319 \tabularnewline
42 & 7.4 & 7.30002644409558 & 0.0999735559044206 \tabularnewline
43 & 8.1 & 7.399993391052 & 0.700006608947995 \tabularnewline
44 & 8.3 & 8.09995372469016 & 0.200046275309845 \tabularnewline
45 & 8.1 & 8.29998677554861 & -0.199986775548611 \tabularnewline
46 & 7.9 & 8.10001322051804 & -0.200013220518041 \tabularnewline
47 & 7.9 & 7.90001322226624 & -1.32222662383441e-05 \tabularnewline
48 & 8.3 & 7.90000000087408 & 0.399999999125916 \tabularnewline
49 & 8.6 & 8.29997355721552 & 0.300026442784482 \tabularnewline
50 & 8.7 & 8.59998016616354 & 0.100019833836457 \tabularnewline
51 & 8.5 & 8.69999338799271 & -0.199993387992709 \tabularnewline
52 & 8.3 & 8.50001322095517 & -0.200013220955171 \tabularnewline
53 & 8 & 8.30001322226627 & -0.300013222266267 \tabularnewline
54 & 8 & 8.00001983296249 & -1.9832962490085e-05 \tabularnewline
55 & 8.8 & 8.0000000013111 & 0.799999998688904 \tabularnewline
56 & 8.7 & 8.79994711443101 & -0.0999471144310071 \tabularnewline
57 & 8.5 & 8.70000660720003 & -0.200006607200031 \tabularnewline
58 & 8.1 & 8.50001322182905 & -0.400013221829052 \tabularnewline
59 & 7.8 & 8.1000264436586 & -0.300026443658596 \tabularnewline
60 & 7.7 & 7.80001983383652 & -0.100019833836515 \tabularnewline
61 & 7.5 & 7.70000661200729 & -0.20000661200729 \tabularnewline
62 & 7.2 & 7.50001322182937 & -0.30001322182937 \tabularnewline
63 & 6.9 & 7.20001983296246 & -0.300019832962461 \tabularnewline
64 & 6.6 & 6.9000198333995 & -0.300019833399503 \tabularnewline
65 & 6.5 & 6.60001983339953 & -0.100019833399531 \tabularnewline
66 & 6.6 & 6.50000661200726 & 0.0999933879927388 \tabularnewline
67 & 7.7 & 6.59999338974096 & 1.10000661025904 \tabularnewline
68 & 8 & 7.69992728190553 & 0.300072718094471 \tabularnewline
69 & 7.7 & 7.99998016310442 & -0.299980163104422 \tabularnewline
70 & 7.2 & 7.70001983077705 & -0.500019830777049 \tabularnewline
71 & 7 & 7.20003305479163 & -0.200033054791628 \tabularnewline
72 & 7 & 7.00001322357742 & -1.32235774223943e-05 \tabularnewline
73 & 7.3 & 7.00000000087417 & 0.299999999125829 \tabularnewline
74 & 7.3 & 7.29998016791165 & 1.98320883475489e-05 \tabularnewline
75 & 7.1 & 7.29999999868896 & -0.199999998688961 \tabularnewline
76 & 6.9 & 7.10001322139218 & -0.200013221392183 \tabularnewline
77 & 6.7 & 6.9000132222663 & -0.200013222266296 \tabularnewline
78 & 6.8 & 6.70001322226635 & 0.0999867777336458 \tabularnewline
79 & 7.5 & 6.79999339017795 & 0.700006609822052 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=204819&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]2[/C][C]8.7[/C][C]8.7[/C][C]0[/C][/ROW]
[ROW][C]3[/C][C]8.6[/C][C]8.7[/C][C]-0.0999999999999996[/C][/ROW]
[ROW][C]4[/C][C]8.5[/C][C]8.60000661069613[/C][C]-0.100006610696134[/C][/ROW]
[ROW][C]5[/C][C]8.3[/C][C]8.50000661113315[/C][C]-0.200006611133148[/C][/ROW]
[ROW][C]6[/C][C]8[/C][C]8.30001322182931[/C][C]-0.300013221829314[/C][/ROW]
[ROW][C]7[/C][C]8.2[/C][C]8.00001983296246[/C][C]0.199980167037539[/C][/ROW]
[ROW][C]8[/C][C]8.1[/C][C]8.19998677991883[/C][C]-0.0999867799188259[/C][/ROW]
[ROW][C]9[/C][C]8.1[/C][C]8.1000066098222[/C][C]-6.60982219535811e-06[/C][/ROW]
[ROW][C]10[/C][C]8[/C][C]8.10000000043696[/C][C]-0.100000000436955[/C][/ROW]
[ROW][C]11[/C][C]7.9[/C][C]8.00000661069616[/C][C]-0.100006610696164[/C][/ROW]
[ROW][C]12[/C][C]7.9[/C][C]7.90000661113315[/C][C]-6.61113314848194e-06[/C][/ROW]
[ROW][C]13[/C][C]8[/C][C]7.90000000043704[/C][C]0.0999999995629581[/C][/ROW]
[ROW][C]14[/C][C]8[/C][C]7.99999338930389[/C][C]6.61069610607967e-06[/C][/ROW]
[ROW][C]15[/C][C]7.9[/C][C]7.99999999956299[/C][C]-0.0999999995629866[/C][/ROW]
[ROW][C]16[/C][C]8[/C][C]7.90000661069611[/C][C]0.0999933893038936[/C][/ROW]
[ROW][C]17[/C][C]7.7[/C][C]7.99999338974088[/C][C]-0.299993389740878[/C][/ROW]
[ROW][C]18[/C][C]7.2[/C][C]7.70001983165142[/C][C]-0.500019831651421[/C][/ROW]
[ROW][C]19[/C][C]7.5[/C][C]7.20003305479169[/C][C]0.299966945208314[/C][/ROW]
[ROW][C]20[/C][C]7.3[/C][C]7.49998017009675[/C][C]-0.199980170096747[/C][/ROW]
[ROW][C]21[/C][C]7[/C][C]7.30001322008138[/C][C]-0.300013220081375[/C][/ROW]
[ROW][C]22[/C][C]7[/C][C]7.00001983296235[/C][C]-1.9832962345312e-05[/C][/ROW]
[ROW][C]23[/C][C]7[/C][C]7.0000000013111[/C][C]-1.31109700873822e-09[/C][/ROW]
[ROW][C]24[/C][C]7.2[/C][C]7.00000000000009[/C][C]0.199999999999913[/C][/ROW]
[ROW][C]25[/C][C]7.3[/C][C]7.19998677860773[/C][C]0.10001322139227[/C][/ROW]
[ROW][C]26[/C][C]7.1[/C][C]7.29999338842984[/C][C]-0.199993388429839[/C][/ROW]
[ROW][C]27[/C][C]6.8[/C][C]7.1000132209552[/C][C]-0.3000132209552[/C][/ROW]
[ROW][C]28[/C][C]6.4[/C][C]6.8000198329624[/C][C]-0.400019832962403[/C][/ROW]
[ROW][C]29[/C][C]6.1[/C][C]6.40002644409564[/C][C]-0.300026444095638[/C][/ROW]
[ROW][C]30[/C][C]6.5[/C][C]6.10001983383654[/C][C]0.399980166163456[/C][/ROW]
[ROW][C]31[/C][C]7.7[/C][C]6.49997355852661[/C][C]1.20002644147339[/C][/ROW]
[ROW][C]32[/C][C]7.9[/C][C]7.69992066989841[/C][C]0.200079330101588[/C][/ROW]
[ROW][C]33[/C][C]7.5[/C][C]7.89998677336346[/C][C]-0.399986773363458[/C][/ROW]
[ROW][C]34[/C][C]6.9[/C][C]7.50002644191017[/C][C]-0.600026441910168[/C][/ROW]
[ROW][C]35[/C][C]6.6[/C][C]6.90003966592481[/C][C]-0.300039665924806[/C][/ROW]
[ROW][C]36[/C][C]6.9[/C][C]6.6000198347106[/C][C]0.299980165289401[/C][/ROW]
[ROW][C]37[/C][C]7.7[/C][C]6.89998016922281[/C][C]0.800019830777193[/C][/ROW]
[ROW][C]38[/C][C]8[/C][C]7.69994711311997[/C][C]0.300052886880033[/C][/ROW]
[ROW][C]39[/C][C]8[/C][C]7.9999801644154[/C][C]1.98355845961729e-05[/C][/ROW]
[ROW][C]40[/C][C]7.7[/C][C]7.99999999868873[/C][C]-0.29999999868873[/C][/ROW]
[ROW][C]41[/C][C]7.3[/C][C]7.70001983208832[/C][C]-0.400019832088319[/C][/ROW]
[ROW][C]42[/C][C]7.4[/C][C]7.30002644409558[/C][C]0.0999735559044206[/C][/ROW]
[ROW][C]43[/C][C]8.1[/C][C]7.399993391052[/C][C]0.700006608947995[/C][/ROW]
[ROW][C]44[/C][C]8.3[/C][C]8.09995372469016[/C][C]0.200046275309845[/C][/ROW]
[ROW][C]45[/C][C]8.1[/C][C]8.29998677554861[/C][C]-0.199986775548611[/C][/ROW]
[ROW][C]46[/C][C]7.9[/C][C]8.10001322051804[/C][C]-0.200013220518041[/C][/ROW]
[ROW][C]47[/C][C]7.9[/C][C]7.90001322226624[/C][C]-1.32222662383441e-05[/C][/ROW]
[ROW][C]48[/C][C]8.3[/C][C]7.90000000087408[/C][C]0.399999999125916[/C][/ROW]
[ROW][C]49[/C][C]8.6[/C][C]8.29997355721552[/C][C]0.300026442784482[/C][/ROW]
[ROW][C]50[/C][C]8.7[/C][C]8.59998016616354[/C][C]0.100019833836457[/C][/ROW]
[ROW][C]51[/C][C]8.5[/C][C]8.69999338799271[/C][C]-0.199993387992709[/C][/ROW]
[ROW][C]52[/C][C]8.3[/C][C]8.50001322095517[/C][C]-0.200013220955171[/C][/ROW]
[ROW][C]53[/C][C]8[/C][C]8.30001322226627[/C][C]-0.300013222266267[/C][/ROW]
[ROW][C]54[/C][C]8[/C][C]8.00001983296249[/C][C]-1.9832962490085e-05[/C][/ROW]
[ROW][C]55[/C][C]8.8[/C][C]8.0000000013111[/C][C]0.799999998688904[/C][/ROW]
[ROW][C]56[/C][C]8.7[/C][C]8.79994711443101[/C][C]-0.0999471144310071[/C][/ROW]
[ROW][C]57[/C][C]8.5[/C][C]8.70000660720003[/C][C]-0.200006607200031[/C][/ROW]
[ROW][C]58[/C][C]8.1[/C][C]8.50001322182905[/C][C]-0.400013221829052[/C][/ROW]
[ROW][C]59[/C][C]7.8[/C][C]8.1000264436586[/C][C]-0.300026443658596[/C][/ROW]
[ROW][C]60[/C][C]7.7[/C][C]7.80001983383652[/C][C]-0.100019833836515[/C][/ROW]
[ROW][C]61[/C][C]7.5[/C][C]7.70000661200729[/C][C]-0.20000661200729[/C][/ROW]
[ROW][C]62[/C][C]7.2[/C][C]7.50001322182937[/C][C]-0.30001322182937[/C][/ROW]
[ROW][C]63[/C][C]6.9[/C][C]7.20001983296246[/C][C]-0.300019832962461[/C][/ROW]
[ROW][C]64[/C][C]6.6[/C][C]6.9000198333995[/C][C]-0.300019833399503[/C][/ROW]
[ROW][C]65[/C][C]6.5[/C][C]6.60001983339953[/C][C]-0.100019833399531[/C][/ROW]
[ROW][C]66[/C][C]6.6[/C][C]6.50000661200726[/C][C]0.0999933879927388[/C][/ROW]
[ROW][C]67[/C][C]7.7[/C][C]6.59999338974096[/C][C]1.10000661025904[/C][/ROW]
[ROW][C]68[/C][C]8[/C][C]7.69992728190553[/C][C]0.300072718094471[/C][/ROW]
[ROW][C]69[/C][C]7.7[/C][C]7.99998016310442[/C][C]-0.299980163104422[/C][/ROW]
[ROW][C]70[/C][C]7.2[/C][C]7.70001983077705[/C][C]-0.500019830777049[/C][/ROW]
[ROW][C]71[/C][C]7[/C][C]7.20003305479163[/C][C]-0.200033054791628[/C][/ROW]
[ROW][C]72[/C][C]7[/C][C]7.00001322357742[/C][C]-1.32235774223943e-05[/C][/ROW]
[ROW][C]73[/C][C]7.3[/C][C]7.00000000087417[/C][C]0.299999999125829[/C][/ROW]
[ROW][C]74[/C][C]7.3[/C][C]7.29998016791165[/C][C]1.98320883475489e-05[/C][/ROW]
[ROW][C]75[/C][C]7.1[/C][C]7.29999999868896[/C][C]-0.199999998688961[/C][/ROW]
[ROW][C]76[/C][C]6.9[/C][C]7.10001322139218[/C][C]-0.200013221392183[/C][/ROW]
[ROW][C]77[/C][C]6.7[/C][C]6.9000132222663[/C][C]-0.200013222266296[/C][/ROW]
[ROW][C]78[/C][C]6.8[/C][C]6.70001322226635[/C][C]0.0999867777336458[/C][/ROW]
[ROW][C]79[/C][C]7.5[/C][C]6.79999339017795[/C][C]0.700006609822052[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=204819&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=204819&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
28.78.70
38.68.7-0.0999999999999996
48.58.60000661069613-0.100006610696134
58.38.50000661113315-0.200006611133148
688.30001322182931-0.300013221829314
78.28.000019832962460.199980167037539
88.18.19998677991883-0.0999867799188259
98.18.1000066098222-6.60982219535811e-06
1088.10000000043696-0.100000000436955
117.98.00000661069616-0.100006610696164
127.97.90000661113315-6.61113314848194e-06
1387.900000000437040.0999999995629581
1487.999993389303896.61069610607967e-06
157.97.99999999956299-0.0999999995629866
1687.900006610696110.0999933893038936
177.77.99999338974088-0.299993389740878
187.27.70001983165142-0.500019831651421
197.57.200033054791690.299966945208314
207.37.49998017009675-0.199980170096747
2177.30001322008138-0.300013220081375
2277.00001983296235-1.9832962345312e-05
2377.0000000013111-1.31109700873822e-09
247.27.000000000000090.199999999999913
257.37.199986778607730.10001322139227
267.17.29999338842984-0.199993388429839
276.87.1000132209552-0.3000132209552
286.46.8000198329624-0.400019832962403
296.16.40002644409564-0.300026444095638
306.56.100019833836540.399980166163456
317.76.499973558526611.20002644147339
327.97.699920669898410.200079330101588
337.57.89998677336346-0.399986773363458
346.97.50002644191017-0.600026441910168
356.66.90003966592481-0.300039665924806
366.96.60001983471060.299980165289401
377.76.899980169222810.800019830777193
3887.699947113119970.300052886880033
3987.99998016441541.98355845961729e-05
407.77.99999999868873-0.29999999868873
417.37.70001983208832-0.400019832088319
427.47.300026444095580.0999735559044206
438.17.3999933910520.700006608947995
448.38.099953724690160.200046275309845
458.18.29998677554861-0.199986775548611
467.98.10001322051804-0.200013220518041
477.97.90001322226624-1.32222662383441e-05
488.37.900000000874080.399999999125916
498.68.299973557215520.300026442784482
508.78.599980166163540.100019833836457
518.58.69999338799271-0.199993387992709
528.38.50001322095517-0.200013220955171
5388.30001322226627-0.300013222266267
5488.00001983296249-1.9832962490085e-05
558.88.00000000131110.799999998688904
568.78.79994711443101-0.0999471144310071
578.58.70000660720003-0.200006607200031
588.18.50001322182905-0.400013221829052
597.88.1000264436586-0.300026443658596
607.77.80001983383652-0.100019833836515
617.57.70000661200729-0.20000661200729
627.27.50001322182937-0.30001322182937
636.97.20001983296246-0.300019832962461
646.66.9000198333995-0.300019833399503
656.56.60001983339953-0.100019833399531
666.66.500006612007260.0999933879927388
677.76.599993389740961.10000661025904
6887.699927281905530.300072718094471
697.77.99998016310442-0.299980163104422
707.27.70001983077705-0.500019830777049
7177.20003305479163-0.200033054791628
7277.00001322357742-1.32235774223943e-05
737.37.000000000874170.299999999125829
747.37.299980167911651.98320883475489e-05
757.17.29999999868896-0.199999998688961
766.97.10001322139218-0.200013221392183
776.76.9000132222663-0.200013222266296
786.86.700013222266350.0999867777336458
797.56.799993390177950.700006609822052







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
807.49995372469016.820195507945488.17971194143472
817.49995372469016.538662209990918.46124523938929
827.49995372469016.322629844343888.67727760503632
837.49995372469016.140504695769088.85940275361112
847.49995372469015.98004852855619.0198589208241
857.49995372469015.834984671453389.16492277792681
867.49995372469015.701584438020429.29832301135977
877.49995372469015.577418358503669.42248909087654
887.49995372469015.460798905349889.53910854403032
897.49995372469015.350497393372979.64941005600722
907.49995372469015.245586260579589.75432118880062
917.49995372469015.145344881115249.85456256826496

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
80 & 7.4999537246901 & 6.82019550794548 & 8.17971194143472 \tabularnewline
81 & 7.4999537246901 & 6.53866220999091 & 8.46124523938929 \tabularnewline
82 & 7.4999537246901 & 6.32262984434388 & 8.67727760503632 \tabularnewline
83 & 7.4999537246901 & 6.14050469576908 & 8.85940275361112 \tabularnewline
84 & 7.4999537246901 & 5.9800485285561 & 9.0198589208241 \tabularnewline
85 & 7.4999537246901 & 5.83498467145338 & 9.16492277792681 \tabularnewline
86 & 7.4999537246901 & 5.70158443802042 & 9.29832301135977 \tabularnewline
87 & 7.4999537246901 & 5.57741835850366 & 9.42248909087654 \tabularnewline
88 & 7.4999537246901 & 5.46079890534988 & 9.53910854403032 \tabularnewline
89 & 7.4999537246901 & 5.35049739337297 & 9.64941005600722 \tabularnewline
90 & 7.4999537246901 & 5.24558626057958 & 9.75432118880062 \tabularnewline
91 & 7.4999537246901 & 5.14534488111524 & 9.85456256826496 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=204819&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]80[/C][C]7.4999537246901[/C][C]6.82019550794548[/C][C]8.17971194143472[/C][/ROW]
[ROW][C]81[/C][C]7.4999537246901[/C][C]6.53866220999091[/C][C]8.46124523938929[/C][/ROW]
[ROW][C]82[/C][C]7.4999537246901[/C][C]6.32262984434388[/C][C]8.67727760503632[/C][/ROW]
[ROW][C]83[/C][C]7.4999537246901[/C][C]6.14050469576908[/C][C]8.85940275361112[/C][/ROW]
[ROW][C]84[/C][C]7.4999537246901[/C][C]5.9800485285561[/C][C]9.0198589208241[/C][/ROW]
[ROW][C]85[/C][C]7.4999537246901[/C][C]5.83498467145338[/C][C]9.16492277792681[/C][/ROW]
[ROW][C]86[/C][C]7.4999537246901[/C][C]5.70158443802042[/C][C]9.29832301135977[/C][/ROW]
[ROW][C]87[/C][C]7.4999537246901[/C][C]5.57741835850366[/C][C]9.42248909087654[/C][/ROW]
[ROW][C]88[/C][C]7.4999537246901[/C][C]5.46079890534988[/C][C]9.53910854403032[/C][/ROW]
[ROW][C]89[/C][C]7.4999537246901[/C][C]5.35049739337297[/C][C]9.64941005600722[/C][/ROW]
[ROW][C]90[/C][C]7.4999537246901[/C][C]5.24558626057958[/C][C]9.75432118880062[/C][/ROW]
[ROW][C]91[/C][C]7.4999537246901[/C][C]5.14534488111524[/C][C]9.85456256826496[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=204819&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=204819&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
807.49995372469016.820195507945488.17971194143472
817.49995372469016.538662209990918.46124523938929
827.49995372469016.322629844343888.67727760503632
837.49995372469016.140504695769088.85940275361112
847.49995372469015.98004852855619.0198589208241
857.49995372469015.834984671453389.16492277792681
867.49995372469015.701584438020429.29832301135977
877.49995372469015.577418358503669.42248909087654
887.49995372469015.460798905349889.53910854403032
897.49995372469015.350497393372979.64941005600722
907.49995372469015.245586260579589.75432118880062
917.49995372469015.145344881115249.85456256826496



Parameters (Session):
par1 = 12 ; par2 = Single ; par3 = additive ;
Parameters (R input):
par1 = 12 ; par2 = Single ; 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')