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Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationThu, 04 Jun 2009 13:19:24 -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/2009/Jun/04/t1244143184y6erz6doumgj2lh.htm/, Retrieved Tue, 14 May 2024 20:42:48 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=41738, Retrieved Tue, 14 May 2024 20:42:48 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact117
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [nen trippel veu d...] [2009-06-04 19:19:24] [d41d8cd98f00b204e9800998ecf8427e] [Current]
-   PD    [Exponential Smoothing] [nen dobbele voor ...] [2009-06-04 19:44:00] [74be16979710d4c4e7c6647856088456]
-   PD    [Exponential Smoothing] [Mattias Dierckx O...] [2009-06-04 19:44:00] [74be16979710d4c4e7c6647856088456]
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Dataseries X:
9.370
9.330
9.310
9.260
9.350
9.380
9.430
9.270
9.290
9.270
9.290
9.310
9.330
9.350
9.340
9.470
9.630
9.620
9.630
9.500
9.550
9.580
9.610
9.570
9.610
9.650
9.620
9.650
9.960
10.030
10.030
9.720
9.750
9.770
9.780
9.820
9.840
9.900
9.940
10.120
10.520
10.570
10.570
10.120
10.050
10.140
10.170
10.200
10.200
10.350
10.430
10.570
10.820
10.900
10.830
10.650
10.570
10.610
10.630
10.710
10.720
10.770
10.790
10.920
10.900
11.000
10.990
10.910
10.880
10.870
11.000
10.990
11.030
11.040
10.990




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time1 seconds
R Server'George Udny Yule' @ 72.249.76.132

\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 & 'George Udny Yule' @ 72.249.76.132 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=41738&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]'George Udny Yule' @ 72.249.76.132[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=41738&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=41738&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'George Udny Yule' @ 72.249.76.132







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha1
beta0.00102339612864802
gamma0.434544625204061

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 1 \tabularnewline
beta & 0.00102339612864802 \tabularnewline
gamma & 0.434544625204061 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=41738&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]1[/C][/ROW]
[ROW][C]beta[/C][C]0.00102339612864802[/C][/ROW]
[ROW][C]gamma[/C][C]0.434544625204061[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=41738&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=41738&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
alpha1
beta0.00102339612864802
gamma0.434544625204061







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
139.339.238151709401710.0918482905982856
149.359.34996287830393.71216960992626e-05
159.349.33746291629410.00253708370589933
169.479.46413217940240.00586782059758839
179.639.62163818450730.00836181549270698
189.629.613730075290230.00626992470976795
199.639.63206982524024-0.00206982524023935
209.59.488734373655770.0112656263442297
219.559.535829236187490.0141707638125137
229.589.537927071825650.0420729281743508
239.619.59755346243080.0124465375692004
249.579.62631620016916-0.0563162001691584
259.619.589591899721260.0204081002787362
269.659.630029451958740.0199705480412575
279.629.6375498897403-0.0175498897402981
289.659.74419859591775-0.0941985959177458
299.969.801602193439360.158397806560641
3010.039.943847630474710.086152369525287
3110.0310.0422691318095-0.0122691318094930
329.729.88892324229416-0.168923242294163
339.759.7558337002353-0.00583370023529284
349.779.737911063382390.0320889366176083
359.789.78752723640923-0.00752723640923314
369.829.796269533064630.0237304669353708
379.849.839627152065960.000372847934039910
389.99.860044200303750.0399557996962461
399.949.887585090914480.0524149090855186
4010.1210.06430539879620.0556946012038093
4110.5210.27186239643540.248137603564553
4210.5710.50419967283160.0658003271683594
4310.5710.5826003459651-0.0126003459650637
4410.1210.4292541174865-0.309254117486452
4510.0510.1560209613532-0.106020961353176
4610.1410.03799579324510.102004206754891
4710.1710.15768351728870.0123164827112578
4810.210.18644612192950.0135538780705353
4910.210.2197933262491-0.0197933262491468
5010.3510.22018973650240.129810263497648
5110.4310.33782258382350.0921774161765239
5210.5710.55458358450100.0154164154989918
5310.8210.72209936160090.0979006383990537
5410.910.80428288606860.095717113931391
5510.8310.9127141759258-0.0827141759257852
5610.6510.6892961932250-0.0392961932250255
5710.5710.6863393109863-0.116339310986339
5810.6110.55830358311920.0516964168807963
5910.6310.62793982236540.00206017763456323
6010.7110.64669193074330.0633080692567489
6110.7210.7300900533096-0.0100900533095771
6210.7710.74049639385470.0295036061452549
6310.7910.75802658773110.0319734122689432
6410.9210.91472597586410.00527402413594125
6510.911.0722313732799-0.172231373279940
661110.88413844569260.115861554307372
6710.9911.0125903512921-0.0225903512920986
6810.9110.84923389908070.0607661009192899
6910.8810.9463794202065-0.0663794202064736
7010.8710.86839482109810.00160517890184941
711110.88797979716540.112020202834643
7210.9911.0168444382073-0.0268444382072666
7311.0311.01015029904650.0198497009535341
7411.0411.0505872798202-0.0105872798202391
7510.9911.0280764448391-0.0380764448390583

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 9.33 & 9.23815170940171 & 0.0918482905982856 \tabularnewline
14 & 9.35 & 9.3499628783039 & 3.71216960992626e-05 \tabularnewline
15 & 9.34 & 9.3374629162941 & 0.00253708370589933 \tabularnewline
16 & 9.47 & 9.4641321794024 & 0.00586782059758839 \tabularnewline
17 & 9.63 & 9.6216381845073 & 0.00836181549270698 \tabularnewline
18 & 9.62 & 9.61373007529023 & 0.00626992470976795 \tabularnewline
19 & 9.63 & 9.63206982524024 & -0.00206982524023935 \tabularnewline
20 & 9.5 & 9.48873437365577 & 0.0112656263442297 \tabularnewline
21 & 9.55 & 9.53582923618749 & 0.0141707638125137 \tabularnewline
22 & 9.58 & 9.53792707182565 & 0.0420729281743508 \tabularnewline
23 & 9.61 & 9.5975534624308 & 0.0124465375692004 \tabularnewline
24 & 9.57 & 9.62631620016916 & -0.0563162001691584 \tabularnewline
25 & 9.61 & 9.58959189972126 & 0.0204081002787362 \tabularnewline
26 & 9.65 & 9.63002945195874 & 0.0199705480412575 \tabularnewline
27 & 9.62 & 9.6375498897403 & -0.0175498897402981 \tabularnewline
28 & 9.65 & 9.74419859591775 & -0.0941985959177458 \tabularnewline
29 & 9.96 & 9.80160219343936 & 0.158397806560641 \tabularnewline
30 & 10.03 & 9.94384763047471 & 0.086152369525287 \tabularnewline
31 & 10.03 & 10.0422691318095 & -0.0122691318094930 \tabularnewline
32 & 9.72 & 9.88892324229416 & -0.168923242294163 \tabularnewline
33 & 9.75 & 9.7558337002353 & -0.00583370023529284 \tabularnewline
34 & 9.77 & 9.73791106338239 & 0.0320889366176083 \tabularnewline
35 & 9.78 & 9.78752723640923 & -0.00752723640923314 \tabularnewline
36 & 9.82 & 9.79626953306463 & 0.0237304669353708 \tabularnewline
37 & 9.84 & 9.83962715206596 & 0.000372847934039910 \tabularnewline
38 & 9.9 & 9.86004420030375 & 0.0399557996962461 \tabularnewline
39 & 9.94 & 9.88758509091448 & 0.0524149090855186 \tabularnewline
40 & 10.12 & 10.0643053987962 & 0.0556946012038093 \tabularnewline
41 & 10.52 & 10.2718623964354 & 0.248137603564553 \tabularnewline
42 & 10.57 & 10.5041996728316 & 0.0658003271683594 \tabularnewline
43 & 10.57 & 10.5826003459651 & -0.0126003459650637 \tabularnewline
44 & 10.12 & 10.4292541174865 & -0.309254117486452 \tabularnewline
45 & 10.05 & 10.1560209613532 & -0.106020961353176 \tabularnewline
46 & 10.14 & 10.0379957932451 & 0.102004206754891 \tabularnewline
47 & 10.17 & 10.1576835172887 & 0.0123164827112578 \tabularnewline
48 & 10.2 & 10.1864461219295 & 0.0135538780705353 \tabularnewline
49 & 10.2 & 10.2197933262491 & -0.0197933262491468 \tabularnewline
50 & 10.35 & 10.2201897365024 & 0.129810263497648 \tabularnewline
51 & 10.43 & 10.3378225838235 & 0.0921774161765239 \tabularnewline
52 & 10.57 & 10.5545835845010 & 0.0154164154989918 \tabularnewline
53 & 10.82 & 10.7220993616009 & 0.0979006383990537 \tabularnewline
54 & 10.9 & 10.8042828860686 & 0.095717113931391 \tabularnewline
55 & 10.83 & 10.9127141759258 & -0.0827141759257852 \tabularnewline
56 & 10.65 & 10.6892961932250 & -0.0392961932250255 \tabularnewline
57 & 10.57 & 10.6863393109863 & -0.116339310986339 \tabularnewline
58 & 10.61 & 10.5583035831192 & 0.0516964168807963 \tabularnewline
59 & 10.63 & 10.6279398223654 & 0.00206017763456323 \tabularnewline
60 & 10.71 & 10.6466919307433 & 0.0633080692567489 \tabularnewline
61 & 10.72 & 10.7300900533096 & -0.0100900533095771 \tabularnewline
62 & 10.77 & 10.7404963938547 & 0.0295036061452549 \tabularnewline
63 & 10.79 & 10.7580265877311 & 0.0319734122689432 \tabularnewline
64 & 10.92 & 10.9147259758641 & 0.00527402413594125 \tabularnewline
65 & 10.9 & 11.0722313732799 & -0.172231373279940 \tabularnewline
66 & 11 & 10.8841384456926 & 0.115861554307372 \tabularnewline
67 & 10.99 & 11.0125903512921 & -0.0225903512920986 \tabularnewline
68 & 10.91 & 10.8492338990807 & 0.0607661009192899 \tabularnewline
69 & 10.88 & 10.9463794202065 & -0.0663794202064736 \tabularnewline
70 & 10.87 & 10.8683948210981 & 0.00160517890184941 \tabularnewline
71 & 11 & 10.8879797971654 & 0.112020202834643 \tabularnewline
72 & 10.99 & 11.0168444382073 & -0.0268444382072666 \tabularnewline
73 & 11.03 & 11.0101502990465 & 0.0198497009535341 \tabularnewline
74 & 11.04 & 11.0505872798202 & -0.0105872798202391 \tabularnewline
75 & 10.99 & 11.0280764448391 & -0.0380764448390583 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=41738&T=2

[TABLE]
[ROW][C]Interpolation Forecasts of Exponential Smoothing[/C][/ROW]
[ROW][C]t[/C][C]Observed[/C][C]Fitted[/C][C]Residuals[/C][/ROW]
[ROW][C]13[/C][C]9.33[/C][C]9.23815170940171[/C][C]0.0918482905982856[/C][/ROW]
[ROW][C]14[/C][C]9.35[/C][C]9.3499628783039[/C][C]3.71216960992626e-05[/C][/ROW]
[ROW][C]15[/C][C]9.34[/C][C]9.3374629162941[/C][C]0.00253708370589933[/C][/ROW]
[ROW][C]16[/C][C]9.47[/C][C]9.4641321794024[/C][C]0.00586782059758839[/C][/ROW]
[ROW][C]17[/C][C]9.63[/C][C]9.6216381845073[/C][C]0.00836181549270698[/C][/ROW]
[ROW][C]18[/C][C]9.62[/C][C]9.61373007529023[/C][C]0.00626992470976795[/C][/ROW]
[ROW][C]19[/C][C]9.63[/C][C]9.63206982524024[/C][C]-0.00206982524023935[/C][/ROW]
[ROW][C]20[/C][C]9.5[/C][C]9.48873437365577[/C][C]0.0112656263442297[/C][/ROW]
[ROW][C]21[/C][C]9.55[/C][C]9.53582923618749[/C][C]0.0141707638125137[/C][/ROW]
[ROW][C]22[/C][C]9.58[/C][C]9.53792707182565[/C][C]0.0420729281743508[/C][/ROW]
[ROW][C]23[/C][C]9.61[/C][C]9.5975534624308[/C][C]0.0124465375692004[/C][/ROW]
[ROW][C]24[/C][C]9.57[/C][C]9.62631620016916[/C][C]-0.0563162001691584[/C][/ROW]
[ROW][C]25[/C][C]9.61[/C][C]9.58959189972126[/C][C]0.0204081002787362[/C][/ROW]
[ROW][C]26[/C][C]9.65[/C][C]9.63002945195874[/C][C]0.0199705480412575[/C][/ROW]
[ROW][C]27[/C][C]9.62[/C][C]9.6375498897403[/C][C]-0.0175498897402981[/C][/ROW]
[ROW][C]28[/C][C]9.65[/C][C]9.74419859591775[/C][C]-0.0941985959177458[/C][/ROW]
[ROW][C]29[/C][C]9.96[/C][C]9.80160219343936[/C][C]0.158397806560641[/C][/ROW]
[ROW][C]30[/C][C]10.03[/C][C]9.94384763047471[/C][C]0.086152369525287[/C][/ROW]
[ROW][C]31[/C][C]10.03[/C][C]10.0422691318095[/C][C]-0.0122691318094930[/C][/ROW]
[ROW][C]32[/C][C]9.72[/C][C]9.88892324229416[/C][C]-0.168923242294163[/C][/ROW]
[ROW][C]33[/C][C]9.75[/C][C]9.7558337002353[/C][C]-0.00583370023529284[/C][/ROW]
[ROW][C]34[/C][C]9.77[/C][C]9.73791106338239[/C][C]0.0320889366176083[/C][/ROW]
[ROW][C]35[/C][C]9.78[/C][C]9.78752723640923[/C][C]-0.00752723640923314[/C][/ROW]
[ROW][C]36[/C][C]9.82[/C][C]9.79626953306463[/C][C]0.0237304669353708[/C][/ROW]
[ROW][C]37[/C][C]9.84[/C][C]9.83962715206596[/C][C]0.000372847934039910[/C][/ROW]
[ROW][C]38[/C][C]9.9[/C][C]9.86004420030375[/C][C]0.0399557996962461[/C][/ROW]
[ROW][C]39[/C][C]9.94[/C][C]9.88758509091448[/C][C]0.0524149090855186[/C][/ROW]
[ROW][C]40[/C][C]10.12[/C][C]10.0643053987962[/C][C]0.0556946012038093[/C][/ROW]
[ROW][C]41[/C][C]10.52[/C][C]10.2718623964354[/C][C]0.248137603564553[/C][/ROW]
[ROW][C]42[/C][C]10.57[/C][C]10.5041996728316[/C][C]0.0658003271683594[/C][/ROW]
[ROW][C]43[/C][C]10.57[/C][C]10.5826003459651[/C][C]-0.0126003459650637[/C][/ROW]
[ROW][C]44[/C][C]10.12[/C][C]10.4292541174865[/C][C]-0.309254117486452[/C][/ROW]
[ROW][C]45[/C][C]10.05[/C][C]10.1560209613532[/C][C]-0.106020961353176[/C][/ROW]
[ROW][C]46[/C][C]10.14[/C][C]10.0379957932451[/C][C]0.102004206754891[/C][/ROW]
[ROW][C]47[/C][C]10.17[/C][C]10.1576835172887[/C][C]0.0123164827112578[/C][/ROW]
[ROW][C]48[/C][C]10.2[/C][C]10.1864461219295[/C][C]0.0135538780705353[/C][/ROW]
[ROW][C]49[/C][C]10.2[/C][C]10.2197933262491[/C][C]-0.0197933262491468[/C][/ROW]
[ROW][C]50[/C][C]10.35[/C][C]10.2201897365024[/C][C]0.129810263497648[/C][/ROW]
[ROW][C]51[/C][C]10.43[/C][C]10.3378225838235[/C][C]0.0921774161765239[/C][/ROW]
[ROW][C]52[/C][C]10.57[/C][C]10.5545835845010[/C][C]0.0154164154989918[/C][/ROW]
[ROW][C]53[/C][C]10.82[/C][C]10.7220993616009[/C][C]0.0979006383990537[/C][/ROW]
[ROW][C]54[/C][C]10.9[/C][C]10.8042828860686[/C][C]0.095717113931391[/C][/ROW]
[ROW][C]55[/C][C]10.83[/C][C]10.9127141759258[/C][C]-0.0827141759257852[/C][/ROW]
[ROW][C]56[/C][C]10.65[/C][C]10.6892961932250[/C][C]-0.0392961932250255[/C][/ROW]
[ROW][C]57[/C][C]10.57[/C][C]10.6863393109863[/C][C]-0.116339310986339[/C][/ROW]
[ROW][C]58[/C][C]10.61[/C][C]10.5583035831192[/C][C]0.0516964168807963[/C][/ROW]
[ROW][C]59[/C][C]10.63[/C][C]10.6279398223654[/C][C]0.00206017763456323[/C][/ROW]
[ROW][C]60[/C][C]10.71[/C][C]10.6466919307433[/C][C]0.0633080692567489[/C][/ROW]
[ROW][C]61[/C][C]10.72[/C][C]10.7300900533096[/C][C]-0.0100900533095771[/C][/ROW]
[ROW][C]62[/C][C]10.77[/C][C]10.7404963938547[/C][C]0.0295036061452549[/C][/ROW]
[ROW][C]63[/C][C]10.79[/C][C]10.7580265877311[/C][C]0.0319734122689432[/C][/ROW]
[ROW][C]64[/C][C]10.92[/C][C]10.9147259758641[/C][C]0.00527402413594125[/C][/ROW]
[ROW][C]65[/C][C]10.9[/C][C]11.0722313732799[/C][C]-0.172231373279940[/C][/ROW]
[ROW][C]66[/C][C]11[/C][C]10.8841384456926[/C][C]0.115861554307372[/C][/ROW]
[ROW][C]67[/C][C]10.99[/C][C]11.0125903512921[/C][C]-0.0225903512920986[/C][/ROW]
[ROW][C]68[/C][C]10.91[/C][C]10.8492338990807[/C][C]0.0607661009192899[/C][/ROW]
[ROW][C]69[/C][C]10.88[/C][C]10.9463794202065[/C][C]-0.0663794202064736[/C][/ROW]
[ROW][C]70[/C][C]10.87[/C][C]10.8683948210981[/C][C]0.00160517890184941[/C][/ROW]
[ROW][C]71[/C][C]11[/C][C]10.8879797971654[/C][C]0.112020202834643[/C][/ROW]
[ROW][C]72[/C][C]10.99[/C][C]11.0168444382073[/C][C]-0.0268444382072666[/C][/ROW]
[ROW][C]73[/C][C]11.03[/C][C]11.0101502990465[/C][C]0.0198497009535341[/C][/ROW]
[ROW][C]74[/C][C]11.04[/C][C]11.0505872798202[/C][C]-0.0105872798202391[/C][/ROW]
[ROW][C]75[/C][C]10.99[/C][C]11.0280764448391[/C][C]-0.0380764448390583[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=41738&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=41738&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
139.339.238151709401710.0918482905982856
149.359.34996287830393.71216960992626e-05
159.349.33746291629410.00253708370589933
169.479.46413217940240.00586782059758839
179.639.62163818450730.00836181549270698
189.629.613730075290230.00626992470976795
199.639.63206982524024-0.00206982524023935
209.59.488734373655770.0112656263442297
219.559.535829236187490.0141707638125137
229.589.537927071825650.0420729281743508
239.619.59755346243080.0124465375692004
249.579.62631620016916-0.0563162001691584
259.619.589591899721260.0204081002787362
269.659.630029451958740.0199705480412575
279.629.6375498897403-0.0175498897402981
289.659.74419859591775-0.0941985959177458
299.969.801602193439360.158397806560641
3010.039.943847630474710.086152369525287
3110.0310.0422691318095-0.0122691318094930
329.729.88892324229416-0.168923242294163
339.759.7558337002353-0.00583370023529284
349.779.737911063382390.0320889366176083
359.789.78752723640923-0.00752723640923314
369.829.796269533064630.0237304669353708
379.849.839627152065960.000372847934039910
389.99.860044200303750.0399557996962461
399.949.887585090914480.0524149090855186
4010.1210.06430539879620.0556946012038093
4110.5210.27186239643540.248137603564553
4210.5710.50419967283160.0658003271683594
4310.5710.5826003459651-0.0126003459650637
4410.1210.4292541174865-0.309254117486452
4510.0510.1560209613532-0.106020961353176
4610.1410.03799579324510.102004206754891
4710.1710.15768351728870.0123164827112578
4810.210.18644612192950.0135538780705353
4910.210.2197933262491-0.0197933262491468
5010.3510.22018973650240.129810263497648
5110.4310.33782258382350.0921774161765239
5210.5710.55458358450100.0154164154989918
5310.8210.72209936160090.0979006383990537
5410.910.80428288606860.095717113931391
5510.8310.9127141759258-0.0827141759257852
5610.6510.6892961932250-0.0392961932250255
5710.5710.6863393109863-0.116339310986339
5810.6110.55830358311920.0516964168807963
5910.6310.62793982236540.00206017763456323
6010.7110.64669193074330.0633080692567489
6110.7210.7300900533096-0.0100900533095771
6210.7710.74049639385470.0295036061452549
6310.7910.75802658773110.0319734122689432
6410.9210.91472597586410.00527402413594125
6510.911.0722313732799-0.172231373279940
661110.88413844569260.115861554307372
6710.9911.0125903512921-0.0225903512920986
6810.9110.84923389908070.0607661009192899
6910.8810.9463794202065-0.0663794202064736
7010.8710.86839482109810.00160517890184941
711110.88797979716540.112020202834643
7210.9911.0168444382073-0.0268444382072666
7311.0311.01015029904650.0198497009535341
7411.0411.0505872798202-0.0105872798202391
7510.9911.0280764448391-0.0380764448390583







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
7611.114704144219510.954637954713811.2747703337251
7711.266908288439011.040424650789511.4933919260884
7811.251195765991810.973669167323511.5287223646600
7911.263816576877910.943192555277311.5844405984785
8011.123104054430810.764452214106411.4817558947551
8111.159474865316910.766390644495711.5525590861381
8211.147929009536410.72313258397811.5727254350948
8311.165966487089210.711608047350311.6203249268281
8411.182753964642010.70058799310211.6649199361821
8511.202874775528210.694367790440611.7113817606158
8611.22341225308110.689813494887911.7570110112741
8711.211449730633810.653839723221411.7690597380463

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
76 & 11.1147041442195 & 10.9546379547138 & 11.2747703337251 \tabularnewline
77 & 11.2669082884390 & 11.0404246507895 & 11.4933919260884 \tabularnewline
78 & 11.2511957659918 & 10.9736691673235 & 11.5287223646600 \tabularnewline
79 & 11.2638165768779 & 10.9431925552773 & 11.5844405984785 \tabularnewline
80 & 11.1231040544308 & 10.7644522141064 & 11.4817558947551 \tabularnewline
81 & 11.1594748653169 & 10.7663906444957 & 11.5525590861381 \tabularnewline
82 & 11.1479290095364 & 10.723132583978 & 11.5727254350948 \tabularnewline
83 & 11.1659664870892 & 10.7116080473503 & 11.6203249268281 \tabularnewline
84 & 11.1827539646420 & 10.700587993102 & 11.6649199361821 \tabularnewline
85 & 11.2028747755282 & 10.6943677904406 & 11.7113817606158 \tabularnewline
86 & 11.223412253081 & 10.6898134948879 & 11.7570110112741 \tabularnewline
87 & 11.2114497306338 & 10.6538397232214 & 11.7690597380463 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=41738&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]76[/C][C]11.1147041442195[/C][C]10.9546379547138[/C][C]11.2747703337251[/C][/ROW]
[ROW][C]77[/C][C]11.2669082884390[/C][C]11.0404246507895[/C][C]11.4933919260884[/C][/ROW]
[ROW][C]78[/C][C]11.2511957659918[/C][C]10.9736691673235[/C][C]11.5287223646600[/C][/ROW]
[ROW][C]79[/C][C]11.2638165768779[/C][C]10.9431925552773[/C][C]11.5844405984785[/C][/ROW]
[ROW][C]80[/C][C]11.1231040544308[/C][C]10.7644522141064[/C][C]11.4817558947551[/C][/ROW]
[ROW][C]81[/C][C]11.1594748653169[/C][C]10.7663906444957[/C][C]11.5525590861381[/C][/ROW]
[ROW][C]82[/C][C]11.1479290095364[/C][C]10.723132583978[/C][C]11.5727254350948[/C][/ROW]
[ROW][C]83[/C][C]11.1659664870892[/C][C]10.7116080473503[/C][C]11.6203249268281[/C][/ROW]
[ROW][C]84[/C][C]11.1827539646420[/C][C]10.700587993102[/C][C]11.6649199361821[/C][/ROW]
[ROW][C]85[/C][C]11.2028747755282[/C][C]10.6943677904406[/C][C]11.7113817606158[/C][/ROW]
[ROW][C]86[/C][C]11.223412253081[/C][C]10.6898134948879[/C][C]11.7570110112741[/C][/ROW]
[ROW][C]87[/C][C]11.2114497306338[/C][C]10.6538397232214[/C][C]11.7690597380463[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=41738&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=41738&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
7611.114704144219510.954637954713811.2747703337251
7711.266908288439011.040424650789511.4933919260884
7811.251195765991810.973669167323511.5287223646600
7911.263816576877910.943192555277311.5844405984785
8011.123104054430810.764452214106411.4817558947551
8111.159474865316910.766390644495711.5525590861381
8211.147929009536410.72313258397811.5727254350948
8311.165966487089210.711608047350311.6203249268281
8411.182753964642010.70058799310211.6649199361821
8511.202874775528210.694367790440611.7113817606158
8611.22341225308110.689813494887911.7570110112741
8711.211449730633810.653839723221411.7690597380463



Parameters (Session):
par1 = 12 ; par2 = Triple ; par3 = additive ;
Parameters (R input):
par1 = 12 ; par2 = Triple ; par3 = additive ;
R code (references can be found in the software module):
par1 <- as.numeric(par1)
if (par2 == 'Single') K <- 1
if (par2 == 'Double') K <- 2
if (par2 == 'Triple') K <- par1
nx <- length(x)
nxmK <- nx - K
x <- ts(x, frequency = par1)
if (par2 == 'Single') fit <- HoltWinters(x, gamma=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')