FreeStatistics.org

Free Statistics

of Irreproducible Research!

Description of Statistical Computation

Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationSun, 15 Jan 2012 06:50:32 -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/Jan/15/t1326628324dgyzqi4umywmuoh.htm/, Retrieved Fri, 03 May 2024 05:31:59 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=161069, Retrieved Fri, 03 May 2024 05:31:59 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywordsKDGP2W102
Estimated Impact111

Tree of Dependent Computations

Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [] [2012-01-15 11:50:32] [f824ea295e177f9d3dd7528a75f4b680] [Current]
Feedback Forum

Post a new message

Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
8,29
8,27
8,27
8,43
8,46
8,48
8,46
8,46
8,43
8,4
8,38
8,3
8,39
8,53
8,52
8,54
8,62
8,52
8,49
8,44
8,31
8,26
8,21
8,03
7,89
7,83
7,85
7,84
7,88
8,01
8,08
8,11
8,11
8,07
8,06
7,95
7,95
8,07
8,17
8,21
8,2
8,19
8,18
8,16
8,17
8,17
8,19
8,01
8,04
8,13
8,14
8,17
8,25
8,27
8,27
8,26
8,24
8,21
8,25
8,06
8,16
8,32
8,43
8,39
8,41
8,45
8,43
8,52
8,52
8,51
8,56
8,36
8,4
8,44
8,5
8,31
8,38
8,45
8,42
8,46
8,45
8,32
8,4
8,18

Tables (Output of Computation)





Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time3 seconds
R Server'AstonUniversity' @ aston.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 & 3 seconds \tabularnewline
R Server & 'AstonUniversity' @ aston.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=161069&T=0

[TABLE]
[ROW][C]Summary of computational transaction[/C][/ROW]
[ROW][C]Raw Input[/C][C]view raw input (R code) [/C][/ROW]
[ROW][C]Raw Output[/C][C]view raw output of R engine [/C][/ROW]
[ROW][C]Computing time[/C][C]3 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'AstonUniversity' @ aston.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=161069&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=161069&T=0

As an alternative you can also use a QR Code:  
QR Code


The GUIDs for individual cells are displayed in the table below:

Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time3 seconds
R Server'AstonUniversity' @ aston.wessa.net






Estimated Parameters of Exponential Smoothing
ParameterValue
alpha1
beta0.0171685510677451
gammaFALSE

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 1 \tabularnewline
beta & 0.0171685510677451 \tabularnewline
gamma & FALSE \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=161069&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]0.0171685510677451[/C][/ROW]
[ROW][C]gamma[/C][C]FALSE[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=161069&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=161069&T=1

As an alternative you can also use a QR Code:  
QR Code


The GUIDs for individual cells are displayed in the table below:

Estimated Parameters of Exponential Smoothing
ParameterValue
alpha1
beta0.0171685510677451
gammaFALSE






Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
38.278.250.0199999999999996
48.438.250343371021350.179656628978645
58.468.413427815030630.0465721849693672
68.488.444227391966620.0357726080333816
78.468.46484155581446-0.00484155581446366
88.468.444758433316220.015241566683784
98.438.44502010893218-0.0150201089321804
108.48.41476223542493-0.0147622354249339
118.388.38450878923217-0.00450878923216713
128.38.36443137985398-0.064431379853982
138.398.28332518641860.106674813581407
148.538.37515663840320.154843361596791
158.528.517815074564280.00218492543571713
168.548.50785258656820.0321474134317938
178.628.52840451107740.0915954889225947
188.528.60997707290655-0.0899770729065477
198.498.50843229693542-0.0184322969354245
208.448.4781158411042-0.0381158411041955
218.318.4274614473397-0.117461447339705
228.268.29544480448256-0.0354448044825642
238.218.24483626854672-0.0348362685467176
248.038.19423818029117-0.164238180291166
257.898.01141844870556-0.121418448705561
267.837.8693338698684-0.0393338698683934
277.857.808658564314870.0413414356851334
287.847.829368336864640.0106316631353591
297.887.819550867116120.0604491328838845
308.017.860588691141030.149411308858967
318.087.993153866827280.086846133172723
328.118.064644889099690.0453551109003101
338.118.095423570637360.014576429362636
348.078.09567382680926-0.0256738268092604
358.068.055233044402580.00476695559741813
367.958.0453148861232-0.0953148861231954
377.957.933678467633270.0163215323667281
388.077.933958684695210.136041315304785
398.178.056294316964350.113705683035652
408.218.158246478790240.0517535212097631
418.28.199135011762070.000864988237934128
428.198.18914986235680.000850137643199744
438.188.179164457988340.00083554201165903
448.168.16917880303404-0.00917880303403784
458.178.14902121628540.0209787837145932
468.178.159381391604950.010618608395049
478.198.159563697725450.0304363022745502
488.018.18008624493536-0.170086244935362
498.047.997166110553270.0428338894467304
508.138.027901506371660.102098493628336
518.148.119654389573460.0203456104265367
528.178.130003694225080.039996305774924
538.258.16069037284330.0893096271567053
548.278.242223689737970.0277763102620252
558.278.262700568739180.007299431260817
568.268.26282588939755-0.00282588939754902
578.248.25277737297112-0.0127773729711151
588.218.23255800399075-0.0225580039907491
598.258.202170715747250.0478292842527512
608.068.24299187525648-0.182991875256475
618.168.049850169901150.110149830098848
628.328.151741282884310.168258717115693
638.438.31463004126170.115369958738299
648.398.42661077628998-0.036610776289983
658.418.385982222307620.0240177776923804
668.458.406394572750460.0436054272495348
678.438.44714321475503-0.0171432147550288
688.528.426848890597040.0931511094029585
698.528.518448160175840.00155183982415608
708.518.51847480301711-0.00847480301711379
718.568.508329302928730.051670697071275
728.368.5592164139301-0.199216413930101
738.48.3557961567540.0442038432459935
748.448.396555072694170.043444927305833
758.58.437300959147250.062699040852749
768.318.49837741083203-0.188377410832031
778.388.305143243634150.0748567563658487
788.458.376428425678580.0735715743214147
798.428.44769154300946-0.0276915430094551
808.468.417216119339150.0427838806608474
818.458.45795065657916-0.0079506565791565
828.328.44781415532565-0.127814155325654
838.48.315619771472760.0843802285272357
848.188.39706845773534-0.217068457735342

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
3 & 8.27 & 8.25 & 0.0199999999999996 \tabularnewline
4 & 8.43 & 8.25034337102135 & 0.179656628978645 \tabularnewline
5 & 8.46 & 8.41342781503063 & 0.0465721849693672 \tabularnewline
6 & 8.48 & 8.44422739196662 & 0.0357726080333816 \tabularnewline
7 & 8.46 & 8.46484155581446 & -0.00484155581446366 \tabularnewline
8 & 8.46 & 8.44475843331622 & 0.015241566683784 \tabularnewline
9 & 8.43 & 8.44502010893218 & -0.0150201089321804 \tabularnewline
10 & 8.4 & 8.41476223542493 & -0.0147622354249339 \tabularnewline
11 & 8.38 & 8.38450878923217 & -0.00450878923216713 \tabularnewline
12 & 8.3 & 8.36443137985398 & -0.064431379853982 \tabularnewline
13 & 8.39 & 8.2833251864186 & 0.106674813581407 \tabularnewline
14 & 8.53 & 8.3751566384032 & 0.154843361596791 \tabularnewline
15 & 8.52 & 8.51781507456428 & 0.00218492543571713 \tabularnewline
16 & 8.54 & 8.5078525865682 & 0.0321474134317938 \tabularnewline
17 & 8.62 & 8.5284045110774 & 0.0915954889225947 \tabularnewline
18 & 8.52 & 8.60997707290655 & -0.0899770729065477 \tabularnewline
19 & 8.49 & 8.50843229693542 & -0.0184322969354245 \tabularnewline
20 & 8.44 & 8.4781158411042 & -0.0381158411041955 \tabularnewline
21 & 8.31 & 8.4274614473397 & -0.117461447339705 \tabularnewline
22 & 8.26 & 8.29544480448256 & -0.0354448044825642 \tabularnewline
23 & 8.21 & 8.24483626854672 & -0.0348362685467176 \tabularnewline
24 & 8.03 & 8.19423818029117 & -0.164238180291166 \tabularnewline
25 & 7.89 & 8.01141844870556 & -0.121418448705561 \tabularnewline
26 & 7.83 & 7.8693338698684 & -0.0393338698683934 \tabularnewline
27 & 7.85 & 7.80865856431487 & 0.0413414356851334 \tabularnewline
28 & 7.84 & 7.82936833686464 & 0.0106316631353591 \tabularnewline
29 & 7.88 & 7.81955086711612 & 0.0604491328838845 \tabularnewline
30 & 8.01 & 7.86058869114103 & 0.149411308858967 \tabularnewline
31 & 8.08 & 7.99315386682728 & 0.086846133172723 \tabularnewline
32 & 8.11 & 8.06464488909969 & 0.0453551109003101 \tabularnewline
33 & 8.11 & 8.09542357063736 & 0.014576429362636 \tabularnewline
34 & 8.07 & 8.09567382680926 & -0.0256738268092604 \tabularnewline
35 & 8.06 & 8.05523304440258 & 0.00476695559741813 \tabularnewline
36 & 7.95 & 8.0453148861232 & -0.0953148861231954 \tabularnewline
37 & 7.95 & 7.93367846763327 & 0.0163215323667281 \tabularnewline
38 & 8.07 & 7.93395868469521 & 0.136041315304785 \tabularnewline
39 & 8.17 & 8.05629431696435 & 0.113705683035652 \tabularnewline
40 & 8.21 & 8.15824647879024 & 0.0517535212097631 \tabularnewline
41 & 8.2 & 8.19913501176207 & 0.000864988237934128 \tabularnewline
42 & 8.19 & 8.1891498623568 & 0.000850137643199744 \tabularnewline
43 & 8.18 & 8.17916445798834 & 0.00083554201165903 \tabularnewline
44 & 8.16 & 8.16917880303404 & -0.00917880303403784 \tabularnewline
45 & 8.17 & 8.1490212162854 & 0.0209787837145932 \tabularnewline
46 & 8.17 & 8.15938139160495 & 0.010618608395049 \tabularnewline
47 & 8.19 & 8.15956369772545 & 0.0304363022745502 \tabularnewline
48 & 8.01 & 8.18008624493536 & -0.170086244935362 \tabularnewline
49 & 8.04 & 7.99716611055327 & 0.0428338894467304 \tabularnewline
50 & 8.13 & 8.02790150637166 & 0.102098493628336 \tabularnewline
51 & 8.14 & 8.11965438957346 & 0.0203456104265367 \tabularnewline
52 & 8.17 & 8.13000369422508 & 0.039996305774924 \tabularnewline
53 & 8.25 & 8.1606903728433 & 0.0893096271567053 \tabularnewline
54 & 8.27 & 8.24222368973797 & 0.0277763102620252 \tabularnewline
55 & 8.27 & 8.26270056873918 & 0.007299431260817 \tabularnewline
56 & 8.26 & 8.26282588939755 & -0.00282588939754902 \tabularnewline
57 & 8.24 & 8.25277737297112 & -0.0127773729711151 \tabularnewline
58 & 8.21 & 8.23255800399075 & -0.0225580039907491 \tabularnewline
59 & 8.25 & 8.20217071574725 & 0.0478292842527512 \tabularnewline
60 & 8.06 & 8.24299187525648 & -0.182991875256475 \tabularnewline
61 & 8.16 & 8.04985016990115 & 0.110149830098848 \tabularnewline
62 & 8.32 & 8.15174128288431 & 0.168258717115693 \tabularnewline
63 & 8.43 & 8.3146300412617 & 0.115369958738299 \tabularnewline
64 & 8.39 & 8.42661077628998 & -0.036610776289983 \tabularnewline
65 & 8.41 & 8.38598222230762 & 0.0240177776923804 \tabularnewline
66 & 8.45 & 8.40639457275046 & 0.0436054272495348 \tabularnewline
67 & 8.43 & 8.44714321475503 & -0.0171432147550288 \tabularnewline
68 & 8.52 & 8.42684889059704 & 0.0931511094029585 \tabularnewline
69 & 8.52 & 8.51844816017584 & 0.00155183982415608 \tabularnewline
70 & 8.51 & 8.51847480301711 & -0.00847480301711379 \tabularnewline
71 & 8.56 & 8.50832930292873 & 0.051670697071275 \tabularnewline
72 & 8.36 & 8.5592164139301 & -0.199216413930101 \tabularnewline
73 & 8.4 & 8.355796156754 & 0.0442038432459935 \tabularnewline
74 & 8.44 & 8.39655507269417 & 0.043444927305833 \tabularnewline
75 & 8.5 & 8.43730095914725 & 0.062699040852749 \tabularnewline
76 & 8.31 & 8.49837741083203 & -0.188377410832031 \tabularnewline
77 & 8.38 & 8.30514324363415 & 0.0748567563658487 \tabularnewline
78 & 8.45 & 8.37642842567858 & 0.0735715743214147 \tabularnewline
79 & 8.42 & 8.44769154300946 & -0.0276915430094551 \tabularnewline
80 & 8.46 & 8.41721611933915 & 0.0427838806608474 \tabularnewline
81 & 8.45 & 8.45795065657916 & -0.0079506565791565 \tabularnewline
82 & 8.32 & 8.44781415532565 & -0.127814155325654 \tabularnewline
83 & 8.4 & 8.31561977147276 & 0.0843802285272357 \tabularnewline
84 & 8.18 & 8.39706845773534 & -0.217068457735342 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=161069&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]8.27[/C][C]8.25[/C][C]0.0199999999999996[/C][/ROW]
[ROW][C]4[/C][C]8.43[/C][C]8.25034337102135[/C][C]0.179656628978645[/C][/ROW]
[ROW][C]5[/C][C]8.46[/C][C]8.41342781503063[/C][C]0.0465721849693672[/C][/ROW]
[ROW][C]6[/C][C]8.48[/C][C]8.44422739196662[/C][C]0.0357726080333816[/C][/ROW]
[ROW][C]7[/C][C]8.46[/C][C]8.46484155581446[/C][C]-0.00484155581446366[/C][/ROW]
[ROW][C]8[/C][C]8.46[/C][C]8.44475843331622[/C][C]0.015241566683784[/C][/ROW]
[ROW][C]9[/C][C]8.43[/C][C]8.44502010893218[/C][C]-0.0150201089321804[/C][/ROW]
[ROW][C]10[/C][C]8.4[/C][C]8.41476223542493[/C][C]-0.0147622354249339[/C][/ROW]
[ROW][C]11[/C][C]8.38[/C][C]8.38450878923217[/C][C]-0.00450878923216713[/C][/ROW]
[ROW][C]12[/C][C]8.3[/C][C]8.36443137985398[/C][C]-0.064431379853982[/C][/ROW]
[ROW][C]13[/C][C]8.39[/C][C]8.2833251864186[/C][C]0.106674813581407[/C][/ROW]
[ROW][C]14[/C][C]8.53[/C][C]8.3751566384032[/C][C]0.154843361596791[/C][/ROW]
[ROW][C]15[/C][C]8.52[/C][C]8.51781507456428[/C][C]0.00218492543571713[/C][/ROW]
[ROW][C]16[/C][C]8.54[/C][C]8.5078525865682[/C][C]0.0321474134317938[/C][/ROW]
[ROW][C]17[/C][C]8.62[/C][C]8.5284045110774[/C][C]0.0915954889225947[/C][/ROW]
[ROW][C]18[/C][C]8.52[/C][C]8.60997707290655[/C][C]-0.0899770729065477[/C][/ROW]
[ROW][C]19[/C][C]8.49[/C][C]8.50843229693542[/C][C]-0.0184322969354245[/C][/ROW]
[ROW][C]20[/C][C]8.44[/C][C]8.4781158411042[/C][C]-0.0381158411041955[/C][/ROW]
[ROW][C]21[/C][C]8.31[/C][C]8.4274614473397[/C][C]-0.117461447339705[/C][/ROW]
[ROW][C]22[/C][C]8.26[/C][C]8.29544480448256[/C][C]-0.0354448044825642[/C][/ROW]
[ROW][C]23[/C][C]8.21[/C][C]8.24483626854672[/C][C]-0.0348362685467176[/C][/ROW]
[ROW][C]24[/C][C]8.03[/C][C]8.19423818029117[/C][C]-0.164238180291166[/C][/ROW]
[ROW][C]25[/C][C]7.89[/C][C]8.01141844870556[/C][C]-0.121418448705561[/C][/ROW]
[ROW][C]26[/C][C]7.83[/C][C]7.8693338698684[/C][C]-0.0393338698683934[/C][/ROW]
[ROW][C]27[/C][C]7.85[/C][C]7.80865856431487[/C][C]0.0413414356851334[/C][/ROW]
[ROW][C]28[/C][C]7.84[/C][C]7.82936833686464[/C][C]0.0106316631353591[/C][/ROW]
[ROW][C]29[/C][C]7.88[/C][C]7.81955086711612[/C][C]0.0604491328838845[/C][/ROW]
[ROW][C]30[/C][C]8.01[/C][C]7.86058869114103[/C][C]0.149411308858967[/C][/ROW]
[ROW][C]31[/C][C]8.08[/C][C]7.99315386682728[/C][C]0.086846133172723[/C][/ROW]
[ROW][C]32[/C][C]8.11[/C][C]8.06464488909969[/C][C]0.0453551109003101[/C][/ROW]
[ROW][C]33[/C][C]8.11[/C][C]8.09542357063736[/C][C]0.014576429362636[/C][/ROW]
[ROW][C]34[/C][C]8.07[/C][C]8.09567382680926[/C][C]-0.0256738268092604[/C][/ROW]
[ROW][C]35[/C][C]8.06[/C][C]8.05523304440258[/C][C]0.00476695559741813[/C][/ROW]
[ROW][C]36[/C][C]7.95[/C][C]8.0453148861232[/C][C]-0.0953148861231954[/C][/ROW]
[ROW][C]37[/C][C]7.95[/C][C]7.93367846763327[/C][C]0.0163215323667281[/C][/ROW]
[ROW][C]38[/C][C]8.07[/C][C]7.93395868469521[/C][C]0.136041315304785[/C][/ROW]
[ROW][C]39[/C][C]8.17[/C][C]8.05629431696435[/C][C]0.113705683035652[/C][/ROW]
[ROW][C]40[/C][C]8.21[/C][C]8.15824647879024[/C][C]0.0517535212097631[/C][/ROW]
[ROW][C]41[/C][C]8.2[/C][C]8.19913501176207[/C][C]0.000864988237934128[/C][/ROW]
[ROW][C]42[/C][C]8.19[/C][C]8.1891498623568[/C][C]0.000850137643199744[/C][/ROW]
[ROW][C]43[/C][C]8.18[/C][C]8.17916445798834[/C][C]0.00083554201165903[/C][/ROW]
[ROW][C]44[/C][C]8.16[/C][C]8.16917880303404[/C][C]-0.00917880303403784[/C][/ROW]
[ROW][C]45[/C][C]8.17[/C][C]8.1490212162854[/C][C]0.0209787837145932[/C][/ROW]
[ROW][C]46[/C][C]8.17[/C][C]8.15938139160495[/C][C]0.010618608395049[/C][/ROW]
[ROW][C]47[/C][C]8.19[/C][C]8.15956369772545[/C][C]0.0304363022745502[/C][/ROW]
[ROW][C]48[/C][C]8.01[/C][C]8.18008624493536[/C][C]-0.170086244935362[/C][/ROW]
[ROW][C]49[/C][C]8.04[/C][C]7.99716611055327[/C][C]0.0428338894467304[/C][/ROW]
[ROW][C]50[/C][C]8.13[/C][C]8.02790150637166[/C][C]0.102098493628336[/C][/ROW]
[ROW][C]51[/C][C]8.14[/C][C]8.11965438957346[/C][C]0.0203456104265367[/C][/ROW]
[ROW][C]52[/C][C]8.17[/C][C]8.13000369422508[/C][C]0.039996305774924[/C][/ROW]
[ROW][C]53[/C][C]8.25[/C][C]8.1606903728433[/C][C]0.0893096271567053[/C][/ROW]
[ROW][C]54[/C][C]8.27[/C][C]8.24222368973797[/C][C]0.0277763102620252[/C][/ROW]
[ROW][C]55[/C][C]8.27[/C][C]8.26270056873918[/C][C]0.007299431260817[/C][/ROW]
[ROW][C]56[/C][C]8.26[/C][C]8.26282588939755[/C][C]-0.00282588939754902[/C][/ROW]
[ROW][C]57[/C][C]8.24[/C][C]8.25277737297112[/C][C]-0.0127773729711151[/C][/ROW]
[ROW][C]58[/C][C]8.21[/C][C]8.23255800399075[/C][C]-0.0225580039907491[/C][/ROW]
[ROW][C]59[/C][C]8.25[/C][C]8.20217071574725[/C][C]0.0478292842527512[/C][/ROW]
[ROW][C]60[/C][C]8.06[/C][C]8.24299187525648[/C][C]-0.182991875256475[/C][/ROW]
[ROW][C]61[/C][C]8.16[/C][C]8.04985016990115[/C][C]0.110149830098848[/C][/ROW]
[ROW][C]62[/C][C]8.32[/C][C]8.15174128288431[/C][C]0.168258717115693[/C][/ROW]
[ROW][C]63[/C][C]8.43[/C][C]8.3146300412617[/C][C]0.115369958738299[/C][/ROW]
[ROW][C]64[/C][C]8.39[/C][C]8.42661077628998[/C][C]-0.036610776289983[/C][/ROW]
[ROW][C]65[/C][C]8.41[/C][C]8.38598222230762[/C][C]0.0240177776923804[/C][/ROW]
[ROW][C]66[/C][C]8.45[/C][C]8.40639457275046[/C][C]0.0436054272495348[/C][/ROW]
[ROW][C]67[/C][C]8.43[/C][C]8.44714321475503[/C][C]-0.0171432147550288[/C][/ROW]
[ROW][C]68[/C][C]8.52[/C][C]8.42684889059704[/C][C]0.0931511094029585[/C][/ROW]
[ROW][C]69[/C][C]8.52[/C][C]8.51844816017584[/C][C]0.00155183982415608[/C][/ROW]
[ROW][C]70[/C][C]8.51[/C][C]8.51847480301711[/C][C]-0.00847480301711379[/C][/ROW]
[ROW][C]71[/C][C]8.56[/C][C]8.50832930292873[/C][C]0.051670697071275[/C][/ROW]
[ROW][C]72[/C][C]8.36[/C][C]8.5592164139301[/C][C]-0.199216413930101[/C][/ROW]
[ROW][C]73[/C][C]8.4[/C][C]8.355796156754[/C][C]0.0442038432459935[/C][/ROW]
[ROW][C]74[/C][C]8.44[/C][C]8.39655507269417[/C][C]0.043444927305833[/C][/ROW]
[ROW][C]75[/C][C]8.5[/C][C]8.43730095914725[/C][C]0.062699040852749[/C][/ROW]
[ROW][C]76[/C][C]8.31[/C][C]8.49837741083203[/C][C]-0.188377410832031[/C][/ROW]
[ROW][C]77[/C][C]8.38[/C][C]8.30514324363415[/C][C]0.0748567563658487[/C][/ROW]
[ROW][C]78[/C][C]8.45[/C][C]8.37642842567858[/C][C]0.0735715743214147[/C][/ROW]
[ROW][C]79[/C][C]8.42[/C][C]8.44769154300946[/C][C]-0.0276915430094551[/C][/ROW]
[ROW][C]80[/C][C]8.46[/C][C]8.41721611933915[/C][C]0.0427838806608474[/C][/ROW]
[ROW][C]81[/C][C]8.45[/C][C]8.45795065657916[/C][C]-0.0079506565791565[/C][/ROW]
[ROW][C]82[/C][C]8.32[/C][C]8.44781415532565[/C][C]-0.127814155325654[/C][/ROW]
[ROW][C]83[/C][C]8.4[/C][C]8.31561977147276[/C][C]0.0843802285272357[/C][/ROW]
[ROW][C]84[/C][C]8.18[/C][C]8.39706845773534[/C][C]-0.217068457735342[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=161069&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=161069&T=2

As an alternative you can also use a QR Code:  
QR Code


The GUIDs for individual cells are displayed in the table below:

Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
38.278.250.0199999999999996
48.438.250343371021350.179656628978645
58.468.413427815030630.0465721849693672
68.488.444227391966620.0357726080333816
78.468.46484155581446-0.00484155581446366
88.468.444758433316220.015241566683784
98.438.44502010893218-0.0150201089321804
108.48.41476223542493-0.0147622354249339
118.388.38450878923217-0.00450878923216713
128.38.36443137985398-0.064431379853982
138.398.28332518641860.106674813581407
148.538.37515663840320.154843361596791
158.528.517815074564280.00218492543571713
168.548.50785258656820.0321474134317938
178.628.52840451107740.0915954889225947
188.528.60997707290655-0.0899770729065477
198.498.50843229693542-0.0184322969354245
208.448.4781158411042-0.0381158411041955
218.318.4274614473397-0.117461447339705
228.268.29544480448256-0.0354448044825642
238.218.24483626854672-0.0348362685467176
248.038.19423818029117-0.164238180291166
257.898.01141844870556-0.121418448705561
267.837.8693338698684-0.0393338698683934
277.857.808658564314870.0413414356851334
287.847.829368336864640.0106316631353591
297.887.819550867116120.0604491328838845
308.017.860588691141030.149411308858967
318.087.993153866827280.086846133172723
328.118.064644889099690.0453551109003101
338.118.095423570637360.014576429362636
348.078.09567382680926-0.0256738268092604
358.068.055233044402580.00476695559741813
367.958.0453148861232-0.0953148861231954
377.957.933678467633270.0163215323667281
388.077.933958684695210.136041315304785
398.178.056294316964350.113705683035652
408.218.158246478790240.0517535212097631
418.28.199135011762070.000864988237934128
428.198.18914986235680.000850137643199744
438.188.179164457988340.00083554201165903
448.168.16917880303404-0.00917880303403784
458.178.14902121628540.0209787837145932
468.178.159381391604950.010618608395049
478.198.159563697725450.0304363022745502
488.018.18008624493536-0.170086244935362
498.047.997166110553270.0428338894467304
508.138.027901506371660.102098493628336
518.148.119654389573460.0203456104265367
528.178.130003694225080.039996305774924
538.258.16069037284330.0893096271567053
548.278.242223689737970.0277763102620252
558.278.262700568739180.007299431260817
568.268.26282588939755-0.00282588939754902
578.248.25277737297112-0.0127773729711151
588.218.23255800399075-0.0225580039907491
598.258.202170715747250.0478292842527512
608.068.24299187525648-0.182991875256475
618.168.049850169901150.110149830098848
628.328.151741282884310.168258717115693
638.438.31463004126170.115369958738299
648.398.42661077628998-0.036610776289983
658.418.385982222307620.0240177776923804
668.458.406394572750460.0436054272495348
678.438.44714321475503-0.0171432147550288
688.528.426848890597040.0931511094029585
698.528.518448160175840.00155183982415608
708.518.51847480301711-0.00847480301711379
718.568.508329302928730.051670697071275
728.368.5592164139301-0.199216413930101
738.48.3557961567540.0442038432459935
748.448.396555072694170.043444927305833
758.58.437300959147250.062699040852749
768.318.49837741083203-0.188377410832031
778.388.305143243634150.0748567563658487
788.458.376428425678580.0735715743214147
798.428.44769154300946-0.0276915430094551
808.468.417216119339150.0427838806608474
818.458.45795065657916-0.0079506565791565
828.328.44781415532565-0.127814155325654
838.48.315619771472760.0843802285272357
848.188.39706845773534-0.217068457735342






Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
858.173341706833528.01094281690868.33574059675843
868.166683413667037.935036788807278.3983300385268
878.160025120500557.873885599144968.44616464185614
888.153366827334077.820146258238638.4865873964295
898.146708534167587.771001104948588.5224159633866
908.14005024100117.72501801648218.5550824655201
918.133391947834627.6813537632468.58543013242323
928.126733654668137.639463771766788.61400353756948
938.120075361501657.59897311591058.6411776070928
948.113417068335177.559611233533938.6672229031364
958.106758775168687.521175695423948.69234185491342
968.10010048200227.483510650889288.71669031311512

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
85 & 8.17334170683352 & 8.0109428169086 & 8.33574059675843 \tabularnewline
86 & 8.16668341366703 & 7.93503678880727 & 8.3983300385268 \tabularnewline
87 & 8.16002512050055 & 7.87388559914496 & 8.44616464185614 \tabularnewline
88 & 8.15336682733407 & 7.82014625823863 & 8.4865873964295 \tabularnewline
89 & 8.14670853416758 & 7.77100110494858 & 8.5224159633866 \tabularnewline
90 & 8.1400502410011 & 7.7250180164821 & 8.5550824655201 \tabularnewline
91 & 8.13339194783462 & 7.681353763246 & 8.58543013242323 \tabularnewline
92 & 8.12673365466813 & 7.63946377176678 & 8.61400353756948 \tabularnewline
93 & 8.12007536150165 & 7.5989731159105 & 8.6411776070928 \tabularnewline
94 & 8.11341706833517 & 7.55961123353393 & 8.6672229031364 \tabularnewline
95 & 8.10675877516868 & 7.52117569542394 & 8.69234185491342 \tabularnewline
96 & 8.1001004820022 & 7.48351065088928 & 8.71669031311512 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=161069&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]8.17334170683352[/C][C]8.0109428169086[/C][C]8.33574059675843[/C][/ROW]
[ROW][C]86[/C][C]8.16668341366703[/C][C]7.93503678880727[/C][C]8.3983300385268[/C][/ROW]
[ROW][C]87[/C][C]8.16002512050055[/C][C]7.87388559914496[/C][C]8.44616464185614[/C][/ROW]
[ROW][C]88[/C][C]8.15336682733407[/C][C]7.82014625823863[/C][C]8.4865873964295[/C][/ROW]
[ROW][C]89[/C][C]8.14670853416758[/C][C]7.77100110494858[/C][C]8.5224159633866[/C][/ROW]
[ROW][C]90[/C][C]8.1400502410011[/C][C]7.7250180164821[/C][C]8.5550824655201[/C][/ROW]
[ROW][C]91[/C][C]8.13339194783462[/C][C]7.681353763246[/C][C]8.58543013242323[/C][/ROW]
[ROW][C]92[/C][C]8.12673365466813[/C][C]7.63946377176678[/C][C]8.61400353756948[/C][/ROW]
[ROW][C]93[/C][C]8.12007536150165[/C][C]7.5989731159105[/C][C]8.6411776070928[/C][/ROW]
[ROW][C]94[/C][C]8.11341706833517[/C][C]7.55961123353393[/C][C]8.6672229031364[/C][/ROW]
[ROW][C]95[/C][C]8.10675877516868[/C][C]7.52117569542394[/C][C]8.69234185491342[/C][/ROW]
[ROW][C]96[/C][C]8.1001004820022[/C][C]7.48351065088928[/C][C]8.71669031311512[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=161069&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=161069&T=3

As an alternative you can also use a QR Code:  
QR Code


The GUIDs for individual cells are displayed in the table below:

Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
858.173341706833528.01094281690868.33574059675843
868.166683413667037.935036788807278.3983300385268
878.160025120500557.873885599144968.44616464185614
888.153366827334077.820146258238638.4865873964295
898.146708534167587.771001104948588.5224159633866
908.14005024100117.72501801648218.5550824655201
918.133391947834627.6813537632468.58543013242323
928.126733654668137.639463771766788.61400353756948
938.120075361501657.59897311591058.6411776070928
948.113417068335177.559611233533938.6672229031364
958.106758775168687.521175695423948.69234185491342
968.10010048200227.483510650889288.71669031311512


Figures (Output of Computation)

Input Parameters & R Code

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')