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Description of Statistical Computation

Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationWed, 01 Apr 2015 13:57:17 +0100
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2015/Apr/01/t1427893112fx52aeunlup86w7.htm/, Retrieved Thu, 09 May 2024 19:54:38 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=278508, Retrieved Thu, 09 May 2024 19:54:38 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact170

Tree of Dependent Computations

Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [] [2015-04-01 12:57:17] [7657461249ddfb44f7ff766614f926c4] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
8,09
8,18
8,26
8,28
8,28
8,28
8,29
8,3
8,3
8,31
8,33
8,33
8,34
8,48
8,59
8,67
8,67
8,67
8,71
8,72
8,72
8,72
8,74
8,74
8,74
8,74
8,79
8,85
8,86
8,87
8,92
8,96
8,97
8,99
8,98
8,98
9,01
9,01
9,03
9,05
9,05
9,05
9,13
9,13
9,13
9,14
9,16
9,16
9,16
9,16
9,22
9,22
9,25
9,25
9,26
9,26
9,29
9,28
9,37
9,41
9,41
9,45
9,49
9,49
9,56
9,54
9,55
9,55
9,57
9,57
9,58
9,59
9,59
9,59
9,61
9,61
9,62
9,62
9,63
9,65
9,65
9,68
9,73
9,73
9,73
9,74
9,68
9,68
9,74
9,74
9,76
9,78
9,79
9,81
9,84
9,84

Tables (Output of Computation)





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' @ yule.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 & 'George Udny Yule' @ yule.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=278508&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' @ yule.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=278508&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=278508&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 time1 seconds
R Server'George Udny Yule' @ yule.wessa.net






Estimated Parameters of Exponential Smoothing
ParameterValue
alpha1
beta0.302009667782302
gammaFALSE

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 1 \tabularnewline
beta & 0.302009667782302 \tabularnewline
gamma & FALSE \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=278508&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]0.302009667782302[/C][/ROW]
[ROW][C]gamma[/C][C]FALSE[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=278508&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=278508&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
beta0.302009667782302
gammaFALSE






Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
38.268.27-0.00999999999999979
48.288.34697990332218-0.0669799033221778
58.288.34675132497176-0.0667513249717562
68.288.32659177949301-0.0465917794930064
78.298.31252061164694-0.0225206116469376
88.38.31571916920519-0.015719169205191
98.38.32097182813572-0.0209718281357176
108.318.31463813328766-0.00463813328766349
118.338.323237372194330.00676262780567427
128.338.34527975117125-0.0152797511712528
138.348.34066511859623-0.000665118596225867
148.488.350464246349940.129535753650057
158.598.529585296275730.0604147037242715
168.678.657831120876660.0121688791233385
178.678.74150624001798-0.0715062400179836
188.678.71991066422579-0.0499106642257914
198.718.704837161104170.00516283889583491
208.728.74639638836391-0.02639638836391
218.728.74842442388347-0.0284244238834734
228.728.73983997306952-0.0198399730695229
238.748.733848109393990.00615189060601296
248.748.75570603983214-0.0157060398321409
258.748.75096266396026-0.0109626639602602
268.748.74765183345961-0.0076518334596134
278.798.745340905778550.0446590942214495
288.858.808828383987830.0411716160121713
298.868.88126261006173-0.0212626100617257
308.878.8848410962608-0.014841096260799
318.928.890358941709550.0296410582904514
328.968.949310827876560.0106891721234366
338.978.99253906119843-0.0225390611984313
348.998.99573204681377-0.00573204681376893
358.989.01400091325983-0.0340009132598293
368.988.99373230874193-0.0137323087419343
379.018.98958501874090.0204149812591012
389.019.02575054044874-0.0157505404487406
399.039.020993724960420.00900627503957452
409.059.043713707093080.00628629290691762
419.059.06561222832548-0.0156122283254838
429.059.06089718443556-0.0108971844355636
439.139.057606129384420.0723938706155831
449.139.1594697781985-0.0294697781985036
459.139.15056962027516-0.0205696202751557
469.149.14435739608945-0.00435739608944807
479.169.153041420344080.00695857965592239
489.169.1751429786742-0.0151429786741986
499.169.17056965271557-0.010569652715569
509.169.16737751541037-0.0073775154103668
519.229.165149434432220.0548505655677776
529.229.24171483551702-0.0217148355170185
539.259.235156745256580.0148432547434236
549.259.26963955169045-0.019639551690446
559.269.26370821720902-0.00370821720902192
569.269.27258829976166-0.01258829976166
579.299.26878651153270.0212134884673016
589.289.30519319013721-0.0251931901372107
599.379.287584603153490.0824153968465051
609.419.402474849775250.00752515022474576
619.419.44474751789464-0.0347475178946421
629.459.434253431559020.0157465684409779
639.499.479009047462590.0109909525374086
649.499.52232842138703-0.0323284213870263
659.569.512564925584010.0474350744159953
669.549.59689077664961-0.0568907766496096
679.559.55970921209378-0.00970921209378162
689.559.56677693617491-0.0167769361749119
699.579.561710139254320.00828986074567872
709.579.58421375734409-0.0142137573440859
719.589.579921065210667.89347893395131e-05
729.599.589944904280165.50957198353075e-05
739.599.59996154372021-0.00996154372020897
749.599.59695306121067-0.00695306121066963
759.619.594853169504360.0151468304956346
769.619.61942765875031-0.00942765875030638
779.629.616580414663160.00341958533683773
789.629.62761316249469-0.00761316249469246
799.639.62531391381890.00468608618110267
809.659.636729157149650.0132708428503463
819.659.66073707999008-0.0107370799900774
829.689.657494378029320.0225056219706783
839.739.694291293443920.0357087065560808
849.739.75507566804786-0.0250756680478581
859.739.74750257387131-0.0175025738713046
869.749.7422166273511-0.00221662735109796
879.689.7515471844612-0.0715471844611955
889.689.669939243051310.0100607569486897
899.749.672977688915020.0670223110849779
909.749.7532190748198-0.0132190748197996
919.769.749226786425080.0107732135749181
929.789.772480401077790.0075195989222081
939.799.79475139265014-0.00475139265014413
949.819.803316426134370.00668357386563123
959.849.825334930057130.0146650699428719
969.849.85976392295858-0.0197639229585782

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
3 & 8.26 & 8.27 & -0.00999999999999979 \tabularnewline
4 & 8.28 & 8.34697990332218 & -0.0669799033221778 \tabularnewline
5 & 8.28 & 8.34675132497176 & -0.0667513249717562 \tabularnewline
6 & 8.28 & 8.32659177949301 & -0.0465917794930064 \tabularnewline
7 & 8.29 & 8.31252061164694 & -0.0225206116469376 \tabularnewline
8 & 8.3 & 8.31571916920519 & -0.015719169205191 \tabularnewline
9 & 8.3 & 8.32097182813572 & -0.0209718281357176 \tabularnewline
10 & 8.31 & 8.31463813328766 & -0.00463813328766349 \tabularnewline
11 & 8.33 & 8.32323737219433 & 0.00676262780567427 \tabularnewline
12 & 8.33 & 8.34527975117125 & -0.0152797511712528 \tabularnewline
13 & 8.34 & 8.34066511859623 & -0.000665118596225867 \tabularnewline
14 & 8.48 & 8.35046424634994 & 0.129535753650057 \tabularnewline
15 & 8.59 & 8.52958529627573 & 0.0604147037242715 \tabularnewline
16 & 8.67 & 8.65783112087666 & 0.0121688791233385 \tabularnewline
17 & 8.67 & 8.74150624001798 & -0.0715062400179836 \tabularnewline
18 & 8.67 & 8.71991066422579 & -0.0499106642257914 \tabularnewline
19 & 8.71 & 8.70483716110417 & 0.00516283889583491 \tabularnewline
20 & 8.72 & 8.74639638836391 & -0.02639638836391 \tabularnewline
21 & 8.72 & 8.74842442388347 & -0.0284244238834734 \tabularnewline
22 & 8.72 & 8.73983997306952 & -0.0198399730695229 \tabularnewline
23 & 8.74 & 8.73384810939399 & 0.00615189060601296 \tabularnewline
24 & 8.74 & 8.75570603983214 & -0.0157060398321409 \tabularnewline
25 & 8.74 & 8.75096266396026 & -0.0109626639602602 \tabularnewline
26 & 8.74 & 8.74765183345961 & -0.0076518334596134 \tabularnewline
27 & 8.79 & 8.74534090577855 & 0.0446590942214495 \tabularnewline
28 & 8.85 & 8.80882838398783 & 0.0411716160121713 \tabularnewline
29 & 8.86 & 8.88126261006173 & -0.0212626100617257 \tabularnewline
30 & 8.87 & 8.8848410962608 & -0.014841096260799 \tabularnewline
31 & 8.92 & 8.89035894170955 & 0.0296410582904514 \tabularnewline
32 & 8.96 & 8.94931082787656 & 0.0106891721234366 \tabularnewline
33 & 8.97 & 8.99253906119843 & -0.0225390611984313 \tabularnewline
34 & 8.99 & 8.99573204681377 & -0.00573204681376893 \tabularnewline
35 & 8.98 & 9.01400091325983 & -0.0340009132598293 \tabularnewline
36 & 8.98 & 8.99373230874193 & -0.0137323087419343 \tabularnewline
37 & 9.01 & 8.9895850187409 & 0.0204149812591012 \tabularnewline
38 & 9.01 & 9.02575054044874 & -0.0157505404487406 \tabularnewline
39 & 9.03 & 9.02099372496042 & 0.00900627503957452 \tabularnewline
40 & 9.05 & 9.04371370709308 & 0.00628629290691762 \tabularnewline
41 & 9.05 & 9.06561222832548 & -0.0156122283254838 \tabularnewline
42 & 9.05 & 9.06089718443556 & -0.0108971844355636 \tabularnewline
43 & 9.13 & 9.05760612938442 & 0.0723938706155831 \tabularnewline
44 & 9.13 & 9.1594697781985 & -0.0294697781985036 \tabularnewline
45 & 9.13 & 9.15056962027516 & -0.0205696202751557 \tabularnewline
46 & 9.14 & 9.14435739608945 & -0.00435739608944807 \tabularnewline
47 & 9.16 & 9.15304142034408 & 0.00695857965592239 \tabularnewline
48 & 9.16 & 9.1751429786742 & -0.0151429786741986 \tabularnewline
49 & 9.16 & 9.17056965271557 & -0.010569652715569 \tabularnewline
50 & 9.16 & 9.16737751541037 & -0.0073775154103668 \tabularnewline
51 & 9.22 & 9.16514943443222 & 0.0548505655677776 \tabularnewline
52 & 9.22 & 9.24171483551702 & -0.0217148355170185 \tabularnewline
53 & 9.25 & 9.23515674525658 & 0.0148432547434236 \tabularnewline
54 & 9.25 & 9.26963955169045 & -0.019639551690446 \tabularnewline
55 & 9.26 & 9.26370821720902 & -0.00370821720902192 \tabularnewline
56 & 9.26 & 9.27258829976166 & -0.01258829976166 \tabularnewline
57 & 9.29 & 9.2687865115327 & 0.0212134884673016 \tabularnewline
58 & 9.28 & 9.30519319013721 & -0.0251931901372107 \tabularnewline
59 & 9.37 & 9.28758460315349 & 0.0824153968465051 \tabularnewline
60 & 9.41 & 9.40247484977525 & 0.00752515022474576 \tabularnewline
61 & 9.41 & 9.44474751789464 & -0.0347475178946421 \tabularnewline
62 & 9.45 & 9.43425343155902 & 0.0157465684409779 \tabularnewline
63 & 9.49 & 9.47900904746259 & 0.0109909525374086 \tabularnewline
64 & 9.49 & 9.52232842138703 & -0.0323284213870263 \tabularnewline
65 & 9.56 & 9.51256492558401 & 0.0474350744159953 \tabularnewline
66 & 9.54 & 9.59689077664961 & -0.0568907766496096 \tabularnewline
67 & 9.55 & 9.55970921209378 & -0.00970921209378162 \tabularnewline
68 & 9.55 & 9.56677693617491 & -0.0167769361749119 \tabularnewline
69 & 9.57 & 9.56171013925432 & 0.00828986074567872 \tabularnewline
70 & 9.57 & 9.58421375734409 & -0.0142137573440859 \tabularnewline
71 & 9.58 & 9.57992106521066 & 7.89347893395131e-05 \tabularnewline
72 & 9.59 & 9.58994490428016 & 5.50957198353075e-05 \tabularnewline
73 & 9.59 & 9.59996154372021 & -0.00996154372020897 \tabularnewline
74 & 9.59 & 9.59695306121067 & -0.00695306121066963 \tabularnewline
75 & 9.61 & 9.59485316950436 & 0.0151468304956346 \tabularnewline
76 & 9.61 & 9.61942765875031 & -0.00942765875030638 \tabularnewline
77 & 9.62 & 9.61658041466316 & 0.00341958533683773 \tabularnewline
78 & 9.62 & 9.62761316249469 & -0.00761316249469246 \tabularnewline
79 & 9.63 & 9.6253139138189 & 0.00468608618110267 \tabularnewline
80 & 9.65 & 9.63672915714965 & 0.0132708428503463 \tabularnewline
81 & 9.65 & 9.66073707999008 & -0.0107370799900774 \tabularnewline
82 & 9.68 & 9.65749437802932 & 0.0225056219706783 \tabularnewline
83 & 9.73 & 9.69429129344392 & 0.0357087065560808 \tabularnewline
84 & 9.73 & 9.75507566804786 & -0.0250756680478581 \tabularnewline
85 & 9.73 & 9.74750257387131 & -0.0175025738713046 \tabularnewline
86 & 9.74 & 9.7422166273511 & -0.00221662735109796 \tabularnewline
87 & 9.68 & 9.7515471844612 & -0.0715471844611955 \tabularnewline
88 & 9.68 & 9.66993924305131 & 0.0100607569486897 \tabularnewline
89 & 9.74 & 9.67297768891502 & 0.0670223110849779 \tabularnewline
90 & 9.74 & 9.7532190748198 & -0.0132190748197996 \tabularnewline
91 & 9.76 & 9.74922678642508 & 0.0107732135749181 \tabularnewline
92 & 9.78 & 9.77248040107779 & 0.0075195989222081 \tabularnewline
93 & 9.79 & 9.79475139265014 & -0.00475139265014413 \tabularnewline
94 & 9.81 & 9.80331642613437 & 0.00668357386563123 \tabularnewline
95 & 9.84 & 9.82533493005713 & 0.0146650699428719 \tabularnewline
96 & 9.84 & 9.85976392295858 & -0.0197639229585782 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=278508&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]8.26[/C][C]8.27[/C][C]-0.00999999999999979[/C][/ROW]
[ROW][C]4[/C][C]8.28[/C][C]8.34697990332218[/C][C]-0.0669799033221778[/C][/ROW]
[ROW][C]5[/C][C]8.28[/C][C]8.34675132497176[/C][C]-0.0667513249717562[/C][/ROW]
[ROW][C]6[/C][C]8.28[/C][C]8.32659177949301[/C][C]-0.0465917794930064[/C][/ROW]
[ROW][C]7[/C][C]8.29[/C][C]8.31252061164694[/C][C]-0.0225206116469376[/C][/ROW]
[ROW][C]8[/C][C]8.3[/C][C]8.31571916920519[/C][C]-0.015719169205191[/C][/ROW]
[ROW][C]9[/C][C]8.3[/C][C]8.32097182813572[/C][C]-0.0209718281357176[/C][/ROW]
[ROW][C]10[/C][C]8.31[/C][C]8.31463813328766[/C][C]-0.00463813328766349[/C][/ROW]
[ROW][C]11[/C][C]8.33[/C][C]8.32323737219433[/C][C]0.00676262780567427[/C][/ROW]
[ROW][C]12[/C][C]8.33[/C][C]8.34527975117125[/C][C]-0.0152797511712528[/C][/ROW]
[ROW][C]13[/C][C]8.34[/C][C]8.34066511859623[/C][C]-0.000665118596225867[/C][/ROW]
[ROW][C]14[/C][C]8.48[/C][C]8.35046424634994[/C][C]0.129535753650057[/C][/ROW]
[ROW][C]15[/C][C]8.59[/C][C]8.52958529627573[/C][C]0.0604147037242715[/C][/ROW]
[ROW][C]16[/C][C]8.67[/C][C]8.65783112087666[/C][C]0.0121688791233385[/C][/ROW]
[ROW][C]17[/C][C]8.67[/C][C]8.74150624001798[/C][C]-0.0715062400179836[/C][/ROW]
[ROW][C]18[/C][C]8.67[/C][C]8.71991066422579[/C][C]-0.0499106642257914[/C][/ROW]
[ROW][C]19[/C][C]8.71[/C][C]8.70483716110417[/C][C]0.00516283889583491[/C][/ROW]
[ROW][C]20[/C][C]8.72[/C][C]8.74639638836391[/C][C]-0.02639638836391[/C][/ROW]
[ROW][C]21[/C][C]8.72[/C][C]8.74842442388347[/C][C]-0.0284244238834734[/C][/ROW]
[ROW][C]22[/C][C]8.72[/C][C]8.73983997306952[/C][C]-0.0198399730695229[/C][/ROW]
[ROW][C]23[/C][C]8.74[/C][C]8.73384810939399[/C][C]0.00615189060601296[/C][/ROW]
[ROW][C]24[/C][C]8.74[/C][C]8.75570603983214[/C][C]-0.0157060398321409[/C][/ROW]
[ROW][C]25[/C][C]8.74[/C][C]8.75096266396026[/C][C]-0.0109626639602602[/C][/ROW]
[ROW][C]26[/C][C]8.74[/C][C]8.74765183345961[/C][C]-0.0076518334596134[/C][/ROW]
[ROW][C]27[/C][C]8.79[/C][C]8.74534090577855[/C][C]0.0446590942214495[/C][/ROW]
[ROW][C]28[/C][C]8.85[/C][C]8.80882838398783[/C][C]0.0411716160121713[/C][/ROW]
[ROW][C]29[/C][C]8.86[/C][C]8.88126261006173[/C][C]-0.0212626100617257[/C][/ROW]
[ROW][C]30[/C][C]8.87[/C][C]8.8848410962608[/C][C]-0.014841096260799[/C][/ROW]
[ROW][C]31[/C][C]8.92[/C][C]8.89035894170955[/C][C]0.0296410582904514[/C][/ROW]
[ROW][C]32[/C][C]8.96[/C][C]8.94931082787656[/C][C]0.0106891721234366[/C][/ROW]
[ROW][C]33[/C][C]8.97[/C][C]8.99253906119843[/C][C]-0.0225390611984313[/C][/ROW]
[ROW][C]34[/C][C]8.99[/C][C]8.99573204681377[/C][C]-0.00573204681376893[/C][/ROW]
[ROW][C]35[/C][C]8.98[/C][C]9.01400091325983[/C][C]-0.0340009132598293[/C][/ROW]
[ROW][C]36[/C][C]8.98[/C][C]8.99373230874193[/C][C]-0.0137323087419343[/C][/ROW]
[ROW][C]37[/C][C]9.01[/C][C]8.9895850187409[/C][C]0.0204149812591012[/C][/ROW]
[ROW][C]38[/C][C]9.01[/C][C]9.02575054044874[/C][C]-0.0157505404487406[/C][/ROW]
[ROW][C]39[/C][C]9.03[/C][C]9.02099372496042[/C][C]0.00900627503957452[/C][/ROW]
[ROW][C]40[/C][C]9.05[/C][C]9.04371370709308[/C][C]0.00628629290691762[/C][/ROW]
[ROW][C]41[/C][C]9.05[/C][C]9.06561222832548[/C][C]-0.0156122283254838[/C][/ROW]
[ROW][C]42[/C][C]9.05[/C][C]9.06089718443556[/C][C]-0.0108971844355636[/C][/ROW]
[ROW][C]43[/C][C]9.13[/C][C]9.05760612938442[/C][C]0.0723938706155831[/C][/ROW]
[ROW][C]44[/C][C]9.13[/C][C]9.1594697781985[/C][C]-0.0294697781985036[/C][/ROW]
[ROW][C]45[/C][C]9.13[/C][C]9.15056962027516[/C][C]-0.0205696202751557[/C][/ROW]
[ROW][C]46[/C][C]9.14[/C][C]9.14435739608945[/C][C]-0.00435739608944807[/C][/ROW]
[ROW][C]47[/C][C]9.16[/C][C]9.15304142034408[/C][C]0.00695857965592239[/C][/ROW]
[ROW][C]48[/C][C]9.16[/C][C]9.1751429786742[/C][C]-0.0151429786741986[/C][/ROW]
[ROW][C]49[/C][C]9.16[/C][C]9.17056965271557[/C][C]-0.010569652715569[/C][/ROW]
[ROW][C]50[/C][C]9.16[/C][C]9.16737751541037[/C][C]-0.0073775154103668[/C][/ROW]
[ROW][C]51[/C][C]9.22[/C][C]9.16514943443222[/C][C]0.0548505655677776[/C][/ROW]
[ROW][C]52[/C][C]9.22[/C][C]9.24171483551702[/C][C]-0.0217148355170185[/C][/ROW]
[ROW][C]53[/C][C]9.25[/C][C]9.23515674525658[/C][C]0.0148432547434236[/C][/ROW]
[ROW][C]54[/C][C]9.25[/C][C]9.26963955169045[/C][C]-0.019639551690446[/C][/ROW]
[ROW][C]55[/C][C]9.26[/C][C]9.26370821720902[/C][C]-0.00370821720902192[/C][/ROW]
[ROW][C]56[/C][C]9.26[/C][C]9.27258829976166[/C][C]-0.01258829976166[/C][/ROW]
[ROW][C]57[/C][C]9.29[/C][C]9.2687865115327[/C][C]0.0212134884673016[/C][/ROW]
[ROW][C]58[/C][C]9.28[/C][C]9.30519319013721[/C][C]-0.0251931901372107[/C][/ROW]
[ROW][C]59[/C][C]9.37[/C][C]9.28758460315349[/C][C]0.0824153968465051[/C][/ROW]
[ROW][C]60[/C][C]9.41[/C][C]9.40247484977525[/C][C]0.00752515022474576[/C][/ROW]
[ROW][C]61[/C][C]9.41[/C][C]9.44474751789464[/C][C]-0.0347475178946421[/C][/ROW]
[ROW][C]62[/C][C]9.45[/C][C]9.43425343155902[/C][C]0.0157465684409779[/C][/ROW]
[ROW][C]63[/C][C]9.49[/C][C]9.47900904746259[/C][C]0.0109909525374086[/C][/ROW]
[ROW][C]64[/C][C]9.49[/C][C]9.52232842138703[/C][C]-0.0323284213870263[/C][/ROW]
[ROW][C]65[/C][C]9.56[/C][C]9.51256492558401[/C][C]0.0474350744159953[/C][/ROW]
[ROW][C]66[/C][C]9.54[/C][C]9.59689077664961[/C][C]-0.0568907766496096[/C][/ROW]
[ROW][C]67[/C][C]9.55[/C][C]9.55970921209378[/C][C]-0.00970921209378162[/C][/ROW]
[ROW][C]68[/C][C]9.55[/C][C]9.56677693617491[/C][C]-0.0167769361749119[/C][/ROW]
[ROW][C]69[/C][C]9.57[/C][C]9.56171013925432[/C][C]0.00828986074567872[/C][/ROW]
[ROW][C]70[/C][C]9.57[/C][C]9.58421375734409[/C][C]-0.0142137573440859[/C][/ROW]
[ROW][C]71[/C][C]9.58[/C][C]9.57992106521066[/C][C]7.89347893395131e-05[/C][/ROW]
[ROW][C]72[/C][C]9.59[/C][C]9.58994490428016[/C][C]5.50957198353075e-05[/C][/ROW]
[ROW][C]73[/C][C]9.59[/C][C]9.59996154372021[/C][C]-0.00996154372020897[/C][/ROW]
[ROW][C]74[/C][C]9.59[/C][C]9.59695306121067[/C][C]-0.00695306121066963[/C][/ROW]
[ROW][C]75[/C][C]9.61[/C][C]9.59485316950436[/C][C]0.0151468304956346[/C][/ROW]
[ROW][C]76[/C][C]9.61[/C][C]9.61942765875031[/C][C]-0.00942765875030638[/C][/ROW]
[ROW][C]77[/C][C]9.62[/C][C]9.61658041466316[/C][C]0.00341958533683773[/C][/ROW]
[ROW][C]78[/C][C]9.62[/C][C]9.62761316249469[/C][C]-0.00761316249469246[/C][/ROW]
[ROW][C]79[/C][C]9.63[/C][C]9.6253139138189[/C][C]0.00468608618110267[/C][/ROW]
[ROW][C]80[/C][C]9.65[/C][C]9.63672915714965[/C][C]0.0132708428503463[/C][/ROW]
[ROW][C]81[/C][C]9.65[/C][C]9.66073707999008[/C][C]-0.0107370799900774[/C][/ROW]
[ROW][C]82[/C][C]9.68[/C][C]9.65749437802932[/C][C]0.0225056219706783[/C][/ROW]
[ROW][C]83[/C][C]9.73[/C][C]9.69429129344392[/C][C]0.0357087065560808[/C][/ROW]
[ROW][C]84[/C][C]9.73[/C][C]9.75507566804786[/C][C]-0.0250756680478581[/C][/ROW]
[ROW][C]85[/C][C]9.73[/C][C]9.74750257387131[/C][C]-0.0175025738713046[/C][/ROW]
[ROW][C]86[/C][C]9.74[/C][C]9.7422166273511[/C][C]-0.00221662735109796[/C][/ROW]
[ROW][C]87[/C][C]9.68[/C][C]9.7515471844612[/C][C]-0.0715471844611955[/C][/ROW]
[ROW][C]88[/C][C]9.68[/C][C]9.66993924305131[/C][C]0.0100607569486897[/C][/ROW]
[ROW][C]89[/C][C]9.74[/C][C]9.67297768891502[/C][C]0.0670223110849779[/C][/ROW]
[ROW][C]90[/C][C]9.74[/C][C]9.7532190748198[/C][C]-0.0132190748197996[/C][/ROW]
[ROW][C]91[/C][C]9.76[/C][C]9.74922678642508[/C][C]0.0107732135749181[/C][/ROW]
[ROW][C]92[/C][C]9.78[/C][C]9.77248040107779[/C][C]0.0075195989222081[/C][/ROW]
[ROW][C]93[/C][C]9.79[/C][C]9.79475139265014[/C][C]-0.00475139265014413[/C][/ROW]
[ROW][C]94[/C][C]9.81[/C][C]9.80331642613437[/C][C]0.00668357386563123[/C][/ROW]
[ROW][C]95[/C][C]9.84[/C][C]9.82533493005713[/C][C]0.0146650699428719[/C][/ROW]
[ROW][C]96[/C][C]9.84[/C][C]9.85976392295858[/C][C]-0.0197639229585782[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=278508&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=278508&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
38.268.27-0.00999999999999979
48.288.34697990332218-0.0669799033221778
58.288.34675132497176-0.0667513249717562
68.288.32659177949301-0.0465917794930064
78.298.31252061164694-0.0225206116469376
88.38.31571916920519-0.015719169205191
98.38.32097182813572-0.0209718281357176
108.318.31463813328766-0.00463813328766349
118.338.323237372194330.00676262780567427
128.338.34527975117125-0.0152797511712528
138.348.34066511859623-0.000665118596225867
148.488.350464246349940.129535753650057
158.598.529585296275730.0604147037242715
168.678.657831120876660.0121688791233385
178.678.74150624001798-0.0715062400179836
188.678.71991066422579-0.0499106642257914
198.718.704837161104170.00516283889583491
208.728.74639638836391-0.02639638836391
218.728.74842442388347-0.0284244238834734
228.728.73983997306952-0.0198399730695229
238.748.733848109393990.00615189060601296
248.748.75570603983214-0.0157060398321409
258.748.75096266396026-0.0109626639602602
268.748.74765183345961-0.0076518334596134
278.798.745340905778550.0446590942214495
288.858.808828383987830.0411716160121713
298.868.88126261006173-0.0212626100617257
308.878.8848410962608-0.014841096260799
318.928.890358941709550.0296410582904514
328.968.949310827876560.0106891721234366
338.978.99253906119843-0.0225390611984313
348.998.99573204681377-0.00573204681376893
358.989.01400091325983-0.0340009132598293
368.988.99373230874193-0.0137323087419343
379.018.98958501874090.0204149812591012
389.019.02575054044874-0.0157505404487406
399.039.020993724960420.00900627503957452
409.059.043713707093080.00628629290691762
419.059.06561222832548-0.0156122283254838
429.059.06089718443556-0.0108971844355636
439.139.057606129384420.0723938706155831
449.139.1594697781985-0.0294697781985036
459.139.15056962027516-0.0205696202751557
469.149.14435739608945-0.00435739608944807
479.169.153041420344080.00695857965592239
489.169.1751429786742-0.0151429786741986
499.169.17056965271557-0.010569652715569
509.169.16737751541037-0.0073775154103668
519.229.165149434432220.0548505655677776
529.229.24171483551702-0.0217148355170185
539.259.235156745256580.0148432547434236
549.259.26963955169045-0.019639551690446
559.269.26370821720902-0.00370821720902192
569.269.27258829976166-0.01258829976166
579.299.26878651153270.0212134884673016
589.289.30519319013721-0.0251931901372107
599.379.287584603153490.0824153968465051
609.419.402474849775250.00752515022474576
619.419.44474751789464-0.0347475178946421
629.459.434253431559020.0157465684409779
639.499.479009047462590.0109909525374086
649.499.52232842138703-0.0323284213870263
659.569.512564925584010.0474350744159953
669.549.59689077664961-0.0568907766496096
679.559.55970921209378-0.00970921209378162
689.559.56677693617491-0.0167769361749119
699.579.561710139254320.00828986074567872
709.579.58421375734409-0.0142137573440859
719.589.579921065210667.89347893395131e-05
729.599.589944904280165.50957198353075e-05
739.599.59996154372021-0.00996154372020897
749.599.59695306121067-0.00695306121066963
759.619.594853169504360.0151468304956346
769.619.61942765875031-0.00942765875030638
779.629.616580414663160.00341958533683773
789.629.62761316249469-0.00761316249469246
799.639.62531391381890.00468608618110267
809.659.636729157149650.0132708428503463
819.659.66073707999008-0.0107370799900774
829.689.657494378029320.0225056219706783
839.739.694291293443920.0357087065560808
849.739.75507566804786-0.0250756680478581
859.739.74750257387131-0.0175025738713046
869.749.7422166273511-0.00221662735109796
879.689.7515471844612-0.0715471844611955
889.689.669939243051310.0100607569486897
899.749.672977688915020.0670223110849779
909.749.7532190748198-0.0132190748197996
919.769.749226786425080.0107732135749181
929.789.772480401077790.0075195989222081
939.799.79475139265014-0.00475139265014413
949.819.803316426134370.00668357386563123
959.849.825334930057130.0146650699428719
969.849.85976392295858-0.0197639229585782






Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
979.853795027151789.791737681709169.91585237259441
989.867590054303579.765709559891759.96947054871539
999.881385081455359.7389488428911910.0238213200195
1009.895180108607139.7100342907521610.0803259264621
1019.908975135758929.6786387956345110.1393114758833
1029.92277016291079.6447087161113610.20083160971
1039.936565190062489.6082794780469210.264850902078
1049.950360217214279.5694174785568110.3313029558717
1059.964155244366059.5281985131820410.4001119755501
1069.977950271517839.4846990863173810.4712014567183
1079.991745298669629.4389928496940110.5444977476452
10810.00554032582149.3911492411636310.6199314104792

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
97 & 9.85379502715178 & 9.79173768170916 & 9.91585237259441 \tabularnewline
98 & 9.86759005430357 & 9.76570955989175 & 9.96947054871539 \tabularnewline
99 & 9.88138508145535 & 9.73894884289119 & 10.0238213200195 \tabularnewline
100 & 9.89518010860713 & 9.71003429075216 & 10.0803259264621 \tabularnewline
101 & 9.90897513575892 & 9.67863879563451 & 10.1393114758833 \tabularnewline
102 & 9.9227701629107 & 9.64470871611136 & 10.20083160971 \tabularnewline
103 & 9.93656519006248 & 9.60827947804692 & 10.264850902078 \tabularnewline
104 & 9.95036021721427 & 9.56941747855681 & 10.3313029558717 \tabularnewline
105 & 9.96415524436605 & 9.52819851318204 & 10.4001119755501 \tabularnewline
106 & 9.97795027151783 & 9.48469908631738 & 10.4712014567183 \tabularnewline
107 & 9.99174529866962 & 9.43899284969401 & 10.5444977476452 \tabularnewline
108 & 10.0055403258214 & 9.39114924116363 & 10.6199314104792 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=278508&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]97[/C][C]9.85379502715178[/C][C]9.79173768170916[/C][C]9.91585237259441[/C][/ROW]
[ROW][C]98[/C][C]9.86759005430357[/C][C]9.76570955989175[/C][C]9.96947054871539[/C][/ROW]
[ROW][C]99[/C][C]9.88138508145535[/C][C]9.73894884289119[/C][C]10.0238213200195[/C][/ROW]
[ROW][C]100[/C][C]9.89518010860713[/C][C]9.71003429075216[/C][C]10.0803259264621[/C][/ROW]
[ROW][C]101[/C][C]9.90897513575892[/C][C]9.67863879563451[/C][C]10.1393114758833[/C][/ROW]
[ROW][C]102[/C][C]9.9227701629107[/C][C]9.64470871611136[/C][C]10.20083160971[/C][/ROW]
[ROW][C]103[/C][C]9.93656519006248[/C][C]9.60827947804692[/C][C]10.264850902078[/C][/ROW]
[ROW][C]104[/C][C]9.95036021721427[/C][C]9.56941747855681[/C][C]10.3313029558717[/C][/ROW]
[ROW][C]105[/C][C]9.96415524436605[/C][C]9.52819851318204[/C][C]10.4001119755501[/C][/ROW]
[ROW][C]106[/C][C]9.97795027151783[/C][C]9.48469908631738[/C][C]10.4712014567183[/C][/ROW]
[ROW][C]107[/C][C]9.99174529866962[/C][C]9.43899284969401[/C][C]10.5444977476452[/C][/ROW]
[ROW][C]108[/C][C]10.0055403258214[/C][C]9.39114924116363[/C][C]10.6199314104792[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=278508&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=278508&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
979.853795027151789.791737681709169.91585237259441
989.867590054303579.765709559891759.96947054871539
999.881385081455359.7389488428911910.0238213200195
1009.895180108607139.7100342907521610.0803259264621
1019.908975135758929.6786387956345110.1393114758833
1029.92277016291079.6447087161113610.20083160971
1039.936565190062489.6082794780469210.264850902078
1049.950360217214279.5694174785568110.3313029558717
1059.964155244366059.5281985131820410.4001119755501
1069.977950271517839.4846990863173810.4712014567183
1079.991745298669629.4389928496940110.5444977476452
10810.00554032582149.3911492411636310.6199314104792


Figures (Output of Computation)

Input Parameters & R Code

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