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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 computationTue, 26 Apr 2016 13:43:13 +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/2016/Apr/26/t1461674649nzam6bhwmmjsybc.htm/, Retrieved Fri, 03 May 2024 22:10:25 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=294869, Retrieved Fri, 03 May 2024 22:10:25 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact115

Tree of Dependent Computations

Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [] [2016-04-26 12:43:13] [705d764c18df8303d824462e41ab6988] [Current]
- R PD    [Exponential Smoothing] [] [2016-05-25 21:43:10] [abb1dd46b01bd3b5295a6bb2c98eecd5]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
109,12
109,12
109,73
112,59
112,59
112,29
113,8
114,16
112,29
112,29
110,99
110,99
110,99
110,99
111,98
114,26
114,26
114,44
115,47
115,41
114,63
116,48
115,8
115,18
115,18
115,18
115,18
116,38
122,41
122,47
123,09
123,09
123,09
123,09
121,77
121,52
121,52
121,52
121,52
124,73
125,23
124,62
128,94
129,34
127,17
128,08
124,54
121,21
120,85
119,02
119,13
119,84
125,53
124,16
127,32
127,22
122,57
125,45
125,45
127,32
128,79
128,99
129,8
130,33
131,19
132,02
136,97
139,45
128,31
130,73
129,83
125,46
130,23
130,23
132,65
136,34
139,12
133,94
143,09
142,71
136,09
134,57
134,65
134,35

Tables (Output of Computation)





Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 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 & 2 seconds \tabularnewline
R Server & 'George Udny Yule' @ yule.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=294869&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]'George Udny Yule' @ yule.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=294869&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=294869&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 time2 seconds
R Server'George Udny Yule' @ yule.wessa.net






Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.616853138971561
beta0
gamma0.563228145644776

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.616853138971561 \tabularnewline
beta & 0 \tabularnewline
gamma & 0.563228145644776 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=294869&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]0.616853138971561[/C][/ROW]
[ROW][C]beta[/C][C]0[/C][/ROW]
[ROW][C]gamma[/C][C]0.563228145644776[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=294869&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=294869&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
alpha0.616853138971561
beta0
gamma0.563228145644776






Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
13110.99110.0092548076920.980745192307666
14110.99110.6790251385180.310974861481839
15111.98111.8977288717170.0822711282825992
16114.26114.1428559891980.117144010801837
17114.26114.0265778870590.233422112940772
18114.44114.1620262972180.277973702781608
19115.47116.121623162084-0.651623162083681
20115.41116.110295282879-0.700295282878699
21114.63113.8231105198480.806889480152449
22116.48114.3439707422362.13602925776439
23115.8114.4088816752421.39111832475774
24115.18115.29429196097-0.114291960969496
25115.18115.462729112458-0.282729112457943
26115.18115.208585520428-0.0285855204281091
27115.18116.168476307289-0.988476307288934
28116.38117.760635044616-1.38063504461586
29122.41116.7455399399885.66446006001173
30122.47120.2407553484872.2292446515131
31123.09123.203393659935-0.113393659935483
32123.09123.513570938947-0.423570938947478
33123.09121.7223335655381.36766643446242
34123.09122.8759379749830.214062025017
35121.77121.5945262814910.175473718509181
36121.52121.405196197140.114803802859498
37121.52121.67860320464-0.158603204640073
38121.52121.555871025901-0.0358710259014572
39121.52122.304124161734-0.78412416173397
40124.73123.937710660480.79228933951994
41125.23125.783315938096-0.553315938095892
42124.62124.70176032486-0.0817603248602268
43128.94125.7333087324793.20669126752085
44129.34128.024554844221.31544515578025
45127.17127.692582413552-0.522582413551561
46128.08127.4312340989080.648765901091622
47124.54126.409643534234-1.86964353423357
48121.21124.94568394001-3.73568394000957
49120.85122.784904511678-1.9349045116776
50119.02121.592940789161-2.57294078916124
51119.13120.61472212741-1.48472212741039
52119.84122.156331180438-2.31633118043824
53125.53121.7939937299013.73600627009864
54124.16123.4600812599230.699918740077095
55127.32125.6834557334461.63654426655418
56127.22126.5980225376780.62197746232205
57122.57125.441637695554-2.87163769555406
58125.45123.9840431640461.46595683595429
59125.45122.9230689130612.52693108693852
60127.32123.7684603418773.55153965812282
61128.79126.4914342372542.29856576274572
62128.99127.7732122903331.21678770966724
63129.8129.3675361524410.432463847558836
64130.33131.912306910213-1.58230691021339
65131.19133.308843585641-2.11884358564129
66132.02130.7081636594451.31183634055475
67136.97133.5111243675633.45887563243727
68139.45135.3308593958544.11914060414605
69128.31135.577791622255-7.2677916222552
70130.73132.344464720576-1.61446472057557
71129.83129.6122800473810.217719952618609
72125.46129.254336942907-3.79433694290701
73130.23127.1755931644493.05440683555133
74130.23128.6901674298731.53983257012652
75132.65130.3145061477342.33549385226601
76136.34133.5983812291982.74161877080158
77139.12137.5463609040871.57363909591314
78133.94137.963738137504-4.02373813750435
79143.09137.9387621189795.15123788102056
80142.71140.9449206966321.76507930336774
81136.09137.282453139115-1.19245313911495
82134.57139.016700686114-4.44670068611387
83134.65134.932826163535-0.282826163535105
84134.35133.4003213647690.949678635230924

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 110.99 & 110.009254807692 & 0.980745192307666 \tabularnewline
14 & 110.99 & 110.679025138518 & 0.310974861481839 \tabularnewline
15 & 111.98 & 111.897728871717 & 0.0822711282825992 \tabularnewline
16 & 114.26 & 114.142855989198 & 0.117144010801837 \tabularnewline
17 & 114.26 & 114.026577887059 & 0.233422112940772 \tabularnewline
18 & 114.44 & 114.162026297218 & 0.277973702781608 \tabularnewline
19 & 115.47 & 116.121623162084 & -0.651623162083681 \tabularnewline
20 & 115.41 & 116.110295282879 & -0.700295282878699 \tabularnewline
21 & 114.63 & 113.823110519848 & 0.806889480152449 \tabularnewline
22 & 116.48 & 114.343970742236 & 2.13602925776439 \tabularnewline
23 & 115.8 & 114.408881675242 & 1.39111832475774 \tabularnewline
24 & 115.18 & 115.29429196097 & -0.114291960969496 \tabularnewline
25 & 115.18 & 115.462729112458 & -0.282729112457943 \tabularnewline
26 & 115.18 & 115.208585520428 & -0.0285855204281091 \tabularnewline
27 & 115.18 & 116.168476307289 & -0.988476307288934 \tabularnewline
28 & 116.38 & 117.760635044616 & -1.38063504461586 \tabularnewline
29 & 122.41 & 116.745539939988 & 5.66446006001173 \tabularnewline
30 & 122.47 & 120.240755348487 & 2.2292446515131 \tabularnewline
31 & 123.09 & 123.203393659935 & -0.113393659935483 \tabularnewline
32 & 123.09 & 123.513570938947 & -0.423570938947478 \tabularnewline
33 & 123.09 & 121.722333565538 & 1.36766643446242 \tabularnewline
34 & 123.09 & 122.875937974983 & 0.214062025017 \tabularnewline
35 & 121.77 & 121.594526281491 & 0.175473718509181 \tabularnewline
36 & 121.52 & 121.40519619714 & 0.114803802859498 \tabularnewline
37 & 121.52 & 121.67860320464 & -0.158603204640073 \tabularnewline
38 & 121.52 & 121.555871025901 & -0.0358710259014572 \tabularnewline
39 & 121.52 & 122.304124161734 & -0.78412416173397 \tabularnewline
40 & 124.73 & 123.93771066048 & 0.79228933951994 \tabularnewline
41 & 125.23 & 125.783315938096 & -0.553315938095892 \tabularnewline
42 & 124.62 & 124.70176032486 & -0.0817603248602268 \tabularnewline
43 & 128.94 & 125.733308732479 & 3.20669126752085 \tabularnewline
44 & 129.34 & 128.02455484422 & 1.31544515578025 \tabularnewline
45 & 127.17 & 127.692582413552 & -0.522582413551561 \tabularnewline
46 & 128.08 & 127.431234098908 & 0.648765901091622 \tabularnewline
47 & 124.54 & 126.409643534234 & -1.86964353423357 \tabularnewline
48 & 121.21 & 124.94568394001 & -3.73568394000957 \tabularnewline
49 & 120.85 & 122.784904511678 & -1.9349045116776 \tabularnewline
50 & 119.02 & 121.592940789161 & -2.57294078916124 \tabularnewline
51 & 119.13 & 120.61472212741 & -1.48472212741039 \tabularnewline
52 & 119.84 & 122.156331180438 & -2.31633118043824 \tabularnewline
53 & 125.53 & 121.793993729901 & 3.73600627009864 \tabularnewline
54 & 124.16 & 123.460081259923 & 0.699918740077095 \tabularnewline
55 & 127.32 & 125.683455733446 & 1.63654426655418 \tabularnewline
56 & 127.22 & 126.598022537678 & 0.62197746232205 \tabularnewline
57 & 122.57 & 125.441637695554 & -2.87163769555406 \tabularnewline
58 & 125.45 & 123.984043164046 & 1.46595683595429 \tabularnewline
59 & 125.45 & 122.923068913061 & 2.52693108693852 \tabularnewline
60 & 127.32 & 123.768460341877 & 3.55153965812282 \tabularnewline
61 & 128.79 & 126.491434237254 & 2.29856576274572 \tabularnewline
62 & 128.99 & 127.773212290333 & 1.21678770966724 \tabularnewline
63 & 129.8 & 129.367536152441 & 0.432463847558836 \tabularnewline
64 & 130.33 & 131.912306910213 & -1.58230691021339 \tabularnewline
65 & 131.19 & 133.308843585641 & -2.11884358564129 \tabularnewline
66 & 132.02 & 130.708163659445 & 1.31183634055475 \tabularnewline
67 & 136.97 & 133.511124367563 & 3.45887563243727 \tabularnewline
68 & 139.45 & 135.330859395854 & 4.11914060414605 \tabularnewline
69 & 128.31 & 135.577791622255 & -7.2677916222552 \tabularnewline
70 & 130.73 & 132.344464720576 & -1.61446472057557 \tabularnewline
71 & 129.83 & 129.612280047381 & 0.217719952618609 \tabularnewline
72 & 125.46 & 129.254336942907 & -3.79433694290701 \tabularnewline
73 & 130.23 & 127.175593164449 & 3.05440683555133 \tabularnewline
74 & 130.23 & 128.690167429873 & 1.53983257012652 \tabularnewline
75 & 132.65 & 130.314506147734 & 2.33549385226601 \tabularnewline
76 & 136.34 & 133.598381229198 & 2.74161877080158 \tabularnewline
77 & 139.12 & 137.546360904087 & 1.57363909591314 \tabularnewline
78 & 133.94 & 137.963738137504 & -4.02373813750435 \tabularnewline
79 & 143.09 & 137.938762118979 & 5.15123788102056 \tabularnewline
80 & 142.71 & 140.944920696632 & 1.76507930336774 \tabularnewline
81 & 136.09 & 137.282453139115 & -1.19245313911495 \tabularnewline
82 & 134.57 & 139.016700686114 & -4.44670068611387 \tabularnewline
83 & 134.65 & 134.932826163535 & -0.282826163535105 \tabularnewline
84 & 134.35 & 133.400321364769 & 0.949678635230924 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=294869&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]110.99[/C][C]110.009254807692[/C][C]0.980745192307666[/C][/ROW]
[ROW][C]14[/C][C]110.99[/C][C]110.679025138518[/C][C]0.310974861481839[/C][/ROW]
[ROW][C]15[/C][C]111.98[/C][C]111.897728871717[/C][C]0.0822711282825992[/C][/ROW]
[ROW][C]16[/C][C]114.26[/C][C]114.142855989198[/C][C]0.117144010801837[/C][/ROW]
[ROW][C]17[/C][C]114.26[/C][C]114.026577887059[/C][C]0.233422112940772[/C][/ROW]
[ROW][C]18[/C][C]114.44[/C][C]114.162026297218[/C][C]0.277973702781608[/C][/ROW]
[ROW][C]19[/C][C]115.47[/C][C]116.121623162084[/C][C]-0.651623162083681[/C][/ROW]
[ROW][C]20[/C][C]115.41[/C][C]116.110295282879[/C][C]-0.700295282878699[/C][/ROW]
[ROW][C]21[/C][C]114.63[/C][C]113.823110519848[/C][C]0.806889480152449[/C][/ROW]
[ROW][C]22[/C][C]116.48[/C][C]114.343970742236[/C][C]2.13602925776439[/C][/ROW]
[ROW][C]23[/C][C]115.8[/C][C]114.408881675242[/C][C]1.39111832475774[/C][/ROW]
[ROW][C]24[/C][C]115.18[/C][C]115.29429196097[/C][C]-0.114291960969496[/C][/ROW]
[ROW][C]25[/C][C]115.18[/C][C]115.462729112458[/C][C]-0.282729112457943[/C][/ROW]
[ROW][C]26[/C][C]115.18[/C][C]115.208585520428[/C][C]-0.0285855204281091[/C][/ROW]
[ROW][C]27[/C][C]115.18[/C][C]116.168476307289[/C][C]-0.988476307288934[/C][/ROW]
[ROW][C]28[/C][C]116.38[/C][C]117.760635044616[/C][C]-1.38063504461586[/C][/ROW]
[ROW][C]29[/C][C]122.41[/C][C]116.745539939988[/C][C]5.66446006001173[/C][/ROW]
[ROW][C]30[/C][C]122.47[/C][C]120.240755348487[/C][C]2.2292446515131[/C][/ROW]
[ROW][C]31[/C][C]123.09[/C][C]123.203393659935[/C][C]-0.113393659935483[/C][/ROW]
[ROW][C]32[/C][C]123.09[/C][C]123.513570938947[/C][C]-0.423570938947478[/C][/ROW]
[ROW][C]33[/C][C]123.09[/C][C]121.722333565538[/C][C]1.36766643446242[/C][/ROW]
[ROW][C]34[/C][C]123.09[/C][C]122.875937974983[/C][C]0.214062025017[/C][/ROW]
[ROW][C]35[/C][C]121.77[/C][C]121.594526281491[/C][C]0.175473718509181[/C][/ROW]
[ROW][C]36[/C][C]121.52[/C][C]121.40519619714[/C][C]0.114803802859498[/C][/ROW]
[ROW][C]37[/C][C]121.52[/C][C]121.67860320464[/C][C]-0.158603204640073[/C][/ROW]
[ROW][C]38[/C][C]121.52[/C][C]121.555871025901[/C][C]-0.0358710259014572[/C][/ROW]
[ROW][C]39[/C][C]121.52[/C][C]122.304124161734[/C][C]-0.78412416173397[/C][/ROW]
[ROW][C]40[/C][C]124.73[/C][C]123.93771066048[/C][C]0.79228933951994[/C][/ROW]
[ROW][C]41[/C][C]125.23[/C][C]125.783315938096[/C][C]-0.553315938095892[/C][/ROW]
[ROW][C]42[/C][C]124.62[/C][C]124.70176032486[/C][C]-0.0817603248602268[/C][/ROW]
[ROW][C]43[/C][C]128.94[/C][C]125.733308732479[/C][C]3.20669126752085[/C][/ROW]
[ROW][C]44[/C][C]129.34[/C][C]128.02455484422[/C][C]1.31544515578025[/C][/ROW]
[ROW][C]45[/C][C]127.17[/C][C]127.692582413552[/C][C]-0.522582413551561[/C][/ROW]
[ROW][C]46[/C][C]128.08[/C][C]127.431234098908[/C][C]0.648765901091622[/C][/ROW]
[ROW][C]47[/C][C]124.54[/C][C]126.409643534234[/C][C]-1.86964353423357[/C][/ROW]
[ROW][C]48[/C][C]121.21[/C][C]124.94568394001[/C][C]-3.73568394000957[/C][/ROW]
[ROW][C]49[/C][C]120.85[/C][C]122.784904511678[/C][C]-1.9349045116776[/C][/ROW]
[ROW][C]50[/C][C]119.02[/C][C]121.592940789161[/C][C]-2.57294078916124[/C][/ROW]
[ROW][C]51[/C][C]119.13[/C][C]120.61472212741[/C][C]-1.48472212741039[/C][/ROW]
[ROW][C]52[/C][C]119.84[/C][C]122.156331180438[/C][C]-2.31633118043824[/C][/ROW]
[ROW][C]53[/C][C]125.53[/C][C]121.793993729901[/C][C]3.73600627009864[/C][/ROW]
[ROW][C]54[/C][C]124.16[/C][C]123.460081259923[/C][C]0.699918740077095[/C][/ROW]
[ROW][C]55[/C][C]127.32[/C][C]125.683455733446[/C][C]1.63654426655418[/C][/ROW]
[ROW][C]56[/C][C]127.22[/C][C]126.598022537678[/C][C]0.62197746232205[/C][/ROW]
[ROW][C]57[/C][C]122.57[/C][C]125.441637695554[/C][C]-2.87163769555406[/C][/ROW]
[ROW][C]58[/C][C]125.45[/C][C]123.984043164046[/C][C]1.46595683595429[/C][/ROW]
[ROW][C]59[/C][C]125.45[/C][C]122.923068913061[/C][C]2.52693108693852[/C][/ROW]
[ROW][C]60[/C][C]127.32[/C][C]123.768460341877[/C][C]3.55153965812282[/C][/ROW]
[ROW][C]61[/C][C]128.79[/C][C]126.491434237254[/C][C]2.29856576274572[/C][/ROW]
[ROW][C]62[/C][C]128.99[/C][C]127.773212290333[/C][C]1.21678770966724[/C][/ROW]
[ROW][C]63[/C][C]129.8[/C][C]129.367536152441[/C][C]0.432463847558836[/C][/ROW]
[ROW][C]64[/C][C]130.33[/C][C]131.912306910213[/C][C]-1.58230691021339[/C][/ROW]
[ROW][C]65[/C][C]131.19[/C][C]133.308843585641[/C][C]-2.11884358564129[/C][/ROW]
[ROW][C]66[/C][C]132.02[/C][C]130.708163659445[/C][C]1.31183634055475[/C][/ROW]
[ROW][C]67[/C][C]136.97[/C][C]133.511124367563[/C][C]3.45887563243727[/C][/ROW]
[ROW][C]68[/C][C]139.45[/C][C]135.330859395854[/C][C]4.11914060414605[/C][/ROW]
[ROW][C]69[/C][C]128.31[/C][C]135.577791622255[/C][C]-7.2677916222552[/C][/ROW]
[ROW][C]70[/C][C]130.73[/C][C]132.344464720576[/C][C]-1.61446472057557[/C][/ROW]
[ROW][C]71[/C][C]129.83[/C][C]129.612280047381[/C][C]0.217719952618609[/C][/ROW]
[ROW][C]72[/C][C]125.46[/C][C]129.254336942907[/C][C]-3.79433694290701[/C][/ROW]
[ROW][C]73[/C][C]130.23[/C][C]127.175593164449[/C][C]3.05440683555133[/C][/ROW]
[ROW][C]74[/C][C]130.23[/C][C]128.690167429873[/C][C]1.53983257012652[/C][/ROW]
[ROW][C]75[/C][C]132.65[/C][C]130.314506147734[/C][C]2.33549385226601[/C][/ROW]
[ROW][C]76[/C][C]136.34[/C][C]133.598381229198[/C][C]2.74161877080158[/C][/ROW]
[ROW][C]77[/C][C]139.12[/C][C]137.546360904087[/C][C]1.57363909591314[/C][/ROW]
[ROW][C]78[/C][C]133.94[/C][C]137.963738137504[/C][C]-4.02373813750435[/C][/ROW]
[ROW][C]79[/C][C]143.09[/C][C]137.938762118979[/C][C]5.15123788102056[/C][/ROW]
[ROW][C]80[/C][C]142.71[/C][C]140.944920696632[/C][C]1.76507930336774[/C][/ROW]
[ROW][C]81[/C][C]136.09[/C][C]137.282453139115[/C][C]-1.19245313911495[/C][/ROW]
[ROW][C]82[/C][C]134.57[/C][C]139.016700686114[/C][C]-4.44670068611387[/C][/ROW]
[ROW][C]83[/C][C]134.65[/C][C]134.932826163535[/C][C]-0.282826163535105[/C][/ROW]
[ROW][C]84[/C][C]134.35[/C][C]133.400321364769[/C][C]0.949678635230924[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=294869&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=294869&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
13110.99110.0092548076920.980745192307666
14110.99110.6790251385180.310974861481839
15111.98111.8977288717170.0822711282825992
16114.26114.1428559891980.117144010801837
17114.26114.0265778870590.233422112940772
18114.44114.1620262972180.277973702781608
19115.47116.121623162084-0.651623162083681
20115.41116.110295282879-0.700295282878699
21114.63113.8231105198480.806889480152449
22116.48114.3439707422362.13602925776439
23115.8114.4088816752421.39111832475774
24115.18115.29429196097-0.114291960969496
25115.18115.462729112458-0.282729112457943
26115.18115.208585520428-0.0285855204281091
27115.18116.168476307289-0.988476307288934
28116.38117.760635044616-1.38063504461586
29122.41116.7455399399885.66446006001173
30122.47120.2407553484872.2292446515131
31123.09123.203393659935-0.113393659935483
32123.09123.513570938947-0.423570938947478
33123.09121.7223335655381.36766643446242
34123.09122.8759379749830.214062025017
35121.77121.5945262814910.175473718509181
36121.52121.405196197140.114803802859498
37121.52121.67860320464-0.158603204640073
38121.52121.555871025901-0.0358710259014572
39121.52122.304124161734-0.78412416173397
40124.73123.937710660480.79228933951994
41125.23125.783315938096-0.553315938095892
42124.62124.70176032486-0.0817603248602268
43128.94125.7333087324793.20669126752085
44129.34128.024554844221.31544515578025
45127.17127.692582413552-0.522582413551561
46128.08127.4312340989080.648765901091622
47124.54126.409643534234-1.86964353423357
48121.21124.94568394001-3.73568394000957
49120.85122.784904511678-1.9349045116776
50119.02121.592940789161-2.57294078916124
51119.13120.61472212741-1.48472212741039
52119.84122.156331180438-2.31633118043824
53125.53121.7939937299013.73600627009864
54124.16123.4600812599230.699918740077095
55127.32125.6834557334461.63654426655418
56127.22126.5980225376780.62197746232205
57122.57125.441637695554-2.87163769555406
58125.45123.9840431640461.46595683595429
59125.45122.9230689130612.52693108693852
60127.32123.7684603418773.55153965812282
61128.79126.4914342372542.29856576274572
62128.99127.7732122903331.21678770966724
63129.8129.3675361524410.432463847558836
64130.33131.912306910213-1.58230691021339
65131.19133.308843585641-2.11884358564129
66132.02130.7081636594451.31183634055475
67136.97133.5111243675633.45887563243727
68139.45135.3308593958544.11914060414605
69128.31135.577791622255-7.2677916222552
70130.73132.344464720576-1.61446472057557
71129.83129.6122800473810.217719952618609
72125.46129.254336942907-3.79433694290701
73130.23127.1755931644493.05440683555133
74130.23128.6901674298731.53983257012652
75132.65130.3145061477342.33549385226601
76136.34133.5983812291982.74161877080158
77139.12137.5463609040871.57363909591314
78133.94137.963738137504-4.02373813750435
79143.09137.9387621189795.15123788102056
80142.71140.9449206966321.76507930336774
81136.09137.282453139115-1.19245313911495
82134.57139.016700686114-4.44670068611387
83134.65134.932826163535-0.282826163535105
84134.35133.4003213647690.949678635230924






Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
85135.725891203462131.356262091453140.09552031547
86135.029501267306129.895404998139140.163597536473
87135.875692416239130.07705202166141.674332810817
88137.806552174186131.412061080268144.201043268104
89139.8113067464132.871940617224146.750672875576
90138.050070816692130.605603864699145.494537768685
91142.487101829733134.569692270801150.404511388666
92141.584973190761133.221322071278149.948624310245
93136.195478096811127.408217660646144.982738532977
94137.963030426795128.771663178254147.154397675337
95137.520677538537127.942237278134147.099117798941
96136.428608367978126.478140854003146.379075881954

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
85 & 135.725891203462 & 131.356262091453 & 140.09552031547 \tabularnewline
86 & 135.029501267306 & 129.895404998139 & 140.163597536473 \tabularnewline
87 & 135.875692416239 & 130.07705202166 & 141.674332810817 \tabularnewline
88 & 137.806552174186 & 131.412061080268 & 144.201043268104 \tabularnewline
89 & 139.8113067464 & 132.871940617224 & 146.750672875576 \tabularnewline
90 & 138.050070816692 & 130.605603864699 & 145.494537768685 \tabularnewline
91 & 142.487101829733 & 134.569692270801 & 150.404511388666 \tabularnewline
92 & 141.584973190761 & 133.221322071278 & 149.948624310245 \tabularnewline
93 & 136.195478096811 & 127.408217660646 & 144.982738532977 \tabularnewline
94 & 137.963030426795 & 128.771663178254 & 147.154397675337 \tabularnewline
95 & 137.520677538537 & 127.942237278134 & 147.099117798941 \tabularnewline
96 & 136.428608367978 & 126.478140854003 & 146.379075881954 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=294869&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]135.725891203462[/C][C]131.356262091453[/C][C]140.09552031547[/C][/ROW]
[ROW][C]86[/C][C]135.029501267306[/C][C]129.895404998139[/C][C]140.163597536473[/C][/ROW]
[ROW][C]87[/C][C]135.875692416239[/C][C]130.07705202166[/C][C]141.674332810817[/C][/ROW]
[ROW][C]88[/C][C]137.806552174186[/C][C]131.412061080268[/C][C]144.201043268104[/C][/ROW]
[ROW][C]89[/C][C]139.8113067464[/C][C]132.871940617224[/C][C]146.750672875576[/C][/ROW]
[ROW][C]90[/C][C]138.050070816692[/C][C]130.605603864699[/C][C]145.494537768685[/C][/ROW]
[ROW][C]91[/C][C]142.487101829733[/C][C]134.569692270801[/C][C]150.404511388666[/C][/ROW]
[ROW][C]92[/C][C]141.584973190761[/C][C]133.221322071278[/C][C]149.948624310245[/C][/ROW]
[ROW][C]93[/C][C]136.195478096811[/C][C]127.408217660646[/C][C]144.982738532977[/C][/ROW]
[ROW][C]94[/C][C]137.963030426795[/C][C]128.771663178254[/C][C]147.154397675337[/C][/ROW]
[ROW][C]95[/C][C]137.520677538537[/C][C]127.942237278134[/C][C]147.099117798941[/C][/ROW]
[ROW][C]96[/C][C]136.428608367978[/C][C]126.478140854003[/C][C]146.379075881954[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=294869&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=294869&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
85135.725891203462131.356262091453140.09552031547
86135.029501267306129.895404998139140.163597536473
87135.875692416239130.07705202166141.674332810817
88137.806552174186131.412061080268144.201043268104
89139.8113067464132.871940617224146.750672875576
90138.050070816692130.605603864699145.494537768685
91142.487101829733134.569692270801150.404511388666
92141.584973190761133.221322071278149.948624310245
93136.195478096811127.408217660646144.982738532977
94137.963030426795128.771663178254147.154397675337
95137.520677538537127.942237278134147.099117798941
96136.428608367978126.478140854003146.379075881954


Figures (Output of Computation)

Input Parameters & R Code

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=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')