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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, 19 Jan 2010 04:49:31 -0700
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2010/Jan/19/t1263901879s82qpaqipea7xbt.htm/, Retrieved Thu, 02 May 2024 06:11:04 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=72285, Retrieved Thu, 02 May 2024 06:11:04 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywordsKDGP2W62
Estimated Impact222

Tree of Dependent Computations

Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [Classical Decomposition] [Nieuwe personenwa...] [2009-01-13 17:37:29] [74be16979710d4c4e7c6647856088456]
-       [Classical Decomposition] [roger dirkx oefen...] [2009-01-14 16:39:03] [74be16979710d4c4e7c6647856088456]
- RMP     [Exponential Smoothing] [roger dirkx oef 10] [2009-01-24 20:53:30] [74be16979710d4c4e7c6647856088456]
-           [Exponential Smoothing] [Dennis Collin oef 10] [2009-01-25 12:25:31] [2097edf1f094fab6879a8cb46df74ec2]
-             [Exponential Smoothing] [Dennis Collin oef 2] [2009-01-25 12:34:26] [2097edf1f094fab6879a8cb46df74ec2]
-               [Exponential Smoothing] [Dennis Collin oef 10] [2009-01-25 12:39:06] [2097edf1f094fab6879a8cb46df74ec2]
- RM D              [Exponential Smoothing] [exponential smoot...] [2010-01-19 11:49:31] [d41d8cd98f00b204e9800998ecf8427e] [Current]
-   PD                [Exponential Smoothing] [] [2010-06-05 14:15:29] [74be16979710d4c4e7c6647856088456]
-   PD                [Exponential Smoothing] [OPGAVE 10 oef 2 s...] [2010-06-06 16:48:19] [74be16979710d4c4e7c6647856088456]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
76.3
71
85.9
109
83.4
101.3
81.6
84.8
88
88.4
85.2
139.5
85.3
79.4
131
91.4
88.2
113.2
81.9
89
95.7
93.2
98
140.5
93
82.1
86.3
84.8
85.7
110.8
87.4
100.4
100.4
99.4
108
161.7
109.3
99.9
110.3
97.5
102.4
122.3
104.4
122.7
127.3
128.4
125.3
187.1
131.4
125.6
142.9
116.6
129.7
155.4
138.7
167.7
155.8
157.1
159.9
244.6
154.3
143.2
147.3
155.1
152.2
166.5
161.2
180.1
169.2
164.5
166.2
267.3

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'Gwilym Jenkins' @ 72.249.127.135

\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 & 'Gwilym Jenkins' @ 72.249.127.135 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=72285&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]'Gwilym Jenkins' @ 72.249.127.135[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=72285&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=72285&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'Gwilym Jenkins' @ 72.249.127.135






Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.246690113402272
beta0.0345331971607616
gamma0.853252708606075

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.246690113402272 \tabularnewline
beta & 0.0345331971607616 \tabularnewline
gamma & 0.853252708606075 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=72285&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]0.246690113402272[/C][/ROW]
[ROW][C]beta[/C][C]0.0345331971607616[/C][/ROW]
[ROW][C]gamma[/C][C]0.853252708606075[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=72285&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=72285&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
alpha0.246690113402272
beta0.0345331971607616
gamma0.853252708606075






Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
1385.381.62314004185263.67685995814739
1479.477.17857104773022.22142895226980
15131128.4454029141292.55459708587060
1691.490.18957971241191.21042028758814
1788.287.26565128090640.934348719093578
18113.2112.4154991859510.784500814048712
1981.988.2360701997203-6.3360701997203
208989.9336033969772-0.93360339697719
2195.791.46175999592354.23824000407647
2293.292.41505318735060.784946812649366
239890.3448853425647.65511465743604
24140.5150.981461409249-10.4814614092488
259393.4541160966085-0.454116096608516
2682.186.4078620284123-4.30786202841229
2786.3140.160185743814-53.8601857438139
2884.887.9587463038027-3.1587463038027
2985.783.58750344798422.11249655201576
30110.8107.3843403738943.41565962610629
3187.480.1608757359957.23912426400507
32100.488.40545778937311.9945422106271
33100.496.41008076874693.98991923125315
3499.494.89614140540134.50385859459875
3510898.01431289736519.98568710263487
36161.7148.91672455755812.7832754424425
37109.3100.0216460581069.27835394189353
3899.991.99624315398627.9037568460138
39110.3116.142568305204-5.84256830520438
4097.5107.273099402642-9.77309940264182
41102.4105.009987240767-2.60998724076696
42122.3134.260094240738-11.9600942407381
43104.4100.9983574402433.40164255975670
44122.7112.9736399410459.7263600589545
45127.3115.42405515432511.8759448456752
46128.4115.98805389153912.4119461084614
47125.3125.821040363661-0.521040363661271
48187.1184.8666648007082.2333351992919
49131.4122.5846769033018.81532309669932
50125.6111.84043225349813.7595677465016
51142.9130.87620754275612.0237924572444
52116.6121.904635867697-5.30463586769743
53129.7126.6917765207553.00822347924517
54155.4157.269692224559-1.86969222455920
55138.7131.2717853684787.42821463152194
56167.7152.87680754984414.8231924501557
57155.8158.632476671689-2.83247667168857
58157.1155.4997248113341.60027518866619
59159.9154.2522753820015.6477246179989
60244.6231.73717584819212.8628241518083
61154.3161.44561212402-7.14561212402018
62143.2147.629675817796-4.42967581779587
63147.3163.542011807314-16.2420118073143
64155.1133.37211904069121.7278809593095
65152.2152.322602343346-0.122602343345761
66166.5183.765220364102-17.2652203641022
67161.2156.8219306690214.37806933097886
68180.1185.651291455172-5.55129145517157
69169.2173.796727071584-4.59672707158441
70164.5172.901609962885-8.40160996288535
71166.2171.560705224965-5.36070522496462
72267.3255.88824073613311.4117592638675

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 85.3 & 81.6231400418526 & 3.67685995814739 \tabularnewline
14 & 79.4 & 77.1785710477302 & 2.22142895226980 \tabularnewline
15 & 131 & 128.445402914129 & 2.55459708587060 \tabularnewline
16 & 91.4 & 90.1895797124119 & 1.21042028758814 \tabularnewline
17 & 88.2 & 87.2656512809064 & 0.934348719093578 \tabularnewline
18 & 113.2 & 112.415499185951 & 0.784500814048712 \tabularnewline
19 & 81.9 & 88.2360701997203 & -6.3360701997203 \tabularnewline
20 & 89 & 89.9336033969772 & -0.93360339697719 \tabularnewline
21 & 95.7 & 91.4617599959235 & 4.23824000407647 \tabularnewline
22 & 93.2 & 92.4150531873506 & 0.784946812649366 \tabularnewline
23 & 98 & 90.344885342564 & 7.65511465743604 \tabularnewline
24 & 140.5 & 150.981461409249 & -10.4814614092488 \tabularnewline
25 & 93 & 93.4541160966085 & -0.454116096608516 \tabularnewline
26 & 82.1 & 86.4078620284123 & -4.30786202841229 \tabularnewline
27 & 86.3 & 140.160185743814 & -53.8601857438139 \tabularnewline
28 & 84.8 & 87.9587463038027 & -3.1587463038027 \tabularnewline
29 & 85.7 & 83.5875034479842 & 2.11249655201576 \tabularnewline
30 & 110.8 & 107.384340373894 & 3.41565962610629 \tabularnewline
31 & 87.4 & 80.160875735995 & 7.23912426400507 \tabularnewline
32 & 100.4 & 88.405457789373 & 11.9945422106271 \tabularnewline
33 & 100.4 & 96.4100807687469 & 3.98991923125315 \tabularnewline
34 & 99.4 & 94.8961414054013 & 4.50385859459875 \tabularnewline
35 & 108 & 98.0143128973651 & 9.98568710263487 \tabularnewline
36 & 161.7 & 148.916724557558 & 12.7832754424425 \tabularnewline
37 & 109.3 & 100.021646058106 & 9.27835394189353 \tabularnewline
38 & 99.9 & 91.9962431539862 & 7.9037568460138 \tabularnewline
39 & 110.3 & 116.142568305204 & -5.84256830520438 \tabularnewline
40 & 97.5 & 107.273099402642 & -9.77309940264182 \tabularnewline
41 & 102.4 & 105.009987240767 & -2.60998724076696 \tabularnewline
42 & 122.3 & 134.260094240738 & -11.9600942407381 \tabularnewline
43 & 104.4 & 100.998357440243 & 3.40164255975670 \tabularnewline
44 & 122.7 & 112.973639941045 & 9.7263600589545 \tabularnewline
45 & 127.3 & 115.424055154325 & 11.8759448456752 \tabularnewline
46 & 128.4 & 115.988053891539 & 12.4119461084614 \tabularnewline
47 & 125.3 & 125.821040363661 & -0.521040363661271 \tabularnewline
48 & 187.1 & 184.866664800708 & 2.2333351992919 \tabularnewline
49 & 131.4 & 122.584676903301 & 8.81532309669932 \tabularnewline
50 & 125.6 & 111.840432253498 & 13.7595677465016 \tabularnewline
51 & 142.9 & 130.876207542756 & 12.0237924572444 \tabularnewline
52 & 116.6 & 121.904635867697 & -5.30463586769743 \tabularnewline
53 & 129.7 & 126.691776520755 & 3.00822347924517 \tabularnewline
54 & 155.4 & 157.269692224559 & -1.86969222455920 \tabularnewline
55 & 138.7 & 131.271785368478 & 7.42821463152194 \tabularnewline
56 & 167.7 & 152.876807549844 & 14.8231924501557 \tabularnewline
57 & 155.8 & 158.632476671689 & -2.83247667168857 \tabularnewline
58 & 157.1 & 155.499724811334 & 1.60027518866619 \tabularnewline
59 & 159.9 & 154.252275382001 & 5.6477246179989 \tabularnewline
60 & 244.6 & 231.737175848192 & 12.8628241518083 \tabularnewline
61 & 154.3 & 161.44561212402 & -7.14561212402018 \tabularnewline
62 & 143.2 & 147.629675817796 & -4.42967581779587 \tabularnewline
63 & 147.3 & 163.542011807314 & -16.2420118073143 \tabularnewline
64 & 155.1 & 133.372119040691 & 21.7278809593095 \tabularnewline
65 & 152.2 & 152.322602343346 & -0.122602343345761 \tabularnewline
66 & 166.5 & 183.765220364102 & -17.2652203641022 \tabularnewline
67 & 161.2 & 156.821930669021 & 4.37806933097886 \tabularnewline
68 & 180.1 & 185.651291455172 & -5.55129145517157 \tabularnewline
69 & 169.2 & 173.796727071584 & -4.59672707158441 \tabularnewline
70 & 164.5 & 172.901609962885 & -8.40160996288535 \tabularnewline
71 & 166.2 & 171.560705224965 & -5.36070522496462 \tabularnewline
72 & 267.3 & 255.888240736133 & 11.4117592638675 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=72285&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]85.3[/C][C]81.6231400418526[/C][C]3.67685995814739[/C][/ROW]
[ROW][C]14[/C][C]79.4[/C][C]77.1785710477302[/C][C]2.22142895226980[/C][/ROW]
[ROW][C]15[/C][C]131[/C][C]128.445402914129[/C][C]2.55459708587060[/C][/ROW]
[ROW][C]16[/C][C]91.4[/C][C]90.1895797124119[/C][C]1.21042028758814[/C][/ROW]
[ROW][C]17[/C][C]88.2[/C][C]87.2656512809064[/C][C]0.934348719093578[/C][/ROW]
[ROW][C]18[/C][C]113.2[/C][C]112.415499185951[/C][C]0.784500814048712[/C][/ROW]
[ROW][C]19[/C][C]81.9[/C][C]88.2360701997203[/C][C]-6.3360701997203[/C][/ROW]
[ROW][C]20[/C][C]89[/C][C]89.9336033969772[/C][C]-0.93360339697719[/C][/ROW]
[ROW][C]21[/C][C]95.7[/C][C]91.4617599959235[/C][C]4.23824000407647[/C][/ROW]
[ROW][C]22[/C][C]93.2[/C][C]92.4150531873506[/C][C]0.784946812649366[/C][/ROW]
[ROW][C]23[/C][C]98[/C][C]90.344885342564[/C][C]7.65511465743604[/C][/ROW]
[ROW][C]24[/C][C]140.5[/C][C]150.981461409249[/C][C]-10.4814614092488[/C][/ROW]
[ROW][C]25[/C][C]93[/C][C]93.4541160966085[/C][C]-0.454116096608516[/C][/ROW]
[ROW][C]26[/C][C]82.1[/C][C]86.4078620284123[/C][C]-4.30786202841229[/C][/ROW]
[ROW][C]27[/C][C]86.3[/C][C]140.160185743814[/C][C]-53.8601857438139[/C][/ROW]
[ROW][C]28[/C][C]84.8[/C][C]87.9587463038027[/C][C]-3.1587463038027[/C][/ROW]
[ROW][C]29[/C][C]85.7[/C][C]83.5875034479842[/C][C]2.11249655201576[/C][/ROW]
[ROW][C]30[/C][C]110.8[/C][C]107.384340373894[/C][C]3.41565962610629[/C][/ROW]
[ROW][C]31[/C][C]87.4[/C][C]80.160875735995[/C][C]7.23912426400507[/C][/ROW]
[ROW][C]32[/C][C]100.4[/C][C]88.405457789373[/C][C]11.9945422106271[/C][/ROW]
[ROW][C]33[/C][C]100.4[/C][C]96.4100807687469[/C][C]3.98991923125315[/C][/ROW]
[ROW][C]34[/C][C]99.4[/C][C]94.8961414054013[/C][C]4.50385859459875[/C][/ROW]
[ROW][C]35[/C][C]108[/C][C]98.0143128973651[/C][C]9.98568710263487[/C][/ROW]
[ROW][C]36[/C][C]161.7[/C][C]148.916724557558[/C][C]12.7832754424425[/C][/ROW]
[ROW][C]37[/C][C]109.3[/C][C]100.021646058106[/C][C]9.27835394189353[/C][/ROW]
[ROW][C]38[/C][C]99.9[/C][C]91.9962431539862[/C][C]7.9037568460138[/C][/ROW]
[ROW][C]39[/C][C]110.3[/C][C]116.142568305204[/C][C]-5.84256830520438[/C][/ROW]
[ROW][C]40[/C][C]97.5[/C][C]107.273099402642[/C][C]-9.77309940264182[/C][/ROW]
[ROW][C]41[/C][C]102.4[/C][C]105.009987240767[/C][C]-2.60998724076696[/C][/ROW]
[ROW][C]42[/C][C]122.3[/C][C]134.260094240738[/C][C]-11.9600942407381[/C][/ROW]
[ROW][C]43[/C][C]104.4[/C][C]100.998357440243[/C][C]3.40164255975670[/C][/ROW]
[ROW][C]44[/C][C]122.7[/C][C]112.973639941045[/C][C]9.7263600589545[/C][/ROW]
[ROW][C]45[/C][C]127.3[/C][C]115.424055154325[/C][C]11.8759448456752[/C][/ROW]
[ROW][C]46[/C][C]128.4[/C][C]115.988053891539[/C][C]12.4119461084614[/C][/ROW]
[ROW][C]47[/C][C]125.3[/C][C]125.821040363661[/C][C]-0.521040363661271[/C][/ROW]
[ROW][C]48[/C][C]187.1[/C][C]184.866664800708[/C][C]2.2333351992919[/C][/ROW]
[ROW][C]49[/C][C]131.4[/C][C]122.584676903301[/C][C]8.81532309669932[/C][/ROW]
[ROW][C]50[/C][C]125.6[/C][C]111.840432253498[/C][C]13.7595677465016[/C][/ROW]
[ROW][C]51[/C][C]142.9[/C][C]130.876207542756[/C][C]12.0237924572444[/C][/ROW]
[ROW][C]52[/C][C]116.6[/C][C]121.904635867697[/C][C]-5.30463586769743[/C][/ROW]
[ROW][C]53[/C][C]129.7[/C][C]126.691776520755[/C][C]3.00822347924517[/C][/ROW]
[ROW][C]54[/C][C]155.4[/C][C]157.269692224559[/C][C]-1.86969222455920[/C][/ROW]
[ROW][C]55[/C][C]138.7[/C][C]131.271785368478[/C][C]7.42821463152194[/C][/ROW]
[ROW][C]56[/C][C]167.7[/C][C]152.876807549844[/C][C]14.8231924501557[/C][/ROW]
[ROW][C]57[/C][C]155.8[/C][C]158.632476671689[/C][C]-2.83247667168857[/C][/ROW]
[ROW][C]58[/C][C]157.1[/C][C]155.499724811334[/C][C]1.60027518866619[/C][/ROW]
[ROW][C]59[/C][C]159.9[/C][C]154.252275382001[/C][C]5.6477246179989[/C][/ROW]
[ROW][C]60[/C][C]244.6[/C][C]231.737175848192[/C][C]12.8628241518083[/C][/ROW]
[ROW][C]61[/C][C]154.3[/C][C]161.44561212402[/C][C]-7.14561212402018[/C][/ROW]
[ROW][C]62[/C][C]143.2[/C][C]147.629675817796[/C][C]-4.42967581779587[/C][/ROW]
[ROW][C]63[/C][C]147.3[/C][C]163.542011807314[/C][C]-16.2420118073143[/C][/ROW]
[ROW][C]64[/C][C]155.1[/C][C]133.372119040691[/C][C]21.7278809593095[/C][/ROW]
[ROW][C]65[/C][C]152.2[/C][C]152.322602343346[/C][C]-0.122602343345761[/C][/ROW]
[ROW][C]66[/C][C]166.5[/C][C]183.765220364102[/C][C]-17.2652203641022[/C][/ROW]
[ROW][C]67[/C][C]161.2[/C][C]156.821930669021[/C][C]4.37806933097886[/C][/ROW]
[ROW][C]68[/C][C]180.1[/C][C]185.651291455172[/C][C]-5.55129145517157[/C][/ROW]
[ROW][C]69[/C][C]169.2[/C][C]173.796727071584[/C][C]-4.59672707158441[/C][/ROW]
[ROW][C]70[/C][C]164.5[/C][C]172.901609962885[/C][C]-8.40160996288535[/C][/ROW]
[ROW][C]71[/C][C]166.2[/C][C]171.560705224965[/C][C]-5.36070522496462[/C][/ROW]
[ROW][C]72[/C][C]267.3[/C][C]255.888240736133[/C][C]11.4117592638675[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=72285&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=72285&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
1385.381.62314004185263.67685995814739
1479.477.17857104773022.22142895226980
15131128.4454029141292.55459708587060
1691.490.18957971241191.21042028758814
1788.287.26565128090640.934348719093578
18113.2112.4154991859510.784500814048712
1981.988.2360701997203-6.3360701997203
208989.9336033969772-0.93360339697719
2195.791.46175999592354.23824000407647
2293.292.41505318735060.784946812649366
239890.3448853425647.65511465743604
24140.5150.981461409249-10.4814614092488
259393.4541160966085-0.454116096608516
2682.186.4078620284123-4.30786202841229
2786.3140.160185743814-53.8601857438139
2884.887.9587463038027-3.1587463038027
2985.783.58750344798422.11249655201576
30110.8107.3843403738943.41565962610629
3187.480.1608757359957.23912426400507
32100.488.40545778937311.9945422106271
33100.496.41008076874693.98991923125315
3499.494.89614140540134.50385859459875
3510898.01431289736519.98568710263487
36161.7148.91672455755812.7832754424425
37109.3100.0216460581069.27835394189353
3899.991.99624315398627.9037568460138
39110.3116.142568305204-5.84256830520438
4097.5107.273099402642-9.77309940264182
41102.4105.009987240767-2.60998724076696
42122.3134.260094240738-11.9600942407381
43104.4100.9983574402433.40164255975670
44122.7112.9736399410459.7263600589545
45127.3115.42405515432511.8759448456752
46128.4115.98805389153912.4119461084614
47125.3125.821040363661-0.521040363661271
48187.1184.8666648007082.2333351992919
49131.4122.5846769033018.81532309669932
50125.6111.84043225349813.7595677465016
51142.9130.87620754275612.0237924572444
52116.6121.904635867697-5.30463586769743
53129.7126.6917765207553.00822347924517
54155.4157.269692224559-1.86969222455920
55138.7131.2717853684787.42821463152194
56167.7152.87680754984414.8231924501557
57155.8158.632476671689-2.83247667168857
58157.1155.4997248113341.60027518866619
59159.9154.2522753820015.6477246179989
60244.6231.73717584819212.8628241518083
61154.3161.44561212402-7.14561212402018
62143.2147.629675817796-4.42967581779587
63147.3163.542011807314-16.2420118073143
64155.1133.37211904069121.7278809593095
65152.2152.322602343346-0.122602343345761
66166.5183.765220364102-17.2652203641022
67161.2156.8219306690214.37806933097886
68180.1185.651291455172-5.55129145517157
69169.2173.796727071584-4.59672707158441
70164.5172.901609962885-8.40160996288535
71166.2171.560705224965-5.36070522496462
72267.3255.88824073613311.4117592638675






Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
73166.475390173274147.757267638598185.193512707950
74155.121582977313135.755966874575174.487199080051
75164.751956344182144.462586520229185.041326168136
76162.076288326031141.095829861594183.056746790468
77161.298247363775139.575673267784183.020821459766
78182.366241027696158.923520360589205.808961694803
79172.643077140927148.918033160368196.368121121486
80195.307417356729169.395943421752221.218891291705
81184.411287061899158.430042640031210.392531483768
82181.772756403171155.173233321444208.372279484898
83184.58422612996156.94118569666212.227266563260
84291.100628146095250.789083433606331.412172858583

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
73 & 166.475390173274 & 147.757267638598 & 185.193512707950 \tabularnewline
74 & 155.121582977313 & 135.755966874575 & 174.487199080051 \tabularnewline
75 & 164.751956344182 & 144.462586520229 & 185.041326168136 \tabularnewline
76 & 162.076288326031 & 141.095829861594 & 183.056746790468 \tabularnewline
77 & 161.298247363775 & 139.575673267784 & 183.020821459766 \tabularnewline
78 & 182.366241027696 & 158.923520360589 & 205.808961694803 \tabularnewline
79 & 172.643077140927 & 148.918033160368 & 196.368121121486 \tabularnewline
80 & 195.307417356729 & 169.395943421752 & 221.218891291705 \tabularnewline
81 & 184.411287061899 & 158.430042640031 & 210.392531483768 \tabularnewline
82 & 181.772756403171 & 155.173233321444 & 208.372279484898 \tabularnewline
83 & 184.58422612996 & 156.94118569666 & 212.227266563260 \tabularnewline
84 & 291.100628146095 & 250.789083433606 & 331.412172858583 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=72285&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]73[/C][C]166.475390173274[/C][C]147.757267638598[/C][C]185.193512707950[/C][/ROW]
[ROW][C]74[/C][C]155.121582977313[/C][C]135.755966874575[/C][C]174.487199080051[/C][/ROW]
[ROW][C]75[/C][C]164.751956344182[/C][C]144.462586520229[/C][C]185.041326168136[/C][/ROW]
[ROW][C]76[/C][C]162.076288326031[/C][C]141.095829861594[/C][C]183.056746790468[/C][/ROW]
[ROW][C]77[/C][C]161.298247363775[/C][C]139.575673267784[/C][C]183.020821459766[/C][/ROW]
[ROW][C]78[/C][C]182.366241027696[/C][C]158.923520360589[/C][C]205.808961694803[/C][/ROW]
[ROW][C]79[/C][C]172.643077140927[/C][C]148.918033160368[/C][C]196.368121121486[/C][/ROW]
[ROW][C]80[/C][C]195.307417356729[/C][C]169.395943421752[/C][C]221.218891291705[/C][/ROW]
[ROW][C]81[/C][C]184.411287061899[/C][C]158.430042640031[/C][C]210.392531483768[/C][/ROW]
[ROW][C]82[/C][C]181.772756403171[/C][C]155.173233321444[/C][C]208.372279484898[/C][/ROW]
[ROW][C]83[/C][C]184.58422612996[/C][C]156.94118569666[/C][C]212.227266563260[/C][/ROW]
[ROW][C]84[/C][C]291.100628146095[/C][C]250.789083433606[/C][C]331.412172858583[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=72285&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=72285&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
73166.475390173274147.757267638598185.193512707950
74155.121582977313135.755966874575174.487199080051
75164.751956344182144.462586520229185.041326168136
76162.076288326031141.095829861594183.056746790468
77161.298247363775139.575673267784183.020821459766
78182.366241027696158.923520360589205.808961694803
79172.643077140927148.918033160368196.368121121486
80195.307417356729169.395943421752221.218891291705
81184.411287061899158.430042640031210.392531483768
82181.772756403171155.173233321444208.372279484898
83184.58422612996156.94118569666212.227266563260
84291.100628146095250.789083433606331.412172858583


Figures (Output of Computation)

Input Parameters & R Code

Parameters (Session):
par1 = 12 ; par2 = Triple ; par3 = multiplicative ;
Parameters (R input):
par1 = 12 ; par2 = Triple ; 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')