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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 18:44:48 +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/t1461692706w5138of8t4d9e9v.htm/, Retrieved Fri, 03 May 2024 23:53:34 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=294937, Retrieved Fri, 03 May 2024 23:53:34 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact108

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 17:44:48] [98ac3b2d1325a88ddcc6e107efd9e1d0] [Current]
- R P     [Exponential Smoothing] [] [2016-04-26 17:47:31] [dfa7ada218158d619493607d1a8bcc6c]
- R P     [Exponential Smoothing] [] [2016-04-26 17:48:25] [dfa7ada218158d619493607d1a8bcc6c]
- R PD    [Exponential Smoothing] [] [2016-04-26 17:49:30] [dfa7ada218158d619493607d1a8bcc6c]
- R  D    [Exponential Smoothing] [] [2016-04-26 17:50:48] [dfa7ada218158d619493607d1a8bcc6c]
- R PD    [Exponential Smoothing] [] [2016-04-26 17:52:06] [dfa7ada218158d619493607d1a8bcc6c]
- R PD    [Exponential Smoothing] [] [2016-04-26 17:53:52] [dfa7ada218158d619493607d1a8bcc6c]
- R PD    [Exponential Smoothing] [] [2016-04-26 17:56:12] [dfa7ada218158d619493607d1a8bcc6c]
- R P       [Exponential Smoothing] [] [2016-05-25 08:15:19] [dfa7ada218158d619493607d1a8bcc6c]
- RMPD    [Classical Decomposition] [] [2016-04-26 17:58:08] [dfa7ada218158d619493607d1a8bcc6c]
- RMP     [Standard Deviation-Mean Plot] [] [2016-04-26 17:59:08] [dfa7ada218158d619493607d1a8bcc6c]
- RMPD    [Classical Decomposition] [] [2016-04-26 18:02:37] [dfa7ada218158d619493607d1a8bcc6c]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
84.51
84.54
84.27
84.47
84.25
84.33
84.29
84.53
84.01
84.18
84.08
83.44
83.61
83.89
83.4
82.96
82.76
83.35
87.78
88.99
88.92
88.91
89.79
90.54
93.15
92.79
93.21
95.35
100.91
103.69
104.04
104.16
104.71
105.18
104.92
104.83
104.9
105.05
104.6
103.21
102.52
101.09
101.19
102.34
102.62
102.47
101.82
101.86
101.54
101.98
101.23
100.4
99.94
99.94
100
98.8
99.07
99.46
99.18
98.47
97.12
96.91
96.09
97.17
96.8
97.13
99.9
100.56
100.84
99.81
100.44
100.07
101.32
103.98
104.81
106.23
106.48
107.59
107.16
107.54
107.1
106.38
106.64
106.13

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'Herman Ole Andreas Wold' @ wold.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 & 'Herman Ole Andreas Wold' @ wold.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=294937&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]'Herman Ole Andreas Wold' @ wold.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=294937&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=294937&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'Herman Ole Andreas Wold' @ wold.wessa.net






Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.939622928582403
beta0.214033550366
gamma1

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.939622928582403 \tabularnewline
beta & 0.214033550366 \tabularnewline
gamma & 1 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=294937&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]0.939622928582403[/C][/ROW]
[ROW][C]beta[/C][C]0.214033550366[/C][/ROW]
[ROW][C]gamma[/C][C]1[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=294937&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=294937&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
alpha0.939622928582403
beta0.214033550366
gamma1






Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
1383.6184.0838141025642-0.473814102564162
1483.8983.63546579570620.254534204293762
1583.483.09351317674730.306486823252712
1682.9682.70076424960260.259235750397437
1782.7682.52241891496320.237581085036851
1883.3583.06275648977910.287243510220847
1987.7886.33294246581131.4470575341887
2088.9988.60685190212020.383148097879783
2188.9289.1968928706557-0.276892870655743
2288.9189.8368913892559-0.9268913892559
2389.7989.43556183164820.354438168351777
2490.5489.74739692682640.792603073173652
2593.1591.204235368191.94576463181001
2692.7994.0918415722218-1.30184157222178
2793.2192.7961026255640.413897374435962
2895.3593.22851094935332.12148905064674
29100.9195.9002780943595.00972190564104
30103.69102.9889603076470.701039692353291
31104.04108.862536965765-4.82253696576537
32104.16106.064824685936-1.90482468593619
33104.71104.888715282284-0.178715282284472
34105.18106.02499593959-0.844995939590049
35104.92106.237727444993-1.31772744499283
36104.83105.128269181031-0.298269181030506
37104.9105.533794009761-0.633794009760578
38105.05105.186800085545-0.136800085545346
39104.6104.70894785616-0.108947856159858
40103.21104.267624089469-1.05762408946923
41102.52103.001698481768-0.481698481767751
42101.09102.441078260068-1.35107826006823
43101.19103.41094499322-2.22094499322013
44102.34101.1151239665451.22487603345492
45102.62101.4946001251531.12539987484701
46102.47102.588930470266-0.118930470265724
47101.82102.374268484113-0.554268484113152
48101.86101.1161864252840.743813574716057
49101.54101.762652983702-0.222652983701565
50101.98101.1967034311410.783296568859498
51101.23101.1348379529650.0951620470349894
52100.4100.418832153083-0.0188321530832951
5399.9499.9634741928793-0.0234741928793341
5499.9499.67279750669510.26720249330485
55100102.3280478147-2.32804781469989
5698.8100.335429445963-1.53542944596347
5799.0797.75591621967181.31408378032818
5899.4698.63101865620630.828981343793657
5999.1899.14999663318510.0300033668149382
6098.4798.5060323156143-0.0360323156143352
6197.1298.1912980393499-1.07129803934991
6296.9196.54791937459130.362080625408723
6396.0995.62325205464560.466747945354385
6497.1794.89877406150192.27122593849811
6596.896.70474221864080.0952577813592228
6697.1396.67687261037780.45312738962221
6799.999.52121369677150.378786303228551
68100.56100.835313460919-0.275313460918596
69100.84100.5807610997950.259238900204579
7099.81101.19215903494-1.38215903494046
71100.4499.8973155819660.542684418033986
72100.07100.146253525112-0.0762535251119232
73101.32100.1382936758231.18170632417667
74103.98101.5586098661332.42139013386699
75104.81103.8495630219020.960436978097945
76106.23105.0715284102781.1584715897216
77106.48106.850374280465-0.370374280464844
78107.59107.4627753763040.127224623695597
79107.16110.987041824828-3.82704182482756
80107.54108.454558396967-0.91455839696718
81107.1107.647874441438-0.547874441438282
82106.38107.255711037678-0.875711037677974
83106.64106.5087299867110.131270013288798
84106.13106.206759809638-0.076759809638105

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 83.61 & 84.0838141025642 & -0.473814102564162 \tabularnewline
14 & 83.89 & 83.6354657957062 & 0.254534204293762 \tabularnewline
15 & 83.4 & 83.0935131767473 & 0.306486823252712 \tabularnewline
16 & 82.96 & 82.7007642496026 & 0.259235750397437 \tabularnewline
17 & 82.76 & 82.5224189149632 & 0.237581085036851 \tabularnewline
18 & 83.35 & 83.0627564897791 & 0.287243510220847 \tabularnewline
19 & 87.78 & 86.3329424658113 & 1.4470575341887 \tabularnewline
20 & 88.99 & 88.6068519021202 & 0.383148097879783 \tabularnewline
21 & 88.92 & 89.1968928706557 & -0.276892870655743 \tabularnewline
22 & 88.91 & 89.8368913892559 & -0.9268913892559 \tabularnewline
23 & 89.79 & 89.4355618316482 & 0.354438168351777 \tabularnewline
24 & 90.54 & 89.7473969268264 & 0.792603073173652 \tabularnewline
25 & 93.15 & 91.20423536819 & 1.94576463181001 \tabularnewline
26 & 92.79 & 94.0918415722218 & -1.30184157222178 \tabularnewline
27 & 93.21 & 92.796102625564 & 0.413897374435962 \tabularnewline
28 & 95.35 & 93.2285109493533 & 2.12148905064674 \tabularnewline
29 & 100.91 & 95.900278094359 & 5.00972190564104 \tabularnewline
30 & 103.69 & 102.988960307647 & 0.701039692353291 \tabularnewline
31 & 104.04 & 108.862536965765 & -4.82253696576537 \tabularnewline
32 & 104.16 & 106.064824685936 & -1.90482468593619 \tabularnewline
33 & 104.71 & 104.888715282284 & -0.178715282284472 \tabularnewline
34 & 105.18 & 106.02499593959 & -0.844995939590049 \tabularnewline
35 & 104.92 & 106.237727444993 & -1.31772744499283 \tabularnewline
36 & 104.83 & 105.128269181031 & -0.298269181030506 \tabularnewline
37 & 104.9 & 105.533794009761 & -0.633794009760578 \tabularnewline
38 & 105.05 & 105.186800085545 & -0.136800085545346 \tabularnewline
39 & 104.6 & 104.70894785616 & -0.108947856159858 \tabularnewline
40 & 103.21 & 104.267624089469 & -1.05762408946923 \tabularnewline
41 & 102.52 & 103.001698481768 & -0.481698481767751 \tabularnewline
42 & 101.09 & 102.441078260068 & -1.35107826006823 \tabularnewline
43 & 101.19 & 103.41094499322 & -2.22094499322013 \tabularnewline
44 & 102.34 & 101.115123966545 & 1.22487603345492 \tabularnewline
45 & 102.62 & 101.494600125153 & 1.12539987484701 \tabularnewline
46 & 102.47 & 102.588930470266 & -0.118930470265724 \tabularnewline
47 & 101.82 & 102.374268484113 & -0.554268484113152 \tabularnewline
48 & 101.86 & 101.116186425284 & 0.743813574716057 \tabularnewline
49 & 101.54 & 101.762652983702 & -0.222652983701565 \tabularnewline
50 & 101.98 & 101.196703431141 & 0.783296568859498 \tabularnewline
51 & 101.23 & 101.134837952965 & 0.0951620470349894 \tabularnewline
52 & 100.4 & 100.418832153083 & -0.0188321530832951 \tabularnewline
53 & 99.94 & 99.9634741928793 & -0.0234741928793341 \tabularnewline
54 & 99.94 & 99.6727975066951 & 0.26720249330485 \tabularnewline
55 & 100 & 102.3280478147 & -2.32804781469989 \tabularnewline
56 & 98.8 & 100.335429445963 & -1.53542944596347 \tabularnewline
57 & 99.07 & 97.7559162196718 & 1.31408378032818 \tabularnewline
58 & 99.46 & 98.6310186562063 & 0.828981343793657 \tabularnewline
59 & 99.18 & 99.1499966331851 & 0.0300033668149382 \tabularnewline
60 & 98.47 & 98.5060323156143 & -0.0360323156143352 \tabularnewline
61 & 97.12 & 98.1912980393499 & -1.07129803934991 \tabularnewline
62 & 96.91 & 96.5479193745913 & 0.362080625408723 \tabularnewline
63 & 96.09 & 95.6232520546456 & 0.466747945354385 \tabularnewline
64 & 97.17 & 94.8987740615019 & 2.27122593849811 \tabularnewline
65 & 96.8 & 96.7047422186408 & 0.0952577813592228 \tabularnewline
66 & 97.13 & 96.6768726103778 & 0.45312738962221 \tabularnewline
67 & 99.9 & 99.5212136967715 & 0.378786303228551 \tabularnewline
68 & 100.56 & 100.835313460919 & -0.275313460918596 \tabularnewline
69 & 100.84 & 100.580761099795 & 0.259238900204579 \tabularnewline
70 & 99.81 & 101.19215903494 & -1.38215903494046 \tabularnewline
71 & 100.44 & 99.897315581966 & 0.542684418033986 \tabularnewline
72 & 100.07 & 100.146253525112 & -0.0762535251119232 \tabularnewline
73 & 101.32 & 100.138293675823 & 1.18170632417667 \tabularnewline
74 & 103.98 & 101.558609866133 & 2.42139013386699 \tabularnewline
75 & 104.81 & 103.849563021902 & 0.960436978097945 \tabularnewline
76 & 106.23 & 105.071528410278 & 1.1584715897216 \tabularnewline
77 & 106.48 & 106.850374280465 & -0.370374280464844 \tabularnewline
78 & 107.59 & 107.462775376304 & 0.127224623695597 \tabularnewline
79 & 107.16 & 110.987041824828 & -3.82704182482756 \tabularnewline
80 & 107.54 & 108.454558396967 & -0.91455839696718 \tabularnewline
81 & 107.1 & 107.647874441438 & -0.547874441438282 \tabularnewline
82 & 106.38 & 107.255711037678 & -0.875711037677974 \tabularnewline
83 & 106.64 & 106.508729986711 & 0.131270013288798 \tabularnewline
84 & 106.13 & 106.206759809638 & -0.076759809638105 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=294937&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]83.61[/C][C]84.0838141025642[/C][C]-0.473814102564162[/C][/ROW]
[ROW][C]14[/C][C]83.89[/C][C]83.6354657957062[/C][C]0.254534204293762[/C][/ROW]
[ROW][C]15[/C][C]83.4[/C][C]83.0935131767473[/C][C]0.306486823252712[/C][/ROW]
[ROW][C]16[/C][C]82.96[/C][C]82.7007642496026[/C][C]0.259235750397437[/C][/ROW]
[ROW][C]17[/C][C]82.76[/C][C]82.5224189149632[/C][C]0.237581085036851[/C][/ROW]
[ROW][C]18[/C][C]83.35[/C][C]83.0627564897791[/C][C]0.287243510220847[/C][/ROW]
[ROW][C]19[/C][C]87.78[/C][C]86.3329424658113[/C][C]1.4470575341887[/C][/ROW]
[ROW][C]20[/C][C]88.99[/C][C]88.6068519021202[/C][C]0.383148097879783[/C][/ROW]
[ROW][C]21[/C][C]88.92[/C][C]89.1968928706557[/C][C]-0.276892870655743[/C][/ROW]
[ROW][C]22[/C][C]88.91[/C][C]89.8368913892559[/C][C]-0.9268913892559[/C][/ROW]
[ROW][C]23[/C][C]89.79[/C][C]89.4355618316482[/C][C]0.354438168351777[/C][/ROW]
[ROW][C]24[/C][C]90.54[/C][C]89.7473969268264[/C][C]0.792603073173652[/C][/ROW]
[ROW][C]25[/C][C]93.15[/C][C]91.20423536819[/C][C]1.94576463181001[/C][/ROW]
[ROW][C]26[/C][C]92.79[/C][C]94.0918415722218[/C][C]-1.30184157222178[/C][/ROW]
[ROW][C]27[/C][C]93.21[/C][C]92.796102625564[/C][C]0.413897374435962[/C][/ROW]
[ROW][C]28[/C][C]95.35[/C][C]93.2285109493533[/C][C]2.12148905064674[/C][/ROW]
[ROW][C]29[/C][C]100.91[/C][C]95.900278094359[/C][C]5.00972190564104[/C][/ROW]
[ROW][C]30[/C][C]103.69[/C][C]102.988960307647[/C][C]0.701039692353291[/C][/ROW]
[ROW][C]31[/C][C]104.04[/C][C]108.862536965765[/C][C]-4.82253696576537[/C][/ROW]
[ROW][C]32[/C][C]104.16[/C][C]106.064824685936[/C][C]-1.90482468593619[/C][/ROW]
[ROW][C]33[/C][C]104.71[/C][C]104.888715282284[/C][C]-0.178715282284472[/C][/ROW]
[ROW][C]34[/C][C]105.18[/C][C]106.02499593959[/C][C]-0.844995939590049[/C][/ROW]
[ROW][C]35[/C][C]104.92[/C][C]106.237727444993[/C][C]-1.31772744499283[/C][/ROW]
[ROW][C]36[/C][C]104.83[/C][C]105.128269181031[/C][C]-0.298269181030506[/C][/ROW]
[ROW][C]37[/C][C]104.9[/C][C]105.533794009761[/C][C]-0.633794009760578[/C][/ROW]
[ROW][C]38[/C][C]105.05[/C][C]105.186800085545[/C][C]-0.136800085545346[/C][/ROW]
[ROW][C]39[/C][C]104.6[/C][C]104.70894785616[/C][C]-0.108947856159858[/C][/ROW]
[ROW][C]40[/C][C]103.21[/C][C]104.267624089469[/C][C]-1.05762408946923[/C][/ROW]
[ROW][C]41[/C][C]102.52[/C][C]103.001698481768[/C][C]-0.481698481767751[/C][/ROW]
[ROW][C]42[/C][C]101.09[/C][C]102.441078260068[/C][C]-1.35107826006823[/C][/ROW]
[ROW][C]43[/C][C]101.19[/C][C]103.41094499322[/C][C]-2.22094499322013[/C][/ROW]
[ROW][C]44[/C][C]102.34[/C][C]101.115123966545[/C][C]1.22487603345492[/C][/ROW]
[ROW][C]45[/C][C]102.62[/C][C]101.494600125153[/C][C]1.12539987484701[/C][/ROW]
[ROW][C]46[/C][C]102.47[/C][C]102.588930470266[/C][C]-0.118930470265724[/C][/ROW]
[ROW][C]47[/C][C]101.82[/C][C]102.374268484113[/C][C]-0.554268484113152[/C][/ROW]
[ROW][C]48[/C][C]101.86[/C][C]101.116186425284[/C][C]0.743813574716057[/C][/ROW]
[ROW][C]49[/C][C]101.54[/C][C]101.762652983702[/C][C]-0.222652983701565[/C][/ROW]
[ROW][C]50[/C][C]101.98[/C][C]101.196703431141[/C][C]0.783296568859498[/C][/ROW]
[ROW][C]51[/C][C]101.23[/C][C]101.134837952965[/C][C]0.0951620470349894[/C][/ROW]
[ROW][C]52[/C][C]100.4[/C][C]100.418832153083[/C][C]-0.0188321530832951[/C][/ROW]
[ROW][C]53[/C][C]99.94[/C][C]99.9634741928793[/C][C]-0.0234741928793341[/C][/ROW]
[ROW][C]54[/C][C]99.94[/C][C]99.6727975066951[/C][C]0.26720249330485[/C][/ROW]
[ROW][C]55[/C][C]100[/C][C]102.3280478147[/C][C]-2.32804781469989[/C][/ROW]
[ROW][C]56[/C][C]98.8[/C][C]100.335429445963[/C][C]-1.53542944596347[/C][/ROW]
[ROW][C]57[/C][C]99.07[/C][C]97.7559162196718[/C][C]1.31408378032818[/C][/ROW]
[ROW][C]58[/C][C]99.46[/C][C]98.6310186562063[/C][C]0.828981343793657[/C][/ROW]
[ROW][C]59[/C][C]99.18[/C][C]99.1499966331851[/C][C]0.0300033668149382[/C][/ROW]
[ROW][C]60[/C][C]98.47[/C][C]98.5060323156143[/C][C]-0.0360323156143352[/C][/ROW]
[ROW][C]61[/C][C]97.12[/C][C]98.1912980393499[/C][C]-1.07129803934991[/C][/ROW]
[ROW][C]62[/C][C]96.91[/C][C]96.5479193745913[/C][C]0.362080625408723[/C][/ROW]
[ROW][C]63[/C][C]96.09[/C][C]95.6232520546456[/C][C]0.466747945354385[/C][/ROW]
[ROW][C]64[/C][C]97.17[/C][C]94.8987740615019[/C][C]2.27122593849811[/C][/ROW]
[ROW][C]65[/C][C]96.8[/C][C]96.7047422186408[/C][C]0.0952577813592228[/C][/ROW]
[ROW][C]66[/C][C]97.13[/C][C]96.6768726103778[/C][C]0.45312738962221[/C][/ROW]
[ROW][C]67[/C][C]99.9[/C][C]99.5212136967715[/C][C]0.378786303228551[/C][/ROW]
[ROW][C]68[/C][C]100.56[/C][C]100.835313460919[/C][C]-0.275313460918596[/C][/ROW]
[ROW][C]69[/C][C]100.84[/C][C]100.580761099795[/C][C]0.259238900204579[/C][/ROW]
[ROW][C]70[/C][C]99.81[/C][C]101.19215903494[/C][C]-1.38215903494046[/C][/ROW]
[ROW][C]71[/C][C]100.44[/C][C]99.897315581966[/C][C]0.542684418033986[/C][/ROW]
[ROW][C]72[/C][C]100.07[/C][C]100.146253525112[/C][C]-0.0762535251119232[/C][/ROW]
[ROW][C]73[/C][C]101.32[/C][C]100.138293675823[/C][C]1.18170632417667[/C][/ROW]
[ROW][C]74[/C][C]103.98[/C][C]101.558609866133[/C][C]2.42139013386699[/C][/ROW]
[ROW][C]75[/C][C]104.81[/C][C]103.849563021902[/C][C]0.960436978097945[/C][/ROW]
[ROW][C]76[/C][C]106.23[/C][C]105.071528410278[/C][C]1.1584715897216[/C][/ROW]
[ROW][C]77[/C][C]106.48[/C][C]106.850374280465[/C][C]-0.370374280464844[/C][/ROW]
[ROW][C]78[/C][C]107.59[/C][C]107.462775376304[/C][C]0.127224623695597[/C][/ROW]
[ROW][C]79[/C][C]107.16[/C][C]110.987041824828[/C][C]-3.82704182482756[/C][/ROW]
[ROW][C]80[/C][C]107.54[/C][C]108.454558396967[/C][C]-0.91455839696718[/C][/ROW]
[ROW][C]81[/C][C]107.1[/C][C]107.647874441438[/C][C]-0.547874441438282[/C][/ROW]
[ROW][C]82[/C][C]106.38[/C][C]107.255711037678[/C][C]-0.875711037677974[/C][/ROW]
[ROW][C]83[/C][C]106.64[/C][C]106.508729986711[/C][C]0.131270013288798[/C][/ROW]
[ROW][C]84[/C][C]106.13[/C][C]106.206759809638[/C][C]-0.076759809638105[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=294937&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=294937&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
1383.6184.0838141025642-0.473814102564162
1483.8983.63546579570620.254534204293762
1583.483.09351317674730.306486823252712
1682.9682.70076424960260.259235750397437
1782.7682.52241891496320.237581085036851
1883.3583.06275648977910.287243510220847
1987.7886.33294246581131.4470575341887
2088.9988.60685190212020.383148097879783
2188.9289.1968928706557-0.276892870655743
2288.9189.8368913892559-0.9268913892559
2389.7989.43556183164820.354438168351777
2490.5489.74739692682640.792603073173652
2593.1591.204235368191.94576463181001
2692.7994.0918415722218-1.30184157222178
2793.2192.7961026255640.413897374435962
2895.3593.22851094935332.12148905064674
29100.9195.9002780943595.00972190564104
30103.69102.9889603076470.701039692353291
31104.04108.862536965765-4.82253696576537
32104.16106.064824685936-1.90482468593619
33104.71104.888715282284-0.178715282284472
34105.18106.02499593959-0.844995939590049
35104.92106.237727444993-1.31772744499283
36104.83105.128269181031-0.298269181030506
37104.9105.533794009761-0.633794009760578
38105.05105.186800085545-0.136800085545346
39104.6104.70894785616-0.108947856159858
40103.21104.267624089469-1.05762408946923
41102.52103.001698481768-0.481698481767751
42101.09102.441078260068-1.35107826006823
43101.19103.41094499322-2.22094499322013
44102.34101.1151239665451.22487603345492
45102.62101.4946001251531.12539987484701
46102.47102.588930470266-0.118930470265724
47101.82102.374268484113-0.554268484113152
48101.86101.1161864252840.743813574716057
49101.54101.762652983702-0.222652983701565
50101.98101.1967034311410.783296568859498
51101.23101.1348379529650.0951620470349894
52100.4100.418832153083-0.0188321530832951
5399.9499.9634741928793-0.0234741928793341
5499.9499.67279750669510.26720249330485
55100102.3280478147-2.32804781469989
5698.8100.335429445963-1.53542944596347
5799.0797.75591621967181.31408378032818
5899.4698.63101865620630.828981343793657
5999.1899.14999663318510.0300033668149382
6098.4798.5060323156143-0.0360323156143352
6197.1298.1912980393499-1.07129803934991
6296.9196.54791937459130.362080625408723
6396.0995.62325205464560.466747945354385
6497.1794.89877406150192.27122593849811
6596.896.70474221864080.0952577813592228
6697.1396.67687261037780.45312738962221
6799.999.52121369677150.378786303228551
68100.56100.835313460919-0.275313460918596
69100.84100.5807610997950.259238900204579
7099.81101.19215903494-1.38215903494046
71100.4499.8973155819660.542684418033986
72100.07100.146253525112-0.0762535251119232
73101.32100.1382936758231.18170632417667
74103.98101.5586098661332.42139013386699
75104.81103.8495630219020.960436978097945
76106.23105.0715284102781.1584715897216
77106.48106.850374280465-0.370374280464844
78107.59107.4627753763040.127224623695597
79107.16110.987041824828-3.82704182482756
80107.54108.454558396967-0.91455839696718
81107.1107.647874441438-0.547874441438282
82106.38107.255711037678-0.875711037677974
83106.64106.5087299867110.131270013288798
84106.13106.206759809638-0.076759809638105






Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
85106.147210304184103.511014438438108.783406169931
86106.167296802745102.168201132423110.166392473068
87105.24316060106299.9040859166068110.582235285518
88104.52979225846397.8178222938519111.241762223074
89103.84998136518595.71429526104111.985667469331
90103.63710141179994.0202195642301113.253983259367
91105.57415462932194.4162972944015116.73201196424
92106.35423120214193.5952486745243119.113213729757
93106.15369072238991.7339772641834120.573404180594
94106.09137650971889.9523108991422122.230442120294
95106.23899478777388.3231443172249124.154845258321
96105.78568283576786.0368836478593125.534482023676

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
85 & 106.147210304184 & 103.511014438438 & 108.783406169931 \tabularnewline
86 & 106.167296802745 & 102.168201132423 & 110.166392473068 \tabularnewline
87 & 105.243160601062 & 99.9040859166068 & 110.582235285518 \tabularnewline
88 & 104.529792258463 & 97.8178222938519 & 111.241762223074 \tabularnewline
89 & 103.849981365185 & 95.71429526104 & 111.985667469331 \tabularnewline
90 & 103.637101411799 & 94.0202195642301 & 113.253983259367 \tabularnewline
91 & 105.574154629321 & 94.4162972944015 & 116.73201196424 \tabularnewline
92 & 106.354231202141 & 93.5952486745243 & 119.113213729757 \tabularnewline
93 & 106.153690722389 & 91.7339772641834 & 120.573404180594 \tabularnewline
94 & 106.091376509718 & 89.9523108991422 & 122.230442120294 \tabularnewline
95 & 106.238994787773 & 88.3231443172249 & 124.154845258321 \tabularnewline
96 & 105.785682835767 & 86.0368836478593 & 125.534482023676 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=294937&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]106.147210304184[/C][C]103.511014438438[/C][C]108.783406169931[/C][/ROW]
[ROW][C]86[/C][C]106.167296802745[/C][C]102.168201132423[/C][C]110.166392473068[/C][/ROW]
[ROW][C]87[/C][C]105.243160601062[/C][C]99.9040859166068[/C][C]110.582235285518[/C][/ROW]
[ROW][C]88[/C][C]104.529792258463[/C][C]97.8178222938519[/C][C]111.241762223074[/C][/ROW]
[ROW][C]89[/C][C]103.849981365185[/C][C]95.71429526104[/C][C]111.985667469331[/C][/ROW]
[ROW][C]90[/C][C]103.637101411799[/C][C]94.0202195642301[/C][C]113.253983259367[/C][/ROW]
[ROW][C]91[/C][C]105.574154629321[/C][C]94.4162972944015[/C][C]116.73201196424[/C][/ROW]
[ROW][C]92[/C][C]106.354231202141[/C][C]93.5952486745243[/C][C]119.113213729757[/C][/ROW]
[ROW][C]93[/C][C]106.153690722389[/C][C]91.7339772641834[/C][C]120.573404180594[/C][/ROW]
[ROW][C]94[/C][C]106.091376509718[/C][C]89.9523108991422[/C][C]122.230442120294[/C][/ROW]
[ROW][C]95[/C][C]106.238994787773[/C][C]88.3231443172249[/C][C]124.154845258321[/C][/ROW]
[ROW][C]96[/C][C]105.785682835767[/C][C]86.0368836478593[/C][C]125.534482023676[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=294937&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=294937&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
85106.147210304184103.511014438438108.783406169931
86106.167296802745102.168201132423110.166392473068
87105.24316060106299.9040859166068110.582235285518
88104.52979225846397.8178222938519111.241762223074
89103.84998136518595.71429526104111.985667469331
90103.63710141179994.0202195642301113.253983259367
91105.57415462932194.4162972944015116.73201196424
92106.35423120214193.5952486745243119.113213729757
93106.15369072238991.7339772641834120.573404180594
94106.09137650971889.9523108991422122.230442120294
95106.23899478777388.3231443172249124.154845258321
96105.78568283576786.0368836478593125.534482023676


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):
par3 <- 'multiplicative'
par2 <- 'Triple'
par1 <- '12'
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')