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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, 28 May 2008 11:53:44 -0600
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2008/May/28/t121199729318sslpgerfot80t.htm/, Retrieved Mon, 13 May 2024 21:08:25 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=13460, Retrieved Mon, 13 May 2024 21:08:25 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact189

Tree of Dependent Computations

Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [Exponential Smoot...] [2008-05-28 17:53:44] [9d456519644b7519961e155943b4a156] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
120,05
120,05
120,08
120,12
120,18
120,2
120,25
120,25
120,24
120,29
120,25
120,26
120,32
120,31
120,36
120,4
120,4
120,39
120,44
120,5
120,53
120,64
120,78
120,94
121
121,05
121,15
121,07
121,18
121,46
121,71
121,71
121,74
121,76
121,76
121,82
121,82
121,82
121,94
121,99
122,18
122,41
122,48
122,52
122,62
122,63
122,74
122,58
122,59
122,61
122,63
122,37
122,36
122,47
122,46
122,45
122,49
122,5
122,37
122,37
122,51
122,51
122,55
122,56
122,72
122,97
123,03
123,05
123,08
123,08
123,12
123,07
123,04
123,06
123,39
124,02
124,05
123,99
124,46
124,46
124,6
124,84
124,84
124,99

Tables (Output of Computation)





Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time6 seconds
R Server'George Udny Yule' @ 72.249.76.132

\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 & 6 seconds \tabularnewline
R Server & 'George Udny Yule' @ 72.249.76.132 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=13460&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]6 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'George Udny Yule' @ 72.249.76.132[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=13460&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=13460&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 time6 seconds
R Server'George Udny Yule' @ 72.249.76.132






Estimated Parameters of Exponential Smoothing
ParameterValue
alpha1
beta0.109959999025065
gamma0

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 1 \tabularnewline
beta & 0.109959999025065 \tabularnewline
gamma & 0 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=13460&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]0.109959999025065[/C][/ROW]
[ROW][C]gamma[/C][C]0[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=13460&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=13460&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
beta0.109959999025065
gamma0






Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
3120.08120.050.0300000000000011
4120.12120.0832987999710.0367012000292561
5120.18120.1273344638900.0526655361098136
6120.2120.1931255661890.00687443381052333
7120.25120.2138814789250.0361185210754229
8120.25120.267853071467-0.0178530714668170
9120.24120.265889947746-0.0258899477457391
10120.29120.2530430891170.0369569108831627
11120.25120.307106871002-0.0571068710015368
12120.26120.260827399522-0.000827399521881489
13120.32120.2707364186710.0492635813287308
14120.31120.336153442026-0.0261534420261285
15120.36120.3232776095660.0367223904335532
16120.4120.3773156035830.0226843964172900
17120.4120.419809979791-0.0198099797906508
18120.39120.417631674432-0.0276316744321861
19120.44120.4045932955390.0354067044614368
20120.5120.4584866167270.0415133832733829
21120.53120.5230514283110.00694857168912222
22120.64120.5538154932470.0861845067529572
23120.78120.6732923415260.10670765847442
24120.94120.8250259155470.114974084452612
25121120.9976684657620.00233153423829435
26121.05121.057924841264-0.00792484126428405
27121.15121.1070534257270.0429465742734294
28121.07121.211775830992-0.141775830991833
29121.18121.1161861607540.0638138392458387
30121.46121.2332031304550.226796869544543
31121.71121.5381417140090.171858285990552
32121.71121.807039250969-0.0970392509694165
33121.74121.796368815027-0.056368815027426
34121.76121.820170500182-0.0601705001819539
35121.76121.833554152041-0.0735541520406144
36121.82121.825466137554-0.00546613755395242
37121.82121.884865081074-0.0648650810738332
38121.82121.877732516822-0.0577325168221989
39121.94121.8713842493290.0686157506712846
40121.99121.998929237206-0.00892923720563488
41122.18122.0479473782910.132052621708809
42122.41122.2524678844460.157532115554417
43122.48122.499790115718-0.0197901157183367
44122.52122.567613994613-0.0476139946132577
45122.62122.6023783598120.0176216401880112
46122.63122.70431603535-0.0743160353498951
47122.74122.7061442441750.0338557558247317
48122.58122.819867023053-0.239867023052753
49122.59122.633491245432-0.0434912454317242
50122.61122.638708948126-0.0287089481264644
51122.63122.655552112218-0.0255521122184632
52122.37122.672742401984-0.302742401983821
53122.36122.379452847757-0.0194528477568525
54122.47122.3673138126360.102686187363531
55122.46122.488605185699-0.0286051856988507
56122.45122.475459759507-0.0254597595072852
57122.49122.4626602043770.0273397956233055
58122.5122.505666488277-0.00566648827677341
59122.37122.515043401231-0.145043401231376
60122.37122.3690944289730.000905571026606822
61122.51122.3691940055630.140805994437414
62122.51122.524677032574-0.0146770325736583
63122.55122.5230631460860.0269368539138242
64122.56122.566025122516-0.00602512251626308
65122.72122.5753626000500.144637399949744
66122.97122.7512669284080.218733071592283
67123.03123.0253188167470.00468118325325406
68123.05123.085833559653-0.0358335596527155
69123.08123.101893301468-0.0218933014682392
70123.08123.12948591406-0.0494859140601278
71123.12123.124044442998-0.00404444299832107
72123.07123.163599716050-0.0935997160501927
73123.04123.103307491365-0.0633074913645402
74123.06123.066346199676-0.00634619967583205
75123.39123.0856483715660.304351628434333
76124.02123.4491148763320.570885123668418
77124.05124.141889403974-0.0918894039735818
78123.99124.161785245202-0.17178524520223
79124.46124.0828957398070.377104260192723
80124.46124.594362123890-0.134362123890412
81124.6124.5795876648780.0204123351215770
82124.84124.7218322052280.118167794771523
83124.84124.974825935826-0.134825935826356
84124.99124.9600004760540.0299995239456479

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
3 & 120.08 & 120.05 & 0.0300000000000011 \tabularnewline
4 & 120.12 & 120.083298799971 & 0.0367012000292561 \tabularnewline
5 & 120.18 & 120.127334463890 & 0.0526655361098136 \tabularnewline
6 & 120.2 & 120.193125566189 & 0.00687443381052333 \tabularnewline
7 & 120.25 & 120.213881478925 & 0.0361185210754229 \tabularnewline
8 & 120.25 & 120.267853071467 & -0.0178530714668170 \tabularnewline
9 & 120.24 & 120.265889947746 & -0.0258899477457391 \tabularnewline
10 & 120.29 & 120.253043089117 & 0.0369569108831627 \tabularnewline
11 & 120.25 & 120.307106871002 & -0.0571068710015368 \tabularnewline
12 & 120.26 & 120.260827399522 & -0.000827399521881489 \tabularnewline
13 & 120.32 & 120.270736418671 & 0.0492635813287308 \tabularnewline
14 & 120.31 & 120.336153442026 & -0.0261534420261285 \tabularnewline
15 & 120.36 & 120.323277609566 & 0.0367223904335532 \tabularnewline
16 & 120.4 & 120.377315603583 & 0.0226843964172900 \tabularnewline
17 & 120.4 & 120.419809979791 & -0.0198099797906508 \tabularnewline
18 & 120.39 & 120.417631674432 & -0.0276316744321861 \tabularnewline
19 & 120.44 & 120.404593295539 & 0.0354067044614368 \tabularnewline
20 & 120.5 & 120.458486616727 & 0.0415133832733829 \tabularnewline
21 & 120.53 & 120.523051428311 & 0.00694857168912222 \tabularnewline
22 & 120.64 & 120.553815493247 & 0.0861845067529572 \tabularnewline
23 & 120.78 & 120.673292341526 & 0.10670765847442 \tabularnewline
24 & 120.94 & 120.825025915547 & 0.114974084452612 \tabularnewline
25 & 121 & 120.997668465762 & 0.00233153423829435 \tabularnewline
26 & 121.05 & 121.057924841264 & -0.00792484126428405 \tabularnewline
27 & 121.15 & 121.107053425727 & 0.0429465742734294 \tabularnewline
28 & 121.07 & 121.211775830992 & -0.141775830991833 \tabularnewline
29 & 121.18 & 121.116186160754 & 0.0638138392458387 \tabularnewline
30 & 121.46 & 121.233203130455 & 0.226796869544543 \tabularnewline
31 & 121.71 & 121.538141714009 & 0.171858285990552 \tabularnewline
32 & 121.71 & 121.807039250969 & -0.0970392509694165 \tabularnewline
33 & 121.74 & 121.796368815027 & -0.056368815027426 \tabularnewline
34 & 121.76 & 121.820170500182 & -0.0601705001819539 \tabularnewline
35 & 121.76 & 121.833554152041 & -0.0735541520406144 \tabularnewline
36 & 121.82 & 121.825466137554 & -0.00546613755395242 \tabularnewline
37 & 121.82 & 121.884865081074 & -0.0648650810738332 \tabularnewline
38 & 121.82 & 121.877732516822 & -0.0577325168221989 \tabularnewline
39 & 121.94 & 121.871384249329 & 0.0686157506712846 \tabularnewline
40 & 121.99 & 121.998929237206 & -0.00892923720563488 \tabularnewline
41 & 122.18 & 122.047947378291 & 0.132052621708809 \tabularnewline
42 & 122.41 & 122.252467884446 & 0.157532115554417 \tabularnewline
43 & 122.48 & 122.499790115718 & -0.0197901157183367 \tabularnewline
44 & 122.52 & 122.567613994613 & -0.0476139946132577 \tabularnewline
45 & 122.62 & 122.602378359812 & 0.0176216401880112 \tabularnewline
46 & 122.63 & 122.70431603535 & -0.0743160353498951 \tabularnewline
47 & 122.74 & 122.706144244175 & 0.0338557558247317 \tabularnewline
48 & 122.58 & 122.819867023053 & -0.239867023052753 \tabularnewline
49 & 122.59 & 122.633491245432 & -0.0434912454317242 \tabularnewline
50 & 122.61 & 122.638708948126 & -0.0287089481264644 \tabularnewline
51 & 122.63 & 122.655552112218 & -0.0255521122184632 \tabularnewline
52 & 122.37 & 122.672742401984 & -0.302742401983821 \tabularnewline
53 & 122.36 & 122.379452847757 & -0.0194528477568525 \tabularnewline
54 & 122.47 & 122.367313812636 & 0.102686187363531 \tabularnewline
55 & 122.46 & 122.488605185699 & -0.0286051856988507 \tabularnewline
56 & 122.45 & 122.475459759507 & -0.0254597595072852 \tabularnewline
57 & 122.49 & 122.462660204377 & 0.0273397956233055 \tabularnewline
58 & 122.5 & 122.505666488277 & -0.00566648827677341 \tabularnewline
59 & 122.37 & 122.515043401231 & -0.145043401231376 \tabularnewline
60 & 122.37 & 122.369094428973 & 0.000905571026606822 \tabularnewline
61 & 122.51 & 122.369194005563 & 0.140805994437414 \tabularnewline
62 & 122.51 & 122.524677032574 & -0.0146770325736583 \tabularnewline
63 & 122.55 & 122.523063146086 & 0.0269368539138242 \tabularnewline
64 & 122.56 & 122.566025122516 & -0.00602512251626308 \tabularnewline
65 & 122.72 & 122.575362600050 & 0.144637399949744 \tabularnewline
66 & 122.97 & 122.751266928408 & 0.218733071592283 \tabularnewline
67 & 123.03 & 123.025318816747 & 0.00468118325325406 \tabularnewline
68 & 123.05 & 123.085833559653 & -0.0358335596527155 \tabularnewline
69 & 123.08 & 123.101893301468 & -0.0218933014682392 \tabularnewline
70 & 123.08 & 123.12948591406 & -0.0494859140601278 \tabularnewline
71 & 123.12 & 123.124044442998 & -0.00404444299832107 \tabularnewline
72 & 123.07 & 123.163599716050 & -0.0935997160501927 \tabularnewline
73 & 123.04 & 123.103307491365 & -0.0633074913645402 \tabularnewline
74 & 123.06 & 123.066346199676 & -0.00634619967583205 \tabularnewline
75 & 123.39 & 123.085648371566 & 0.304351628434333 \tabularnewline
76 & 124.02 & 123.449114876332 & 0.570885123668418 \tabularnewline
77 & 124.05 & 124.141889403974 & -0.0918894039735818 \tabularnewline
78 & 123.99 & 124.161785245202 & -0.17178524520223 \tabularnewline
79 & 124.46 & 124.082895739807 & 0.377104260192723 \tabularnewline
80 & 124.46 & 124.594362123890 & -0.134362123890412 \tabularnewline
81 & 124.6 & 124.579587664878 & 0.0204123351215770 \tabularnewline
82 & 124.84 & 124.721832205228 & 0.118167794771523 \tabularnewline
83 & 124.84 & 124.974825935826 & -0.134825935826356 \tabularnewline
84 & 124.99 & 124.960000476054 & 0.0299995239456479 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=13460&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]120.08[/C][C]120.05[/C][C]0.0300000000000011[/C][/ROW]
[ROW][C]4[/C][C]120.12[/C][C]120.083298799971[/C][C]0.0367012000292561[/C][/ROW]
[ROW][C]5[/C][C]120.18[/C][C]120.127334463890[/C][C]0.0526655361098136[/C][/ROW]
[ROW][C]6[/C][C]120.2[/C][C]120.193125566189[/C][C]0.00687443381052333[/C][/ROW]
[ROW][C]7[/C][C]120.25[/C][C]120.213881478925[/C][C]0.0361185210754229[/C][/ROW]
[ROW][C]8[/C][C]120.25[/C][C]120.267853071467[/C][C]-0.0178530714668170[/C][/ROW]
[ROW][C]9[/C][C]120.24[/C][C]120.265889947746[/C][C]-0.0258899477457391[/C][/ROW]
[ROW][C]10[/C][C]120.29[/C][C]120.253043089117[/C][C]0.0369569108831627[/C][/ROW]
[ROW][C]11[/C][C]120.25[/C][C]120.307106871002[/C][C]-0.0571068710015368[/C][/ROW]
[ROW][C]12[/C][C]120.26[/C][C]120.260827399522[/C][C]-0.000827399521881489[/C][/ROW]
[ROW][C]13[/C][C]120.32[/C][C]120.270736418671[/C][C]0.0492635813287308[/C][/ROW]
[ROW][C]14[/C][C]120.31[/C][C]120.336153442026[/C][C]-0.0261534420261285[/C][/ROW]
[ROW][C]15[/C][C]120.36[/C][C]120.323277609566[/C][C]0.0367223904335532[/C][/ROW]
[ROW][C]16[/C][C]120.4[/C][C]120.377315603583[/C][C]0.0226843964172900[/C][/ROW]
[ROW][C]17[/C][C]120.4[/C][C]120.419809979791[/C][C]-0.0198099797906508[/C][/ROW]
[ROW][C]18[/C][C]120.39[/C][C]120.417631674432[/C][C]-0.0276316744321861[/C][/ROW]
[ROW][C]19[/C][C]120.44[/C][C]120.404593295539[/C][C]0.0354067044614368[/C][/ROW]
[ROW][C]20[/C][C]120.5[/C][C]120.458486616727[/C][C]0.0415133832733829[/C][/ROW]
[ROW][C]21[/C][C]120.53[/C][C]120.523051428311[/C][C]0.00694857168912222[/C][/ROW]
[ROW][C]22[/C][C]120.64[/C][C]120.553815493247[/C][C]0.0861845067529572[/C][/ROW]
[ROW][C]23[/C][C]120.78[/C][C]120.673292341526[/C][C]0.10670765847442[/C][/ROW]
[ROW][C]24[/C][C]120.94[/C][C]120.825025915547[/C][C]0.114974084452612[/C][/ROW]
[ROW][C]25[/C][C]121[/C][C]120.997668465762[/C][C]0.00233153423829435[/C][/ROW]
[ROW][C]26[/C][C]121.05[/C][C]121.057924841264[/C][C]-0.00792484126428405[/C][/ROW]
[ROW][C]27[/C][C]121.15[/C][C]121.107053425727[/C][C]0.0429465742734294[/C][/ROW]
[ROW][C]28[/C][C]121.07[/C][C]121.211775830992[/C][C]-0.141775830991833[/C][/ROW]
[ROW][C]29[/C][C]121.18[/C][C]121.116186160754[/C][C]0.0638138392458387[/C][/ROW]
[ROW][C]30[/C][C]121.46[/C][C]121.233203130455[/C][C]0.226796869544543[/C][/ROW]
[ROW][C]31[/C][C]121.71[/C][C]121.538141714009[/C][C]0.171858285990552[/C][/ROW]
[ROW][C]32[/C][C]121.71[/C][C]121.807039250969[/C][C]-0.0970392509694165[/C][/ROW]
[ROW][C]33[/C][C]121.74[/C][C]121.796368815027[/C][C]-0.056368815027426[/C][/ROW]
[ROW][C]34[/C][C]121.76[/C][C]121.820170500182[/C][C]-0.0601705001819539[/C][/ROW]
[ROW][C]35[/C][C]121.76[/C][C]121.833554152041[/C][C]-0.0735541520406144[/C][/ROW]
[ROW][C]36[/C][C]121.82[/C][C]121.825466137554[/C][C]-0.00546613755395242[/C][/ROW]
[ROW][C]37[/C][C]121.82[/C][C]121.884865081074[/C][C]-0.0648650810738332[/C][/ROW]
[ROW][C]38[/C][C]121.82[/C][C]121.877732516822[/C][C]-0.0577325168221989[/C][/ROW]
[ROW][C]39[/C][C]121.94[/C][C]121.871384249329[/C][C]0.0686157506712846[/C][/ROW]
[ROW][C]40[/C][C]121.99[/C][C]121.998929237206[/C][C]-0.00892923720563488[/C][/ROW]
[ROW][C]41[/C][C]122.18[/C][C]122.047947378291[/C][C]0.132052621708809[/C][/ROW]
[ROW][C]42[/C][C]122.41[/C][C]122.252467884446[/C][C]0.157532115554417[/C][/ROW]
[ROW][C]43[/C][C]122.48[/C][C]122.499790115718[/C][C]-0.0197901157183367[/C][/ROW]
[ROW][C]44[/C][C]122.52[/C][C]122.567613994613[/C][C]-0.0476139946132577[/C][/ROW]
[ROW][C]45[/C][C]122.62[/C][C]122.602378359812[/C][C]0.0176216401880112[/C][/ROW]
[ROW][C]46[/C][C]122.63[/C][C]122.70431603535[/C][C]-0.0743160353498951[/C][/ROW]
[ROW][C]47[/C][C]122.74[/C][C]122.706144244175[/C][C]0.0338557558247317[/C][/ROW]
[ROW][C]48[/C][C]122.58[/C][C]122.819867023053[/C][C]-0.239867023052753[/C][/ROW]
[ROW][C]49[/C][C]122.59[/C][C]122.633491245432[/C][C]-0.0434912454317242[/C][/ROW]
[ROW][C]50[/C][C]122.61[/C][C]122.638708948126[/C][C]-0.0287089481264644[/C][/ROW]
[ROW][C]51[/C][C]122.63[/C][C]122.655552112218[/C][C]-0.0255521122184632[/C][/ROW]
[ROW][C]52[/C][C]122.37[/C][C]122.672742401984[/C][C]-0.302742401983821[/C][/ROW]
[ROW][C]53[/C][C]122.36[/C][C]122.379452847757[/C][C]-0.0194528477568525[/C][/ROW]
[ROW][C]54[/C][C]122.47[/C][C]122.367313812636[/C][C]0.102686187363531[/C][/ROW]
[ROW][C]55[/C][C]122.46[/C][C]122.488605185699[/C][C]-0.0286051856988507[/C][/ROW]
[ROW][C]56[/C][C]122.45[/C][C]122.475459759507[/C][C]-0.0254597595072852[/C][/ROW]
[ROW][C]57[/C][C]122.49[/C][C]122.462660204377[/C][C]0.0273397956233055[/C][/ROW]
[ROW][C]58[/C][C]122.5[/C][C]122.505666488277[/C][C]-0.00566648827677341[/C][/ROW]
[ROW][C]59[/C][C]122.37[/C][C]122.515043401231[/C][C]-0.145043401231376[/C][/ROW]
[ROW][C]60[/C][C]122.37[/C][C]122.369094428973[/C][C]0.000905571026606822[/C][/ROW]
[ROW][C]61[/C][C]122.51[/C][C]122.369194005563[/C][C]0.140805994437414[/C][/ROW]
[ROW][C]62[/C][C]122.51[/C][C]122.524677032574[/C][C]-0.0146770325736583[/C][/ROW]
[ROW][C]63[/C][C]122.55[/C][C]122.523063146086[/C][C]0.0269368539138242[/C][/ROW]
[ROW][C]64[/C][C]122.56[/C][C]122.566025122516[/C][C]-0.00602512251626308[/C][/ROW]
[ROW][C]65[/C][C]122.72[/C][C]122.575362600050[/C][C]0.144637399949744[/C][/ROW]
[ROW][C]66[/C][C]122.97[/C][C]122.751266928408[/C][C]0.218733071592283[/C][/ROW]
[ROW][C]67[/C][C]123.03[/C][C]123.025318816747[/C][C]0.00468118325325406[/C][/ROW]
[ROW][C]68[/C][C]123.05[/C][C]123.085833559653[/C][C]-0.0358335596527155[/C][/ROW]
[ROW][C]69[/C][C]123.08[/C][C]123.101893301468[/C][C]-0.0218933014682392[/C][/ROW]
[ROW][C]70[/C][C]123.08[/C][C]123.12948591406[/C][C]-0.0494859140601278[/C][/ROW]
[ROW][C]71[/C][C]123.12[/C][C]123.124044442998[/C][C]-0.00404444299832107[/C][/ROW]
[ROW][C]72[/C][C]123.07[/C][C]123.163599716050[/C][C]-0.0935997160501927[/C][/ROW]
[ROW][C]73[/C][C]123.04[/C][C]123.103307491365[/C][C]-0.0633074913645402[/C][/ROW]
[ROW][C]74[/C][C]123.06[/C][C]123.066346199676[/C][C]-0.00634619967583205[/C][/ROW]
[ROW][C]75[/C][C]123.39[/C][C]123.085648371566[/C][C]0.304351628434333[/C][/ROW]
[ROW][C]76[/C][C]124.02[/C][C]123.449114876332[/C][C]0.570885123668418[/C][/ROW]
[ROW][C]77[/C][C]124.05[/C][C]124.141889403974[/C][C]-0.0918894039735818[/C][/ROW]
[ROW][C]78[/C][C]123.99[/C][C]124.161785245202[/C][C]-0.17178524520223[/C][/ROW]
[ROW][C]79[/C][C]124.46[/C][C]124.082895739807[/C][C]0.377104260192723[/C][/ROW]
[ROW][C]80[/C][C]124.46[/C][C]124.594362123890[/C][C]-0.134362123890412[/C][/ROW]
[ROW][C]81[/C][C]124.6[/C][C]124.579587664878[/C][C]0.0204123351215770[/C][/ROW]
[ROW][C]82[/C][C]124.84[/C][C]124.721832205228[/C][C]0.118167794771523[/C][/ROW]
[ROW][C]83[/C][C]124.84[/C][C]124.974825935826[/C][C]-0.134825935826356[/C][/ROW]
[ROW][C]84[/C][C]124.99[/C][C]124.960000476054[/C][C]0.0299995239456479[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=13460&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=13460&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
3120.08120.050.0300000000000011
4120.12120.0832987999710.0367012000292561
5120.18120.1273344638900.0526655361098136
6120.2120.1931255661890.00687443381052333
7120.25120.2138814789250.0361185210754229
8120.25120.267853071467-0.0178530714668170
9120.24120.265889947746-0.0258899477457391
10120.29120.2530430891170.0369569108831627
11120.25120.307106871002-0.0571068710015368
12120.26120.260827399522-0.000827399521881489
13120.32120.2707364186710.0492635813287308
14120.31120.336153442026-0.0261534420261285
15120.36120.3232776095660.0367223904335532
16120.4120.3773156035830.0226843964172900
17120.4120.419809979791-0.0198099797906508
18120.39120.417631674432-0.0276316744321861
19120.44120.4045932955390.0354067044614368
20120.5120.4584866167270.0415133832733829
21120.53120.5230514283110.00694857168912222
22120.64120.5538154932470.0861845067529572
23120.78120.6732923415260.10670765847442
24120.94120.8250259155470.114974084452612
25121120.9976684657620.00233153423829435
26121.05121.057924841264-0.00792484126428405
27121.15121.1070534257270.0429465742734294
28121.07121.211775830992-0.141775830991833
29121.18121.1161861607540.0638138392458387
30121.46121.2332031304550.226796869544543
31121.71121.5381417140090.171858285990552
32121.71121.807039250969-0.0970392509694165
33121.74121.796368815027-0.056368815027426
34121.76121.820170500182-0.0601705001819539
35121.76121.833554152041-0.0735541520406144
36121.82121.825466137554-0.00546613755395242
37121.82121.884865081074-0.0648650810738332
38121.82121.877732516822-0.0577325168221989
39121.94121.8713842493290.0686157506712846
40121.99121.998929237206-0.00892923720563488
41122.18122.0479473782910.132052621708809
42122.41122.2524678844460.157532115554417
43122.48122.499790115718-0.0197901157183367
44122.52122.567613994613-0.0476139946132577
45122.62122.6023783598120.0176216401880112
46122.63122.70431603535-0.0743160353498951
47122.74122.7061442441750.0338557558247317
48122.58122.819867023053-0.239867023052753
49122.59122.633491245432-0.0434912454317242
50122.61122.638708948126-0.0287089481264644
51122.63122.655552112218-0.0255521122184632
52122.37122.672742401984-0.302742401983821
53122.36122.379452847757-0.0194528477568525
54122.47122.3673138126360.102686187363531
55122.46122.488605185699-0.0286051856988507
56122.45122.475459759507-0.0254597595072852
57122.49122.4626602043770.0273397956233055
58122.5122.505666488277-0.00566648827677341
59122.37122.515043401231-0.145043401231376
60122.37122.3690944289730.000905571026606822
61122.51122.3691940055630.140805994437414
62122.51122.524677032574-0.0146770325736583
63122.55122.5230631460860.0269368539138242
64122.56122.566025122516-0.00602512251626308
65122.72122.5753626000500.144637399949744
66122.97122.7512669284080.218733071592283
67123.03123.0253188167470.00468118325325406
68123.05123.085833559653-0.0358335596527155
69123.08123.101893301468-0.0218933014682392
70123.08123.12948591406-0.0494859140601278
71123.12123.124044442998-0.00404444299832107
72123.07123.163599716050-0.0935997160501927
73123.04123.103307491365-0.0633074913645402
74123.06123.066346199676-0.00634619967583205
75123.39123.0856483715660.304351628434333
76124.02123.4491148763320.570885123668418
77124.05124.141889403974-0.0918894039735818
78123.99124.161785245202-0.17178524520223
79124.46124.0828957398070.377104260192723
80124.46124.594362123890-0.134362123890412
81124.6124.5795876648780.0204123351215770
82124.84124.7218322052280.118167794771523
83124.84124.974825935826-0.134825935826356
84124.99124.9600004760540.0299995239456479






Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
85125.113299223678124.877300129219125.349298318137
86125.236598447356124.884017759046125.589179135667
87125.359897671034124.904705886924125.815089455145
88125.483196894713124.930293936672126.036099852753
89125.606496118391124.957522808768126.255469428014
90125.729795342069124.984852095995126.474738588143
91125.853094565747125.011446905748126.694742225746
92125.976393789425125.036817161095126.915970417755
93126.099693013103125.060660933037127.138725093170
94126.222992236782125.082787033733127.363197439830
95126.346291460460125.103073129582127.589509791337
96126.469590684138125.121441487762127.817739880513

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
85 & 125.113299223678 & 124.877300129219 & 125.349298318137 \tabularnewline
86 & 125.236598447356 & 124.884017759046 & 125.589179135667 \tabularnewline
87 & 125.359897671034 & 124.904705886924 & 125.815089455145 \tabularnewline
88 & 125.483196894713 & 124.930293936672 & 126.036099852753 \tabularnewline
89 & 125.606496118391 & 124.957522808768 & 126.255469428014 \tabularnewline
90 & 125.729795342069 & 124.984852095995 & 126.474738588143 \tabularnewline
91 & 125.853094565747 & 125.011446905748 & 126.694742225746 \tabularnewline
92 & 125.976393789425 & 125.036817161095 & 126.915970417755 \tabularnewline
93 & 126.099693013103 & 125.060660933037 & 127.138725093170 \tabularnewline
94 & 126.222992236782 & 125.082787033733 & 127.363197439830 \tabularnewline
95 & 126.346291460460 & 125.103073129582 & 127.589509791337 \tabularnewline
96 & 126.469590684138 & 125.121441487762 & 127.817739880513 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=13460&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]125.113299223678[/C][C]124.877300129219[/C][C]125.349298318137[/C][/ROW]
[ROW][C]86[/C][C]125.236598447356[/C][C]124.884017759046[/C][C]125.589179135667[/C][/ROW]
[ROW][C]87[/C][C]125.359897671034[/C][C]124.904705886924[/C][C]125.815089455145[/C][/ROW]
[ROW][C]88[/C][C]125.483196894713[/C][C]124.930293936672[/C][C]126.036099852753[/C][/ROW]
[ROW][C]89[/C][C]125.606496118391[/C][C]124.957522808768[/C][C]126.255469428014[/C][/ROW]
[ROW][C]90[/C][C]125.729795342069[/C][C]124.984852095995[/C][C]126.474738588143[/C][/ROW]
[ROW][C]91[/C][C]125.853094565747[/C][C]125.011446905748[/C][C]126.694742225746[/C][/ROW]
[ROW][C]92[/C][C]125.976393789425[/C][C]125.036817161095[/C][C]126.915970417755[/C][/ROW]
[ROW][C]93[/C][C]126.099693013103[/C][C]125.060660933037[/C][C]127.138725093170[/C][/ROW]
[ROW][C]94[/C][C]126.222992236782[/C][C]125.082787033733[/C][C]127.363197439830[/C][/ROW]
[ROW][C]95[/C][C]126.346291460460[/C][C]125.103073129582[/C][C]127.589509791337[/C][/ROW]
[ROW][C]96[/C][C]126.469590684138[/C][C]125.121441487762[/C][C]127.817739880513[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=13460&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=13460&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
85125.113299223678124.877300129219125.349298318137
86125.236598447356124.884017759046125.589179135667
87125.359897671034124.904705886924125.815089455145
88125.483196894713124.930293936672126.036099852753
89125.606496118391124.957522808768126.255469428014
90125.729795342069124.984852095995126.474738588143
91125.853094565747125.011446905748126.694742225746
92125.976393789425125.036817161095126.915970417755
93126.099693013103125.060660933037127.138725093170
94126.222992236782125.082787033733127.363197439830
95126.346291460460125.103073129582127.589509791337
96126.469590684138125.121441487762127.817739880513


Figures (Output of Computation)

Input Parameters & R Code

Parameters (Session):
par1 = 12 ; par2 = Double ; par3 = multiplicative ;
Parameters (R input):
par1 = 12 ; par2 = Double ; par3 = multiplicative ;
R code (references can be found in the software module):
par1 <- as.numeric(par1)
if (par2 == 'Single') K <- 1
if (par2 == 'Double') K <- 2
if (par2 == 'Triple') K <- par1
nx <- length(x)
nxmK <- nx - K
x <- ts(x, frequency = par1)
if (par2 == 'Single') fit <- HoltWinters(x, gamma=0, beta=0)
if (par2 == 'Double') fit <- HoltWinters(x, gamma=0)
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')