Free Statistics

of Irreproducible Research!

Author's title

Author*The author of this computation has been verified*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationFri, 10 Dec 2010 15:51:42 +0000
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/Dec/10/t1291996240g3bu39mppisxvs0.htm/, Retrieved Mon, 29 Apr 2024 12:33:43 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=107786, Retrieved Mon, 29 Apr 2024 12:33:43 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact158
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [Exponential Smoothing] [HPC Retail Sales] [2008-03-10 17:56:43] [74be16979710d4c4e7c6647856088456]
- RM D    [Exponential Smoothing] [Workshop 8 (Tripl...] [2010-12-10 15:51:42] [6427096bd21c899f2c90594929aeeec2] [Current]
Feedback Forum

Post a new message
Dataseries X:
37
30
47
35
30
43
82
40
47
19
52
136
80
42
54
66
81
63
137
72
107
58
36
52
79
77
54
84
48
96
83
66
61
53
30
74
69
59
42
65
70
100
63
105
82
81
75
102
121
98
76
77
63
37
35
23
40
29
37
51
20
28
13
22
25
13
16
13
16
17
9
17
25
14
8
7
10
7
10
3




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'Sir Ronald Aylmer Fisher' @ 193.190.124.24

\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 & 'Sir Ronald Aylmer Fisher' @ 193.190.124.24 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=107786&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]'Sir Ronald Aylmer Fisher' @ 193.190.124.24[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=107786&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=107786&T=0

As an alternative you can also use a 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'Sir Ronald Aylmer Fisher' @ 193.190.124.24







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.350759329200033
beta0
gamma0.714202236422672

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.350759329200033 \tabularnewline
beta & 0 \tabularnewline
gamma & 0.714202236422672 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=107786&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]0.350759329200033[/C][/ROW]
[ROW][C]beta[/C][C]0[/C][/ROW]
[ROW][C]gamma[/C][C]0.714202236422672[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=107786&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=107786&T=1

As an alternative you can also use a QR Code:  

The GUIDs for individual cells are displayed in the table below:

Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.350759329200033
beta0
gamma0.714202236422672







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
138063.354166666666716.6458333333333
144227.567848000642214.4321519993578
155440.796726621516613.2032733784834
166653.30289793499812.6971020650019
178171.79819160476919.20180839523086
186361.19247841157421.80752158842579
19137103.36815013811233.6318498618883
207270.87316856875721.12683143124282
2110777.476748539034829.5232514609652
225858.2489710839535-0.248971083953485
233687.744975486889-51.7449754868891
2452150.636609262302-98.6366092623024
257964.632390490192514.3676095098075
267727.020503572152149.9794964278479
275452.14812720988141.85187279011862
288460.437982726941123.5620172730589
294881.1235170544008-33.1235170544008
309652.243150614895943.7568493851041
3183123.889535798133-40.8895357981334
326650.183258972315815.8167410276842
336175.1065733346721-14.1065733346721
345326.770171561345726.2298284386543
353041.6757239761287-11.6757239761287
367496.8788802384768-22.8788802384768
376989.8462205932832-20.8462205932832
385956.39559943511442.6044005648856
394242.5897098574903-0.589709857490305
406560.08991568709224.91008431290784
417047.948643911602222.0513560883978
4210074.06996988945925.9300301105410
4363100.213822431864-37.2138224318639
4410554.090921041499250.9090789585008
458277.44808444197034.55191555802971
468154.359873127662526.6401268723375
477551.832948580939923.1670514190601
48102114.062751486308-12.0627514863078
49121111.7664721076529.23352789234812
509899.7404016861067-1.74040168610671
517682.9294578735977-6.92945787359767
5277100.756132765662-23.756132765662
536386.5081394689932-23.5081394689932
543798.447546364477-61.447546364477
553564.6637801729412-29.6637801729412
562362.0507588180824-39.0507588180824
574032.35835667857957.64164332142052
582920.59595988971798.40404011028209
593710.062130416276026.937869583724
605157.2789059931065-6.2789059931065
612066.886217830153-46.886217830153
622830.0871310857474-2.08713108574736
631310.74845970548502.25154029451503
642223.9931089624076-1.99310896240757
652517.49369109455817.50630890544188
661322.7196141774821-9.7196141774821
671621.8176899622591-5.81768996225912
681323.2162671673847-10.2162671673847
691625.2885917259022-9.28859172590225
70177.941272159293639.05872784070637
7196.231015947071022.76898405292898
721729.5680713779749-12.5680713779749
732518.1402303180596.85976968194101
741420.9659000638613-6.96590006386126
7581.927749746500056.07225025349995
76714.5443509061419-7.54435090614195
771010.5025600306134-0.502560030613406
7874.931824174008262.06817582599174
79109.973857153196110.0261428468038893
80311.3826407570439-8.38264075704385

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 80 & 63.3541666666667 & 16.6458333333333 \tabularnewline
14 & 42 & 27.5678480006422 & 14.4321519993578 \tabularnewline
15 & 54 & 40.7967266215166 & 13.2032733784834 \tabularnewline
16 & 66 & 53.302897934998 & 12.6971020650019 \tabularnewline
17 & 81 & 71.7981916047691 & 9.20180839523086 \tabularnewline
18 & 63 & 61.1924784115742 & 1.80752158842579 \tabularnewline
19 & 137 & 103.368150138112 & 33.6318498618883 \tabularnewline
20 & 72 & 70.8731685687572 & 1.12683143124282 \tabularnewline
21 & 107 & 77.4767485390348 & 29.5232514609652 \tabularnewline
22 & 58 & 58.2489710839535 & -0.248971083953485 \tabularnewline
23 & 36 & 87.744975486889 & -51.7449754868891 \tabularnewline
24 & 52 & 150.636609262302 & -98.6366092623024 \tabularnewline
25 & 79 & 64.6323904901925 & 14.3676095098075 \tabularnewline
26 & 77 & 27.0205035721521 & 49.9794964278479 \tabularnewline
27 & 54 & 52.1481272098814 & 1.85187279011862 \tabularnewline
28 & 84 & 60.4379827269411 & 23.5620172730589 \tabularnewline
29 & 48 & 81.1235170544008 & -33.1235170544008 \tabularnewline
30 & 96 & 52.2431506148959 & 43.7568493851041 \tabularnewline
31 & 83 & 123.889535798133 & -40.8895357981334 \tabularnewline
32 & 66 & 50.1832589723158 & 15.8167410276842 \tabularnewline
33 & 61 & 75.1065733346721 & -14.1065733346721 \tabularnewline
34 & 53 & 26.7701715613457 & 26.2298284386543 \tabularnewline
35 & 30 & 41.6757239761287 & -11.6757239761287 \tabularnewline
36 & 74 & 96.8788802384768 & -22.8788802384768 \tabularnewline
37 & 69 & 89.8462205932832 & -20.8462205932832 \tabularnewline
38 & 59 & 56.3955994351144 & 2.6044005648856 \tabularnewline
39 & 42 & 42.5897098574903 & -0.589709857490305 \tabularnewline
40 & 65 & 60.0899156870922 & 4.91008431290784 \tabularnewline
41 & 70 & 47.9486439116022 & 22.0513560883978 \tabularnewline
42 & 100 & 74.069969889459 & 25.9300301105410 \tabularnewline
43 & 63 & 100.213822431864 & -37.2138224318639 \tabularnewline
44 & 105 & 54.0909210414992 & 50.9090789585008 \tabularnewline
45 & 82 & 77.4480844419703 & 4.55191555802971 \tabularnewline
46 & 81 & 54.3598731276625 & 26.6401268723375 \tabularnewline
47 & 75 & 51.8329485809399 & 23.1670514190601 \tabularnewline
48 & 102 & 114.062751486308 & -12.0627514863078 \tabularnewline
49 & 121 & 111.766472107652 & 9.23352789234812 \tabularnewline
50 & 98 & 99.7404016861067 & -1.74040168610671 \tabularnewline
51 & 76 & 82.9294578735977 & -6.92945787359767 \tabularnewline
52 & 77 & 100.756132765662 & -23.756132765662 \tabularnewline
53 & 63 & 86.5081394689932 & -23.5081394689932 \tabularnewline
54 & 37 & 98.447546364477 & -61.447546364477 \tabularnewline
55 & 35 & 64.6637801729412 & -29.6637801729412 \tabularnewline
56 & 23 & 62.0507588180824 & -39.0507588180824 \tabularnewline
57 & 40 & 32.3583566785795 & 7.64164332142052 \tabularnewline
58 & 29 & 20.5959598897179 & 8.40404011028209 \tabularnewline
59 & 37 & 10.0621304162760 & 26.937869583724 \tabularnewline
60 & 51 & 57.2789059931065 & -6.2789059931065 \tabularnewline
61 & 20 & 66.886217830153 & -46.886217830153 \tabularnewline
62 & 28 & 30.0871310857474 & -2.08713108574736 \tabularnewline
63 & 13 & 10.7484597054850 & 2.25154029451503 \tabularnewline
64 & 22 & 23.9931089624076 & -1.99310896240757 \tabularnewline
65 & 25 & 17.4936910945581 & 7.50630890544188 \tabularnewline
66 & 13 & 22.7196141774821 & -9.7196141774821 \tabularnewline
67 & 16 & 21.8176899622591 & -5.81768996225912 \tabularnewline
68 & 13 & 23.2162671673847 & -10.2162671673847 \tabularnewline
69 & 16 & 25.2885917259022 & -9.28859172590225 \tabularnewline
70 & 17 & 7.94127215929363 & 9.05872784070637 \tabularnewline
71 & 9 & 6.23101594707102 & 2.76898405292898 \tabularnewline
72 & 17 & 29.5680713779749 & -12.5680713779749 \tabularnewline
73 & 25 & 18.140230318059 & 6.85976968194101 \tabularnewline
74 & 14 & 20.9659000638613 & -6.96590006386126 \tabularnewline
75 & 8 & 1.92774974650005 & 6.07225025349995 \tabularnewline
76 & 7 & 14.5443509061419 & -7.54435090614195 \tabularnewline
77 & 10 & 10.5025600306134 & -0.502560030613406 \tabularnewline
78 & 7 & 4.93182417400826 & 2.06817582599174 \tabularnewline
79 & 10 & 9.97385715319611 & 0.0261428468038893 \tabularnewline
80 & 3 & 11.3826407570439 & -8.38264075704385 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=107786&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]80[/C][C]63.3541666666667[/C][C]16.6458333333333[/C][/ROW]
[ROW][C]14[/C][C]42[/C][C]27.5678480006422[/C][C]14.4321519993578[/C][/ROW]
[ROW][C]15[/C][C]54[/C][C]40.7967266215166[/C][C]13.2032733784834[/C][/ROW]
[ROW][C]16[/C][C]66[/C][C]53.302897934998[/C][C]12.6971020650019[/C][/ROW]
[ROW][C]17[/C][C]81[/C][C]71.7981916047691[/C][C]9.20180839523086[/C][/ROW]
[ROW][C]18[/C][C]63[/C][C]61.1924784115742[/C][C]1.80752158842579[/C][/ROW]
[ROW][C]19[/C][C]137[/C][C]103.368150138112[/C][C]33.6318498618883[/C][/ROW]
[ROW][C]20[/C][C]72[/C][C]70.8731685687572[/C][C]1.12683143124282[/C][/ROW]
[ROW][C]21[/C][C]107[/C][C]77.4767485390348[/C][C]29.5232514609652[/C][/ROW]
[ROW][C]22[/C][C]58[/C][C]58.2489710839535[/C][C]-0.248971083953485[/C][/ROW]
[ROW][C]23[/C][C]36[/C][C]87.744975486889[/C][C]-51.7449754868891[/C][/ROW]
[ROW][C]24[/C][C]52[/C][C]150.636609262302[/C][C]-98.6366092623024[/C][/ROW]
[ROW][C]25[/C][C]79[/C][C]64.6323904901925[/C][C]14.3676095098075[/C][/ROW]
[ROW][C]26[/C][C]77[/C][C]27.0205035721521[/C][C]49.9794964278479[/C][/ROW]
[ROW][C]27[/C][C]54[/C][C]52.1481272098814[/C][C]1.85187279011862[/C][/ROW]
[ROW][C]28[/C][C]84[/C][C]60.4379827269411[/C][C]23.5620172730589[/C][/ROW]
[ROW][C]29[/C][C]48[/C][C]81.1235170544008[/C][C]-33.1235170544008[/C][/ROW]
[ROW][C]30[/C][C]96[/C][C]52.2431506148959[/C][C]43.7568493851041[/C][/ROW]
[ROW][C]31[/C][C]83[/C][C]123.889535798133[/C][C]-40.8895357981334[/C][/ROW]
[ROW][C]32[/C][C]66[/C][C]50.1832589723158[/C][C]15.8167410276842[/C][/ROW]
[ROW][C]33[/C][C]61[/C][C]75.1065733346721[/C][C]-14.1065733346721[/C][/ROW]
[ROW][C]34[/C][C]53[/C][C]26.7701715613457[/C][C]26.2298284386543[/C][/ROW]
[ROW][C]35[/C][C]30[/C][C]41.6757239761287[/C][C]-11.6757239761287[/C][/ROW]
[ROW][C]36[/C][C]74[/C][C]96.8788802384768[/C][C]-22.8788802384768[/C][/ROW]
[ROW][C]37[/C][C]69[/C][C]89.8462205932832[/C][C]-20.8462205932832[/C][/ROW]
[ROW][C]38[/C][C]59[/C][C]56.3955994351144[/C][C]2.6044005648856[/C][/ROW]
[ROW][C]39[/C][C]42[/C][C]42.5897098574903[/C][C]-0.589709857490305[/C][/ROW]
[ROW][C]40[/C][C]65[/C][C]60.0899156870922[/C][C]4.91008431290784[/C][/ROW]
[ROW][C]41[/C][C]70[/C][C]47.9486439116022[/C][C]22.0513560883978[/C][/ROW]
[ROW][C]42[/C][C]100[/C][C]74.069969889459[/C][C]25.9300301105410[/C][/ROW]
[ROW][C]43[/C][C]63[/C][C]100.213822431864[/C][C]-37.2138224318639[/C][/ROW]
[ROW][C]44[/C][C]105[/C][C]54.0909210414992[/C][C]50.9090789585008[/C][/ROW]
[ROW][C]45[/C][C]82[/C][C]77.4480844419703[/C][C]4.55191555802971[/C][/ROW]
[ROW][C]46[/C][C]81[/C][C]54.3598731276625[/C][C]26.6401268723375[/C][/ROW]
[ROW][C]47[/C][C]75[/C][C]51.8329485809399[/C][C]23.1670514190601[/C][/ROW]
[ROW][C]48[/C][C]102[/C][C]114.062751486308[/C][C]-12.0627514863078[/C][/ROW]
[ROW][C]49[/C][C]121[/C][C]111.766472107652[/C][C]9.23352789234812[/C][/ROW]
[ROW][C]50[/C][C]98[/C][C]99.7404016861067[/C][C]-1.74040168610671[/C][/ROW]
[ROW][C]51[/C][C]76[/C][C]82.9294578735977[/C][C]-6.92945787359767[/C][/ROW]
[ROW][C]52[/C][C]77[/C][C]100.756132765662[/C][C]-23.756132765662[/C][/ROW]
[ROW][C]53[/C][C]63[/C][C]86.5081394689932[/C][C]-23.5081394689932[/C][/ROW]
[ROW][C]54[/C][C]37[/C][C]98.447546364477[/C][C]-61.447546364477[/C][/ROW]
[ROW][C]55[/C][C]35[/C][C]64.6637801729412[/C][C]-29.6637801729412[/C][/ROW]
[ROW][C]56[/C][C]23[/C][C]62.0507588180824[/C][C]-39.0507588180824[/C][/ROW]
[ROW][C]57[/C][C]40[/C][C]32.3583566785795[/C][C]7.64164332142052[/C][/ROW]
[ROW][C]58[/C][C]29[/C][C]20.5959598897179[/C][C]8.40404011028209[/C][/ROW]
[ROW][C]59[/C][C]37[/C][C]10.0621304162760[/C][C]26.937869583724[/C][/ROW]
[ROW][C]60[/C][C]51[/C][C]57.2789059931065[/C][C]-6.2789059931065[/C][/ROW]
[ROW][C]61[/C][C]20[/C][C]66.886217830153[/C][C]-46.886217830153[/C][/ROW]
[ROW][C]62[/C][C]28[/C][C]30.0871310857474[/C][C]-2.08713108574736[/C][/ROW]
[ROW][C]63[/C][C]13[/C][C]10.7484597054850[/C][C]2.25154029451503[/C][/ROW]
[ROW][C]64[/C][C]22[/C][C]23.9931089624076[/C][C]-1.99310896240757[/C][/ROW]
[ROW][C]65[/C][C]25[/C][C]17.4936910945581[/C][C]7.50630890544188[/C][/ROW]
[ROW][C]66[/C][C]13[/C][C]22.7196141774821[/C][C]-9.7196141774821[/C][/ROW]
[ROW][C]67[/C][C]16[/C][C]21.8176899622591[/C][C]-5.81768996225912[/C][/ROW]
[ROW][C]68[/C][C]13[/C][C]23.2162671673847[/C][C]-10.2162671673847[/C][/ROW]
[ROW][C]69[/C][C]16[/C][C]25.2885917259022[/C][C]-9.28859172590225[/C][/ROW]
[ROW][C]70[/C][C]17[/C][C]7.94127215929363[/C][C]9.05872784070637[/C][/ROW]
[ROW][C]71[/C][C]9[/C][C]6.23101594707102[/C][C]2.76898405292898[/C][/ROW]
[ROW][C]72[/C][C]17[/C][C]29.5680713779749[/C][C]-12.5680713779749[/C][/ROW]
[ROW][C]73[/C][C]25[/C][C]18.140230318059[/C][C]6.85976968194101[/C][/ROW]
[ROW][C]74[/C][C]14[/C][C]20.9659000638613[/C][C]-6.96590006386126[/C][/ROW]
[ROW][C]75[/C][C]8[/C][C]1.92774974650005[/C][C]6.07225025349995[/C][/ROW]
[ROW][C]76[/C][C]7[/C][C]14.5443509061419[/C][C]-7.54435090614195[/C][/ROW]
[ROW][C]77[/C][C]10[/C][C]10.5025600306134[/C][C]-0.502560030613406[/C][/ROW]
[ROW][C]78[/C][C]7[/C][C]4.93182417400826[/C][C]2.06817582599174[/C][/ROW]
[ROW][C]79[/C][C]10[/C][C]9.97385715319611[/C][C]0.0261428468038893[/C][/ROW]
[ROW][C]80[/C][C]3[/C][C]11.3826407570439[/C][C]-8.38264075704385[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=107786&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=107786&T=2

As an alternative you can also use a QR Code:  

The GUIDs for individual cells are displayed in the table below:

Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
138063.354166666666716.6458333333333
144227.567848000642214.4321519993578
155440.796726621516613.2032733784834
166653.30289793499812.6971020650019
178171.79819160476919.20180839523086
186361.19247841157421.80752158842579
19137103.36815013811233.6318498618883
207270.87316856875721.12683143124282
2110777.476748539034829.5232514609652
225858.2489710839535-0.248971083953485
233687.744975486889-51.7449754868891
2452150.636609262302-98.6366092623024
257964.632390490192514.3676095098075
267727.020503572152149.9794964278479
275452.14812720988141.85187279011862
288460.437982726941123.5620172730589
294881.1235170544008-33.1235170544008
309652.243150614895943.7568493851041
3183123.889535798133-40.8895357981334
326650.183258972315815.8167410276842
336175.1065733346721-14.1065733346721
345326.770171561345726.2298284386543
353041.6757239761287-11.6757239761287
367496.8788802384768-22.8788802384768
376989.8462205932832-20.8462205932832
385956.39559943511442.6044005648856
394242.5897098574903-0.589709857490305
406560.08991568709224.91008431290784
417047.948643911602222.0513560883978
4210074.06996988945925.9300301105410
4363100.213822431864-37.2138224318639
4410554.090921041499250.9090789585008
458277.44808444197034.55191555802971
468154.359873127662526.6401268723375
477551.832948580939923.1670514190601
48102114.062751486308-12.0627514863078
49121111.7664721076529.23352789234812
509899.7404016861067-1.74040168610671
517682.9294578735977-6.92945787359767
5277100.756132765662-23.756132765662
536386.5081394689932-23.5081394689932
543798.447546364477-61.447546364477
553564.6637801729412-29.6637801729412
562362.0507588180824-39.0507588180824
574032.35835667857957.64164332142052
582920.59595988971798.40404011028209
593710.062130416276026.937869583724
605157.2789059931065-6.2789059931065
612066.886217830153-46.886217830153
622830.0871310857474-2.08713108574736
631310.74845970548502.25154029451503
642223.9931089624076-1.99310896240757
652517.49369109455817.50630890544188
661322.7196141774821-9.7196141774821
671621.8176899622591-5.81768996225912
681323.2162671673847-10.2162671673847
691625.2885917259022-9.28859172590225
70177.941272159293639.05872784070637
7196.231015947071022.76898405292898
721729.5680713779749-12.5680713779749
732518.1402303180596.85976968194101
741420.9659000638613-6.96590006386126
7581.927749746500056.07225025349995
76714.5443509061419-7.54435090614195
771010.5025600306134-0.502560030613406
7874.931824174008262.06817582599174
79109.973857153196110.0261428468038893
80311.3826407570439-8.38264075704385







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
8114.5282799120459-35.328702063670764.3852618877625
828.94647336236186-43.888570452420261.7815171771439
831.14229796745304-54.511678153691756.7962740885977
8416.3964803808856-41.940371276329874.733332038101
8518.38548650175-42.516167535385679.2871405388856
8612.3942151340628-50.968507879093575.7569381472191
871.8450679459928-63.886643357037967.5767792490235
886.01790061131881-62.000340133410774.0361413560483
897.887563147406-62.342802629734878.1179289245468
903.68512720612633-68.689781984656176.0600363969087
917.05485970586599-67.402850999990481.5125704117224
924.5554118324795-71.92840270850781.039226373466

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
81 & 14.5282799120459 & -35.3287020636707 & 64.3852618877625 \tabularnewline
82 & 8.94647336236186 & -43.8885704524202 & 61.7815171771439 \tabularnewline
83 & 1.14229796745304 & -54.5116781536917 & 56.7962740885977 \tabularnewline
84 & 16.3964803808856 & -41.9403712763298 & 74.733332038101 \tabularnewline
85 & 18.38548650175 & -42.5161675353856 & 79.2871405388856 \tabularnewline
86 & 12.3942151340628 & -50.9685078790935 & 75.7569381472191 \tabularnewline
87 & 1.8450679459928 & -63.8866433570379 & 67.5767792490235 \tabularnewline
88 & 6.01790061131881 & -62.0003401334107 & 74.0361413560483 \tabularnewline
89 & 7.887563147406 & -62.3428026297348 & 78.1179289245468 \tabularnewline
90 & 3.68512720612633 & -68.6897819846561 & 76.0600363969087 \tabularnewline
91 & 7.05485970586599 & -67.4028509999904 & 81.5125704117224 \tabularnewline
92 & 4.5554118324795 & -71.928402708507 & 81.039226373466 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=107786&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]81[/C][C]14.5282799120459[/C][C]-35.3287020636707[/C][C]64.3852618877625[/C][/ROW]
[ROW][C]82[/C][C]8.94647336236186[/C][C]-43.8885704524202[/C][C]61.7815171771439[/C][/ROW]
[ROW][C]83[/C][C]1.14229796745304[/C][C]-54.5116781536917[/C][C]56.7962740885977[/C][/ROW]
[ROW][C]84[/C][C]16.3964803808856[/C][C]-41.9403712763298[/C][C]74.733332038101[/C][/ROW]
[ROW][C]85[/C][C]18.38548650175[/C][C]-42.5161675353856[/C][C]79.2871405388856[/C][/ROW]
[ROW][C]86[/C][C]12.3942151340628[/C][C]-50.9685078790935[/C][C]75.7569381472191[/C][/ROW]
[ROW][C]87[/C][C]1.8450679459928[/C][C]-63.8866433570379[/C][C]67.5767792490235[/C][/ROW]
[ROW][C]88[/C][C]6.01790061131881[/C][C]-62.0003401334107[/C][C]74.0361413560483[/C][/ROW]
[ROW][C]89[/C][C]7.887563147406[/C][C]-62.3428026297348[/C][C]78.1179289245468[/C][/ROW]
[ROW][C]90[/C][C]3.68512720612633[/C][C]-68.6897819846561[/C][C]76.0600363969087[/C][/ROW]
[ROW][C]91[/C][C]7.05485970586599[/C][C]-67.4028509999904[/C][C]81.5125704117224[/C][/ROW]
[ROW][C]92[/C][C]4.5554118324795[/C][C]-71.928402708507[/C][C]81.039226373466[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=107786&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=107786&T=3

As an alternative you can also use a QR Code:  

The GUIDs for individual cells are displayed in the table below:

Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
8114.5282799120459-35.328702063670764.3852618877625
828.94647336236186-43.888570452420261.7815171771439
831.14229796745304-54.511678153691756.7962740885977
8416.3964803808856-41.940371276329874.733332038101
8518.38548650175-42.516167535385679.2871405388856
8612.3942151340628-50.968507879093575.7569381472191
871.8450679459928-63.886643357037967.5767792490235
886.01790061131881-62.000340133410774.0361413560483
897.887563147406-62.342802629734878.1179289245468
903.68512720612633-68.689781984656176.0600363969087
917.05485970586599-67.402850999990481.5125704117224
924.5554118324795-71.92840270850781.039226373466



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')