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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 computationThu, 19 May 2011 17:56:42 +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/2011/May/19/t13058276703ec8b1w03da0ojb.htm/, Retrieved Sat, 11 May 2024 09:39:05 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=122165, Retrieved Sat, 11 May 2024 09:39:05 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywordsKDGP2W102
Estimated Impact77

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...] [2011-05-19 17:56:42] [d41d8cd98f00b204e9800998ecf8427e] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
12,32
12,34
12,36
12,54
12,77
12,79
12,96
12,96
13
13,19
13,25
13,61
13,8
13,83
14,04
14,16
14,2
14,27
14,31
14,69
14,9
14,92
15,01
15,09
15,14
15,24
15,33
15,36
15,44
15,5
15,58
15,65
15,72
15,82
15,87
16,07
16,18
16,19
16,39
16,54
16,61
16,62
16,66
16,71
16,72
16,79
16,82
16,83
16,91
16,97
17,02
17,03
17,04
17,07
17,11
17,12
17,14
17,18
17,24
17,26
17,26
17,29
17,36
17,44
17,48
17,48
17,52
17,54
17,58
17,64
17,69
17,69
17,76
17,79
17,82
17,89
17,95
18
18,03
18,06
18,08
18,13
18,16
18,18
18,18
18,27
18,31
18,35
18,45
18,5

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'Herman Ole Andreas Wold' @ www.yougetit.org

\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 & 'Herman Ole Andreas Wold' @ www.yougetit.org \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=122165&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]'Herman Ole Andreas Wold' @ www.yougetit.org[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=122165&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=122165&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'Herman Ole Andreas Wold' @ www.yougetit.org






Estimated Parameters of Exponential Smoothing
ParameterValue
alpha1
beta0.1650321679672
gammaFALSE

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 1 \tabularnewline
beta & 0.1650321679672 \tabularnewline
gamma & FALSE \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=122165&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]0.1650321679672[/C][/ROW]
[ROW][C]gamma[/C][C]FALSE[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=122165&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=122165&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
beta0.1650321679672
gammaFALSE






Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
312.3612.360
412.5412.380.16
512.7712.58640514687480.183594853125248
612.7912.8467042035136-0.0567042035136307
712.9612.85734618587490.102653814125079
812.9613.0442873673701-0.0842873673700861
91313.0303772404008-0.030377240400755
1013.1913.06536401856060.124635981439443
1113.2513.2759329647842-0.0259329647842268
1213.6113.33165319138410.278346808615931
1313.813.73758936865670.062410631343294
1413.8313.9378891304515-0.107889130451493
1514.0413.9500839533530.0899160466470121
1614.1614.1749229934662-0.0149229934661825
1714.214.2924602195019-0.0924602195019002
1814.2714.3172013090268-0.0472013090267769
1914.3114.3794115746672-0.069411574667198
2014.6914.40795643201790.282043567982145
2114.914.83450269350320.0654973064968498
2214.9215.0553118559903-0.13531185599034
2315.0115.0529810470446-0.0429810470445879
2415.0915.1358877916693-0.045887791669319
2515.1415.2083148299269-0.0683148299269032
2615.2415.2470406854398-0.00704068543975644
2715.3315.3458787458577-0.015878745857659
2815.3615.4332582420042-0.0732582420041687
2915.4415.4511682755048-0.0111682755047546
3015.515.5293251507858-0.0293251507857502
3115.5815.5844855575756-0.00448555757561309
3215.6515.6637452962844-0.0137452962843678
3315.7215.7314768802392-0.0114768802392078
3415.8215.79958282581180.020417174188168
3515.8715.9029523163319-0.032952316331869
3616.0715.94751412412810.122485875871922
3716.1816.16772823376860.0122717662314145
3816.1916.2797534699545-0.089753469954541
3916.3916.27494126022540.115058739774636
4016.5416.49392965349390.0460703465060526
4116.6116.6515327426568-0.041532742656841
4216.6216.7146785040946-0.0946785040945564
4316.6616.7090535053039-0.0490535053039416
4416.7116.7409580989772-0.0309580989772407
4516.7216.7858490167869-0.0658490167868848
4616.7916.7849818107880.00501818921196318
4716.8216.855809973433-0.0358099734329542
4816.8316.8799001758825-0.0499001758824704
4916.9116.88166504167460.0283349583253631
5016.9716.96634122127630.00365877872366482
5117.0217.0269450374612-0.006945037461211
5217.0317.0757988828724-0.0457988828723757
5317.0417.0782405939415-0.0382405939414738
5417.0717.081929665819-0.011929665818954
5517.1117.10996088720573.91127942691583e-05
5617.1217.149967342075-0.0299673420749613
5717.1417.1550217666441-0.0150217666441179
5817.1817.17254269192810.00745730807185652
5917.2417.21377338764640.0262266123535575
6017.2617.2781016223416-0.0181016223415789
6117.2617.2951142723628-0.0351142723628293
6217.2917.28931928786820.000680712131796213
6317.3617.31943162726710.0405683727329276
6417.4417.39612671377010.043873286229914
6517.4817.4833672173125-0.00336721731245859
6617.4817.5228115181394-0.0428115181393665
6717.5217.51574624048690.00425375951314066
6817.5417.5564482476413-0.0164482476413248
6917.5817.57373375767380.00626624232618411
7017.6417.61476788922990.0252321107700908
7117.6917.67893199917270.0110680008273114
7217.6917.7307585753443-0.0407585753442845
7317.7617.7240320992920.0359679007080373
7417.7917.799967959923-0.009967959923042
7517.8217.8283229258867-0.008322925886727
7617.8917.85694937538380.0330506246161875
7717.9517.93240379161690.0175962083831074
781817.99530773203440.00469226796564115
7918.0318.0460821071894-0.0160821071894084
8018.0618.0734280421745-0.0134280421744641
8118.0818.1012119832629-0.0212119832628552
8218.1318.11771132367810.0122886763218979
8318.1618.169739350573-0.00973935057294995
8418.1818.1981320444333-0.0181320444333046
8518.1818.2151396738308-0.0351396738307983
8618.2718.20934049727680.0606595027231585
8718.3118.30935126651910.00064873348094352
8818.3518.34945832841180.000541671588152326
8918.4518.38954772164840.0604522783516295
9018.518.49952429220330.000475707796706359

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
3 & 12.36 & 12.36 & 0 \tabularnewline
4 & 12.54 & 12.38 & 0.16 \tabularnewline
5 & 12.77 & 12.5864051468748 & 0.183594853125248 \tabularnewline
6 & 12.79 & 12.8467042035136 & -0.0567042035136307 \tabularnewline
7 & 12.96 & 12.8573461858749 & 0.102653814125079 \tabularnewline
8 & 12.96 & 13.0442873673701 & -0.0842873673700861 \tabularnewline
9 & 13 & 13.0303772404008 & -0.030377240400755 \tabularnewline
10 & 13.19 & 13.0653640185606 & 0.124635981439443 \tabularnewline
11 & 13.25 & 13.2759329647842 & -0.0259329647842268 \tabularnewline
12 & 13.61 & 13.3316531913841 & 0.278346808615931 \tabularnewline
13 & 13.8 & 13.7375893686567 & 0.062410631343294 \tabularnewline
14 & 13.83 & 13.9378891304515 & -0.107889130451493 \tabularnewline
15 & 14.04 & 13.950083953353 & 0.0899160466470121 \tabularnewline
16 & 14.16 & 14.1749229934662 & -0.0149229934661825 \tabularnewline
17 & 14.2 & 14.2924602195019 & -0.0924602195019002 \tabularnewline
18 & 14.27 & 14.3172013090268 & -0.0472013090267769 \tabularnewline
19 & 14.31 & 14.3794115746672 & -0.069411574667198 \tabularnewline
20 & 14.69 & 14.4079564320179 & 0.282043567982145 \tabularnewline
21 & 14.9 & 14.8345026935032 & 0.0654973064968498 \tabularnewline
22 & 14.92 & 15.0553118559903 & -0.13531185599034 \tabularnewline
23 & 15.01 & 15.0529810470446 & -0.0429810470445879 \tabularnewline
24 & 15.09 & 15.1358877916693 & -0.045887791669319 \tabularnewline
25 & 15.14 & 15.2083148299269 & -0.0683148299269032 \tabularnewline
26 & 15.24 & 15.2470406854398 & -0.00704068543975644 \tabularnewline
27 & 15.33 & 15.3458787458577 & -0.015878745857659 \tabularnewline
28 & 15.36 & 15.4332582420042 & -0.0732582420041687 \tabularnewline
29 & 15.44 & 15.4511682755048 & -0.0111682755047546 \tabularnewline
30 & 15.5 & 15.5293251507858 & -0.0293251507857502 \tabularnewline
31 & 15.58 & 15.5844855575756 & -0.00448555757561309 \tabularnewline
32 & 15.65 & 15.6637452962844 & -0.0137452962843678 \tabularnewline
33 & 15.72 & 15.7314768802392 & -0.0114768802392078 \tabularnewline
34 & 15.82 & 15.7995828258118 & 0.020417174188168 \tabularnewline
35 & 15.87 & 15.9029523163319 & -0.032952316331869 \tabularnewline
36 & 16.07 & 15.9475141241281 & 0.122485875871922 \tabularnewline
37 & 16.18 & 16.1677282337686 & 0.0122717662314145 \tabularnewline
38 & 16.19 & 16.2797534699545 & -0.089753469954541 \tabularnewline
39 & 16.39 & 16.2749412602254 & 0.115058739774636 \tabularnewline
40 & 16.54 & 16.4939296534939 & 0.0460703465060526 \tabularnewline
41 & 16.61 & 16.6515327426568 & -0.041532742656841 \tabularnewline
42 & 16.62 & 16.7146785040946 & -0.0946785040945564 \tabularnewline
43 & 16.66 & 16.7090535053039 & -0.0490535053039416 \tabularnewline
44 & 16.71 & 16.7409580989772 & -0.0309580989772407 \tabularnewline
45 & 16.72 & 16.7858490167869 & -0.0658490167868848 \tabularnewline
46 & 16.79 & 16.784981810788 & 0.00501818921196318 \tabularnewline
47 & 16.82 & 16.855809973433 & -0.0358099734329542 \tabularnewline
48 & 16.83 & 16.8799001758825 & -0.0499001758824704 \tabularnewline
49 & 16.91 & 16.8816650416746 & 0.0283349583253631 \tabularnewline
50 & 16.97 & 16.9663412212763 & 0.00365877872366482 \tabularnewline
51 & 17.02 & 17.0269450374612 & -0.006945037461211 \tabularnewline
52 & 17.03 & 17.0757988828724 & -0.0457988828723757 \tabularnewline
53 & 17.04 & 17.0782405939415 & -0.0382405939414738 \tabularnewline
54 & 17.07 & 17.081929665819 & -0.011929665818954 \tabularnewline
55 & 17.11 & 17.1099608872057 & 3.91127942691583e-05 \tabularnewline
56 & 17.12 & 17.149967342075 & -0.0299673420749613 \tabularnewline
57 & 17.14 & 17.1550217666441 & -0.0150217666441179 \tabularnewline
58 & 17.18 & 17.1725426919281 & 0.00745730807185652 \tabularnewline
59 & 17.24 & 17.2137733876464 & 0.0262266123535575 \tabularnewline
60 & 17.26 & 17.2781016223416 & -0.0181016223415789 \tabularnewline
61 & 17.26 & 17.2951142723628 & -0.0351142723628293 \tabularnewline
62 & 17.29 & 17.2893192878682 & 0.000680712131796213 \tabularnewline
63 & 17.36 & 17.3194316272671 & 0.0405683727329276 \tabularnewline
64 & 17.44 & 17.3961267137701 & 0.043873286229914 \tabularnewline
65 & 17.48 & 17.4833672173125 & -0.00336721731245859 \tabularnewline
66 & 17.48 & 17.5228115181394 & -0.0428115181393665 \tabularnewline
67 & 17.52 & 17.5157462404869 & 0.00425375951314066 \tabularnewline
68 & 17.54 & 17.5564482476413 & -0.0164482476413248 \tabularnewline
69 & 17.58 & 17.5737337576738 & 0.00626624232618411 \tabularnewline
70 & 17.64 & 17.6147678892299 & 0.0252321107700908 \tabularnewline
71 & 17.69 & 17.6789319991727 & 0.0110680008273114 \tabularnewline
72 & 17.69 & 17.7307585753443 & -0.0407585753442845 \tabularnewline
73 & 17.76 & 17.724032099292 & 0.0359679007080373 \tabularnewline
74 & 17.79 & 17.799967959923 & -0.009967959923042 \tabularnewline
75 & 17.82 & 17.8283229258867 & -0.008322925886727 \tabularnewline
76 & 17.89 & 17.8569493753838 & 0.0330506246161875 \tabularnewline
77 & 17.95 & 17.9324037916169 & 0.0175962083831074 \tabularnewline
78 & 18 & 17.9953077320344 & 0.00469226796564115 \tabularnewline
79 & 18.03 & 18.0460821071894 & -0.0160821071894084 \tabularnewline
80 & 18.06 & 18.0734280421745 & -0.0134280421744641 \tabularnewline
81 & 18.08 & 18.1012119832629 & -0.0212119832628552 \tabularnewline
82 & 18.13 & 18.1177113236781 & 0.0122886763218979 \tabularnewline
83 & 18.16 & 18.169739350573 & -0.00973935057294995 \tabularnewline
84 & 18.18 & 18.1981320444333 & -0.0181320444333046 \tabularnewline
85 & 18.18 & 18.2151396738308 & -0.0351396738307983 \tabularnewline
86 & 18.27 & 18.2093404972768 & 0.0606595027231585 \tabularnewline
87 & 18.31 & 18.3093512665191 & 0.00064873348094352 \tabularnewline
88 & 18.35 & 18.3494583284118 & 0.000541671588152326 \tabularnewline
89 & 18.45 & 18.3895477216484 & 0.0604522783516295 \tabularnewline
90 & 18.5 & 18.4995242922033 & 0.000475707796706359 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=122165&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]12.36[/C][C]12.36[/C][C]0[/C][/ROW]
[ROW][C]4[/C][C]12.54[/C][C]12.38[/C][C]0.16[/C][/ROW]
[ROW][C]5[/C][C]12.77[/C][C]12.5864051468748[/C][C]0.183594853125248[/C][/ROW]
[ROW][C]6[/C][C]12.79[/C][C]12.8467042035136[/C][C]-0.0567042035136307[/C][/ROW]
[ROW][C]7[/C][C]12.96[/C][C]12.8573461858749[/C][C]0.102653814125079[/C][/ROW]
[ROW][C]8[/C][C]12.96[/C][C]13.0442873673701[/C][C]-0.0842873673700861[/C][/ROW]
[ROW][C]9[/C][C]13[/C][C]13.0303772404008[/C][C]-0.030377240400755[/C][/ROW]
[ROW][C]10[/C][C]13.19[/C][C]13.0653640185606[/C][C]0.124635981439443[/C][/ROW]
[ROW][C]11[/C][C]13.25[/C][C]13.2759329647842[/C][C]-0.0259329647842268[/C][/ROW]
[ROW][C]12[/C][C]13.61[/C][C]13.3316531913841[/C][C]0.278346808615931[/C][/ROW]
[ROW][C]13[/C][C]13.8[/C][C]13.7375893686567[/C][C]0.062410631343294[/C][/ROW]
[ROW][C]14[/C][C]13.83[/C][C]13.9378891304515[/C][C]-0.107889130451493[/C][/ROW]
[ROW][C]15[/C][C]14.04[/C][C]13.950083953353[/C][C]0.0899160466470121[/C][/ROW]
[ROW][C]16[/C][C]14.16[/C][C]14.1749229934662[/C][C]-0.0149229934661825[/C][/ROW]
[ROW][C]17[/C][C]14.2[/C][C]14.2924602195019[/C][C]-0.0924602195019002[/C][/ROW]
[ROW][C]18[/C][C]14.27[/C][C]14.3172013090268[/C][C]-0.0472013090267769[/C][/ROW]
[ROW][C]19[/C][C]14.31[/C][C]14.3794115746672[/C][C]-0.069411574667198[/C][/ROW]
[ROW][C]20[/C][C]14.69[/C][C]14.4079564320179[/C][C]0.282043567982145[/C][/ROW]
[ROW][C]21[/C][C]14.9[/C][C]14.8345026935032[/C][C]0.0654973064968498[/C][/ROW]
[ROW][C]22[/C][C]14.92[/C][C]15.0553118559903[/C][C]-0.13531185599034[/C][/ROW]
[ROW][C]23[/C][C]15.01[/C][C]15.0529810470446[/C][C]-0.0429810470445879[/C][/ROW]
[ROW][C]24[/C][C]15.09[/C][C]15.1358877916693[/C][C]-0.045887791669319[/C][/ROW]
[ROW][C]25[/C][C]15.14[/C][C]15.2083148299269[/C][C]-0.0683148299269032[/C][/ROW]
[ROW][C]26[/C][C]15.24[/C][C]15.2470406854398[/C][C]-0.00704068543975644[/C][/ROW]
[ROW][C]27[/C][C]15.33[/C][C]15.3458787458577[/C][C]-0.015878745857659[/C][/ROW]
[ROW][C]28[/C][C]15.36[/C][C]15.4332582420042[/C][C]-0.0732582420041687[/C][/ROW]
[ROW][C]29[/C][C]15.44[/C][C]15.4511682755048[/C][C]-0.0111682755047546[/C][/ROW]
[ROW][C]30[/C][C]15.5[/C][C]15.5293251507858[/C][C]-0.0293251507857502[/C][/ROW]
[ROW][C]31[/C][C]15.58[/C][C]15.5844855575756[/C][C]-0.00448555757561309[/C][/ROW]
[ROW][C]32[/C][C]15.65[/C][C]15.6637452962844[/C][C]-0.0137452962843678[/C][/ROW]
[ROW][C]33[/C][C]15.72[/C][C]15.7314768802392[/C][C]-0.0114768802392078[/C][/ROW]
[ROW][C]34[/C][C]15.82[/C][C]15.7995828258118[/C][C]0.020417174188168[/C][/ROW]
[ROW][C]35[/C][C]15.87[/C][C]15.9029523163319[/C][C]-0.032952316331869[/C][/ROW]
[ROW][C]36[/C][C]16.07[/C][C]15.9475141241281[/C][C]0.122485875871922[/C][/ROW]
[ROW][C]37[/C][C]16.18[/C][C]16.1677282337686[/C][C]0.0122717662314145[/C][/ROW]
[ROW][C]38[/C][C]16.19[/C][C]16.2797534699545[/C][C]-0.089753469954541[/C][/ROW]
[ROW][C]39[/C][C]16.39[/C][C]16.2749412602254[/C][C]0.115058739774636[/C][/ROW]
[ROW][C]40[/C][C]16.54[/C][C]16.4939296534939[/C][C]0.0460703465060526[/C][/ROW]
[ROW][C]41[/C][C]16.61[/C][C]16.6515327426568[/C][C]-0.041532742656841[/C][/ROW]
[ROW][C]42[/C][C]16.62[/C][C]16.7146785040946[/C][C]-0.0946785040945564[/C][/ROW]
[ROW][C]43[/C][C]16.66[/C][C]16.7090535053039[/C][C]-0.0490535053039416[/C][/ROW]
[ROW][C]44[/C][C]16.71[/C][C]16.7409580989772[/C][C]-0.0309580989772407[/C][/ROW]
[ROW][C]45[/C][C]16.72[/C][C]16.7858490167869[/C][C]-0.0658490167868848[/C][/ROW]
[ROW][C]46[/C][C]16.79[/C][C]16.784981810788[/C][C]0.00501818921196318[/C][/ROW]
[ROW][C]47[/C][C]16.82[/C][C]16.855809973433[/C][C]-0.0358099734329542[/C][/ROW]
[ROW][C]48[/C][C]16.83[/C][C]16.8799001758825[/C][C]-0.0499001758824704[/C][/ROW]
[ROW][C]49[/C][C]16.91[/C][C]16.8816650416746[/C][C]0.0283349583253631[/C][/ROW]
[ROW][C]50[/C][C]16.97[/C][C]16.9663412212763[/C][C]0.00365877872366482[/C][/ROW]
[ROW][C]51[/C][C]17.02[/C][C]17.0269450374612[/C][C]-0.006945037461211[/C][/ROW]
[ROW][C]52[/C][C]17.03[/C][C]17.0757988828724[/C][C]-0.0457988828723757[/C][/ROW]
[ROW][C]53[/C][C]17.04[/C][C]17.0782405939415[/C][C]-0.0382405939414738[/C][/ROW]
[ROW][C]54[/C][C]17.07[/C][C]17.081929665819[/C][C]-0.011929665818954[/C][/ROW]
[ROW][C]55[/C][C]17.11[/C][C]17.1099608872057[/C][C]3.91127942691583e-05[/C][/ROW]
[ROW][C]56[/C][C]17.12[/C][C]17.149967342075[/C][C]-0.0299673420749613[/C][/ROW]
[ROW][C]57[/C][C]17.14[/C][C]17.1550217666441[/C][C]-0.0150217666441179[/C][/ROW]
[ROW][C]58[/C][C]17.18[/C][C]17.1725426919281[/C][C]0.00745730807185652[/C][/ROW]
[ROW][C]59[/C][C]17.24[/C][C]17.2137733876464[/C][C]0.0262266123535575[/C][/ROW]
[ROW][C]60[/C][C]17.26[/C][C]17.2781016223416[/C][C]-0.0181016223415789[/C][/ROW]
[ROW][C]61[/C][C]17.26[/C][C]17.2951142723628[/C][C]-0.0351142723628293[/C][/ROW]
[ROW][C]62[/C][C]17.29[/C][C]17.2893192878682[/C][C]0.000680712131796213[/C][/ROW]
[ROW][C]63[/C][C]17.36[/C][C]17.3194316272671[/C][C]0.0405683727329276[/C][/ROW]
[ROW][C]64[/C][C]17.44[/C][C]17.3961267137701[/C][C]0.043873286229914[/C][/ROW]
[ROW][C]65[/C][C]17.48[/C][C]17.4833672173125[/C][C]-0.00336721731245859[/C][/ROW]
[ROW][C]66[/C][C]17.48[/C][C]17.5228115181394[/C][C]-0.0428115181393665[/C][/ROW]
[ROW][C]67[/C][C]17.52[/C][C]17.5157462404869[/C][C]0.00425375951314066[/C][/ROW]
[ROW][C]68[/C][C]17.54[/C][C]17.5564482476413[/C][C]-0.0164482476413248[/C][/ROW]
[ROW][C]69[/C][C]17.58[/C][C]17.5737337576738[/C][C]0.00626624232618411[/C][/ROW]
[ROW][C]70[/C][C]17.64[/C][C]17.6147678892299[/C][C]0.0252321107700908[/C][/ROW]
[ROW][C]71[/C][C]17.69[/C][C]17.6789319991727[/C][C]0.0110680008273114[/C][/ROW]
[ROW][C]72[/C][C]17.69[/C][C]17.7307585753443[/C][C]-0.0407585753442845[/C][/ROW]
[ROW][C]73[/C][C]17.76[/C][C]17.724032099292[/C][C]0.0359679007080373[/C][/ROW]
[ROW][C]74[/C][C]17.79[/C][C]17.799967959923[/C][C]-0.009967959923042[/C][/ROW]
[ROW][C]75[/C][C]17.82[/C][C]17.8283229258867[/C][C]-0.008322925886727[/C][/ROW]
[ROW][C]76[/C][C]17.89[/C][C]17.8569493753838[/C][C]0.0330506246161875[/C][/ROW]
[ROW][C]77[/C][C]17.95[/C][C]17.9324037916169[/C][C]0.0175962083831074[/C][/ROW]
[ROW][C]78[/C][C]18[/C][C]17.9953077320344[/C][C]0.00469226796564115[/C][/ROW]
[ROW][C]79[/C][C]18.03[/C][C]18.0460821071894[/C][C]-0.0160821071894084[/C][/ROW]
[ROW][C]80[/C][C]18.06[/C][C]18.0734280421745[/C][C]-0.0134280421744641[/C][/ROW]
[ROW][C]81[/C][C]18.08[/C][C]18.1012119832629[/C][C]-0.0212119832628552[/C][/ROW]
[ROW][C]82[/C][C]18.13[/C][C]18.1177113236781[/C][C]0.0122886763218979[/C][/ROW]
[ROW][C]83[/C][C]18.16[/C][C]18.169739350573[/C][C]-0.00973935057294995[/C][/ROW]
[ROW][C]84[/C][C]18.18[/C][C]18.1981320444333[/C][C]-0.0181320444333046[/C][/ROW]
[ROW][C]85[/C][C]18.18[/C][C]18.2151396738308[/C][C]-0.0351396738307983[/C][/ROW]
[ROW][C]86[/C][C]18.27[/C][C]18.2093404972768[/C][C]0.0606595027231585[/C][/ROW]
[ROW][C]87[/C][C]18.31[/C][C]18.3093512665191[/C][C]0.00064873348094352[/C][/ROW]
[ROW][C]88[/C][C]18.35[/C][C]18.3494583284118[/C][C]0.000541671588152326[/C][/ROW]
[ROW][C]89[/C][C]18.45[/C][C]18.3895477216484[/C][C]0.0604522783516295[/C][/ROW]
[ROW][C]90[/C][C]18.5[/C][C]18.4995242922033[/C][C]0.000475707796706359[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=122165&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=122165&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
312.3612.360
412.5412.380.16
512.7712.58640514687480.183594853125248
612.7912.8467042035136-0.0567042035136307
712.9612.85734618587490.102653814125079
812.9613.0442873673701-0.0842873673700861
91313.0303772404008-0.030377240400755
1013.1913.06536401856060.124635981439443
1113.2513.2759329647842-0.0259329647842268
1213.6113.33165319138410.278346808615931
1313.813.73758936865670.062410631343294
1413.8313.9378891304515-0.107889130451493
1514.0413.9500839533530.0899160466470121
1614.1614.1749229934662-0.0149229934661825
1714.214.2924602195019-0.0924602195019002
1814.2714.3172013090268-0.0472013090267769
1914.3114.3794115746672-0.069411574667198
2014.6914.40795643201790.282043567982145
2114.914.83450269350320.0654973064968498
2214.9215.0553118559903-0.13531185599034
2315.0115.0529810470446-0.0429810470445879
2415.0915.1358877916693-0.045887791669319
2515.1415.2083148299269-0.0683148299269032
2615.2415.2470406854398-0.00704068543975644
2715.3315.3458787458577-0.015878745857659
2815.3615.4332582420042-0.0732582420041687
2915.4415.4511682755048-0.0111682755047546
3015.515.5293251507858-0.0293251507857502
3115.5815.5844855575756-0.00448555757561309
3215.6515.6637452962844-0.0137452962843678
3315.7215.7314768802392-0.0114768802392078
3415.8215.79958282581180.020417174188168
3515.8715.9029523163319-0.032952316331869
3616.0715.94751412412810.122485875871922
3716.1816.16772823376860.0122717662314145
3816.1916.2797534699545-0.089753469954541
3916.3916.27494126022540.115058739774636
4016.5416.49392965349390.0460703465060526
4116.6116.6515327426568-0.041532742656841
4216.6216.7146785040946-0.0946785040945564
4316.6616.7090535053039-0.0490535053039416
4416.7116.7409580989772-0.0309580989772407
4516.7216.7858490167869-0.0658490167868848
4616.7916.7849818107880.00501818921196318
4716.8216.855809973433-0.0358099734329542
4816.8316.8799001758825-0.0499001758824704
4916.9116.88166504167460.0283349583253631
5016.9716.96634122127630.00365877872366482
5117.0217.0269450374612-0.006945037461211
5217.0317.0757988828724-0.0457988828723757
5317.0417.0782405939415-0.0382405939414738
5417.0717.081929665819-0.011929665818954
5517.1117.10996088720573.91127942691583e-05
5617.1217.149967342075-0.0299673420749613
5717.1417.1550217666441-0.0150217666441179
5817.1817.17254269192810.00745730807185652
5917.2417.21377338764640.0262266123535575
6017.2617.2781016223416-0.0181016223415789
6117.2617.2951142723628-0.0351142723628293
6217.2917.28931928786820.000680712131796213
6317.3617.31943162726710.0405683727329276
6417.4417.39612671377010.043873286229914
6517.4817.4833672173125-0.00336721731245859
6617.4817.5228115181394-0.0428115181393665
6717.5217.51574624048690.00425375951314066
6817.5417.5564482476413-0.0164482476413248
6917.5817.57373375767380.00626624232618411
7017.6417.61476788922990.0252321107700908
7117.6917.67893199917270.0110680008273114
7217.6917.7307585753443-0.0407585753442845
7317.7617.7240320992920.0359679007080373
7417.7917.799967959923-0.009967959923042
7517.8217.8283229258867-0.008322925886727
7617.8917.85694937538380.0330506246161875
7717.9517.93240379161690.0175962083831074
781817.99530773203440.00469226796564115
7918.0318.0460821071894-0.0160821071894084
8018.0618.0734280421745-0.0134280421744641
8118.0818.1012119832629-0.0212119832628552
8218.1318.11771132367810.0122886763218979
8318.1618.169739350573-0.00973935057294995
8418.1818.1981320444333-0.0181320444333046
8518.1818.2151396738308-0.0351396738307983
8618.2718.20934049727680.0606595027231585
8718.3118.30935126651910.00064873348094352
8818.3518.34945832841180.000541671588152326
8918.4518.38954772164840.0604522783516295
9018.518.49952429220330.000475707796706359






Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
9118.549602799292318.412946678588918.6862589199957
9218.599205598584618.389390608981118.8090205881881
9318.648808397876918.371212381725718.9264044140282
9418.698411197169218.353731933416619.0430904609219
9518.748013996461518.335373336238219.1606546566849
9618.797616795753818.315452558608719.279781032899
9718.847219595046118.293639293038519.4007998970537
9818.896822394338418.269769002185919.5238757864909
9918.946425193630718.243763102955319.6490872843061
10018.99602799292318.215590572926319.7764654129198
10119.045630792215318.185247819487819.9060137649429
10219.095233591507718.15274744416620.0377197388493

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
91 & 18.5496027992923 & 18.4129466785889 & 18.6862589199957 \tabularnewline
92 & 18.5992055985846 & 18.3893906089811 & 18.8090205881881 \tabularnewline
93 & 18.6488083978769 & 18.3712123817257 & 18.9264044140282 \tabularnewline
94 & 18.6984111971692 & 18.3537319334166 & 19.0430904609219 \tabularnewline
95 & 18.7480139964615 & 18.3353733362382 & 19.1606546566849 \tabularnewline
96 & 18.7976167957538 & 18.3154525586087 & 19.279781032899 \tabularnewline
97 & 18.8472195950461 & 18.2936392930385 & 19.4007998970537 \tabularnewline
98 & 18.8968223943384 & 18.2697690021859 & 19.5238757864909 \tabularnewline
99 & 18.9464251936307 & 18.2437631029553 & 19.6490872843061 \tabularnewline
100 & 18.996027992923 & 18.2155905729263 & 19.7764654129198 \tabularnewline
101 & 19.0456307922153 & 18.1852478194878 & 19.9060137649429 \tabularnewline
102 & 19.0952335915077 & 18.152747444166 & 20.0377197388493 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=122165&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]91[/C][C]18.5496027992923[/C][C]18.4129466785889[/C][C]18.6862589199957[/C][/ROW]
[ROW][C]92[/C][C]18.5992055985846[/C][C]18.3893906089811[/C][C]18.8090205881881[/C][/ROW]
[ROW][C]93[/C][C]18.6488083978769[/C][C]18.3712123817257[/C][C]18.9264044140282[/C][/ROW]
[ROW][C]94[/C][C]18.6984111971692[/C][C]18.3537319334166[/C][C]19.0430904609219[/C][/ROW]
[ROW][C]95[/C][C]18.7480139964615[/C][C]18.3353733362382[/C][C]19.1606546566849[/C][/ROW]
[ROW][C]96[/C][C]18.7976167957538[/C][C]18.3154525586087[/C][C]19.279781032899[/C][/ROW]
[ROW][C]97[/C][C]18.8472195950461[/C][C]18.2936392930385[/C][C]19.4007998970537[/C][/ROW]
[ROW][C]98[/C][C]18.8968223943384[/C][C]18.2697690021859[/C][C]19.5238757864909[/C][/ROW]
[ROW][C]99[/C][C]18.9464251936307[/C][C]18.2437631029553[/C][C]19.6490872843061[/C][/ROW]
[ROW][C]100[/C][C]18.996027992923[/C][C]18.2155905729263[/C][C]19.7764654129198[/C][/ROW]
[ROW][C]101[/C][C]19.0456307922153[/C][C]18.1852478194878[/C][C]19.9060137649429[/C][/ROW]
[ROW][C]102[/C][C]19.0952335915077[/C][C]18.152747444166[/C][C]20.0377197388493[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=122165&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=122165&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
9118.549602799292318.412946678588918.6862589199957
9218.599205598584618.389390608981118.8090205881881
9318.648808397876918.371212381725718.9264044140282
9418.698411197169218.353731933416619.0430904609219
9518.748013996461518.335373336238219.1606546566849
9618.797616795753818.315452558608719.279781032899
9718.847219595046118.293639293038519.4007998970537
9818.896822394338418.269769002185919.5238757864909
9918.946425193630718.243763102955319.6490872843061
10018.99602799292318.215590572926319.7764654129198
10119.045630792215318.185247819487819.9060137649429
10219.095233591507718.15274744416620.0377197388493


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=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')