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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, 02 Apr 2015 22:19:55 +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/2015/Apr/02/t1428009720h55riho3wtc8go7.htm/, Retrieved Thu, 09 May 2024 07:41:32 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=278670, Retrieved Thu, 09 May 2024 07:41:32 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact74

Tree of Dependent Computations

Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [] [2015-04-02 21:19:55] [9c6f291f5313961eaf08153dbee9a7d3] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
12374,6
12864,7
14905,8
12259,7
14088,9
14243,7
12732,8
11612
14176,6
14452,6
14512,7
12645,1
13820,5
13644,7
15684,1
13568,3
14531,1
15320,1
14344,2
12899,4
14462
16044,7
14731,2
12798,3
14213,1
14683,3
14652
15623,1
14880,4
15765,7
15433,1
12402,6
15639,8
14861,7
11699,4
10651,9
10086,9
10676,9
11332,1
10756,1
10450,5
11930,2
11419,9
9713,1
12608,5
12357,2
12107,9
11627,2
11105,9
11841,6
14290,8
13271,7
12909,4
14924,1
13257,4
12184,4
15035,5
14401
14165
13375,6
14210,8
15017,5
17157,8
15106,2
16696,1
16035,9
15418,9
13763,9
15595,2
15183,1
15515,9
14142,8
15012,7
16293,2
17771,4
15582,8
16049,9
16105,8
15623,6
14254,9
15266,8
16671
15665,4
13949,5
15146,9
15172,9
16981,4
16553,8
16438,5
15895,1
16989
13803,5
16678,3
17315,1
15895,4
14912,1

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'Sir Ronald Aylmer Fisher' @ fisher.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 & 'Sir Ronald Aylmer Fisher' @ fisher.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=278670&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' @ fisher.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=278670&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=278670&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'Sir Ronald Aylmer Fisher' @ fisher.wessa.net






Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.577374618520068
beta0
gamma0.6328831509647

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.577374618520068 \tabularnewline
beta & 0 \tabularnewline
gamma & 0.6328831509647 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=278670&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]0.577374618520068[/C][/ROW]
[ROW][C]beta[/C][C]0[/C][/ROW]
[ROW][C]gamma[/C][C]0.6328831509647[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=278670&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=278670&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
alpha0.577374618520068
beta0
gamma0.6328831509647






Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
1313820.513355.603258547464.896741452987
1413644.713409.1288104881235.571189511873
1515684.115600.697609360383.4023906396615
1613568.313536.512172699731.7878273002862
1714531.114523.91329722097.18670277905949
1815320.115383.2645235232-63.1645235232227
1914344.213689.5050707101654.694929289859
2012899.412935.6527789494-36.2527789493688
211446215496.0814843933-1034.08148439332
2216044.715169.7642216832874.935778316794
2314731.215743.7692394452-1012.56923944523
2412798.313309.9517676222-511.651767622192
2514213.114283.9817491619-70.8817491619102
2614683.313966.824124655716.475875344966
271465216395.3541165686-1743.35411656862
2815623.113262.64036300862360.45963699139
2914880.415587.9773614457-707.577361445719
3015765.716015.8249416456-250.124941645554
3115433.114406.12693910771026.97306089231
3212402.613682.4090923433-1279.80909234325
3315639.815257.948224171381.85177582902
3414861.716259.764474986-1398.06447498602
3511699.415016.5411846204-3317.14118462042
3610651.911386.1040051208-734.204005120833
3710086.912349.5318247514-2262.63182475142
3810676.910977.5098353811-300.609835381123
3911332.112160.8635170997-828.7635170997
4010756.110653.8684168903102.231583109666
4110450.510854.7463799449-404.246379944898
4211930.211580.0855045021350.11449549789
4311419.910658.5390919176761.360908082423
449713.19164.46277923354548.637220766464
4512608.512240.148962072368.351037928031
4612357.212758.0916101607-400.891610160699
4712107.911577.3104094202530.589590579762
4811627.210859.3199395343767.880060465741
4911105.912281.200589349-1175.30058934899
5011841.612061.7629506348-220.162950634825
5114290.813150.29804503271140.50195496733
5213271.713029.3224167378242.377583262245
5312909.413175.6482047495-266.248204749501
5414924.114182.4347495813741.665250418662
5513257.413596.956903894-339.556903893952
5612184.411410.3408566357774.059143364329
5715035.514567.9583430461467.541656953876
581440114937.4198957583-536.419895758287
591416513927.5336925533237.466307446657
6013375.613103.7699500875271.830049912534
6114210.813719.4965607575491.303439242518
6215017.514717.7868232128299.713176787214
6317157.816470.4256193389687.374380661135
6415106.215847.6020748476-741.402074847607
6516696.115289.87505555781406.22494444223
6616035.917531.8942615017-1495.99426150171
6715418.915365.251434335453.6485656646091
6813763.913703.523894453360.3761055466694
6915595.216367.0939159531-771.893915953135
7015183.115752.4047381283-569.304738128343
7115515.914930.5249260197585.375073980333
7214142.814316.8262304372-174.026230437215
7315012.714733.8298337459278.870166254115
7416293.215558.2213930102734.978606989824
7517771.417665.8601056595105.539894340487
7615582.816324.9417102249-742.141710224914
7716049.916341.218775882-291.318775881995
7816105.816826.8555463431-721.055546343079
7915623.615522.1294791316101.470520868368
8014254.913889.8125541897365.087445810306
8115266.816506.7058402655-1239.90584026549
821667115675.9854866218995.014513378248
8315665.416066.1489821355-400.748982135463
8413949.514679.9683332712-730.468333271157
8515146.914896.8337135416250.066286458421
8615172.915826.5911009073-653.691100907339
8716981.416964.089635272117.3103647278695
8816553.815345.49824517661208.30175482341
8916438.516608.4945921019-169.994592101946
9015895.117049.238105812-1154.13810581196
911698915714.46425065811274.53574934186
9213803.514829.9556880089-1026.45568800893
9316678.316214.1157484422464.184251557823
9417315.116965.073458028350.026541972031
9515895.416609.5089416235-714.108941623477
9614912.114954.2113521131-42.1113521130701

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 13820.5 & 13355.603258547 & 464.896741452987 \tabularnewline
14 & 13644.7 & 13409.1288104881 & 235.571189511873 \tabularnewline
15 & 15684.1 & 15600.6976093603 & 83.4023906396615 \tabularnewline
16 & 13568.3 & 13536.5121726997 & 31.7878273002862 \tabularnewline
17 & 14531.1 & 14523.9132972209 & 7.18670277905949 \tabularnewline
18 & 15320.1 & 15383.2645235232 & -63.1645235232227 \tabularnewline
19 & 14344.2 & 13689.5050707101 & 654.694929289859 \tabularnewline
20 & 12899.4 & 12935.6527789494 & -36.2527789493688 \tabularnewline
21 & 14462 & 15496.0814843933 & -1034.08148439332 \tabularnewline
22 & 16044.7 & 15169.7642216832 & 874.935778316794 \tabularnewline
23 & 14731.2 & 15743.7692394452 & -1012.56923944523 \tabularnewline
24 & 12798.3 & 13309.9517676222 & -511.651767622192 \tabularnewline
25 & 14213.1 & 14283.9817491619 & -70.8817491619102 \tabularnewline
26 & 14683.3 & 13966.824124655 & 716.475875344966 \tabularnewline
27 & 14652 & 16395.3541165686 & -1743.35411656862 \tabularnewline
28 & 15623.1 & 13262.6403630086 & 2360.45963699139 \tabularnewline
29 & 14880.4 & 15587.9773614457 & -707.577361445719 \tabularnewline
30 & 15765.7 & 16015.8249416456 & -250.124941645554 \tabularnewline
31 & 15433.1 & 14406.1269391077 & 1026.97306089231 \tabularnewline
32 & 12402.6 & 13682.4090923433 & -1279.80909234325 \tabularnewline
33 & 15639.8 & 15257.948224171 & 381.85177582902 \tabularnewline
34 & 14861.7 & 16259.764474986 & -1398.06447498602 \tabularnewline
35 & 11699.4 & 15016.5411846204 & -3317.14118462042 \tabularnewline
36 & 10651.9 & 11386.1040051208 & -734.204005120833 \tabularnewline
37 & 10086.9 & 12349.5318247514 & -2262.63182475142 \tabularnewline
38 & 10676.9 & 10977.5098353811 & -300.609835381123 \tabularnewline
39 & 11332.1 & 12160.8635170997 & -828.7635170997 \tabularnewline
40 & 10756.1 & 10653.8684168903 & 102.231583109666 \tabularnewline
41 & 10450.5 & 10854.7463799449 & -404.246379944898 \tabularnewline
42 & 11930.2 & 11580.0855045021 & 350.11449549789 \tabularnewline
43 & 11419.9 & 10658.5390919176 & 761.360908082423 \tabularnewline
44 & 9713.1 & 9164.46277923354 & 548.637220766464 \tabularnewline
45 & 12608.5 & 12240.148962072 & 368.351037928031 \tabularnewline
46 & 12357.2 & 12758.0916101607 & -400.891610160699 \tabularnewline
47 & 12107.9 & 11577.3104094202 & 530.589590579762 \tabularnewline
48 & 11627.2 & 10859.3199395343 & 767.880060465741 \tabularnewline
49 & 11105.9 & 12281.200589349 & -1175.30058934899 \tabularnewline
50 & 11841.6 & 12061.7629506348 & -220.162950634825 \tabularnewline
51 & 14290.8 & 13150.2980450327 & 1140.50195496733 \tabularnewline
52 & 13271.7 & 13029.3224167378 & 242.377583262245 \tabularnewline
53 & 12909.4 & 13175.6482047495 & -266.248204749501 \tabularnewline
54 & 14924.1 & 14182.4347495813 & 741.665250418662 \tabularnewline
55 & 13257.4 & 13596.956903894 & -339.556903893952 \tabularnewline
56 & 12184.4 & 11410.3408566357 & 774.059143364329 \tabularnewline
57 & 15035.5 & 14567.9583430461 & 467.541656953876 \tabularnewline
58 & 14401 & 14937.4198957583 & -536.419895758287 \tabularnewline
59 & 14165 & 13927.5336925533 & 237.466307446657 \tabularnewline
60 & 13375.6 & 13103.7699500875 & 271.830049912534 \tabularnewline
61 & 14210.8 & 13719.4965607575 & 491.303439242518 \tabularnewline
62 & 15017.5 & 14717.7868232128 & 299.713176787214 \tabularnewline
63 & 17157.8 & 16470.4256193389 & 687.374380661135 \tabularnewline
64 & 15106.2 & 15847.6020748476 & -741.402074847607 \tabularnewline
65 & 16696.1 & 15289.8750555578 & 1406.22494444223 \tabularnewline
66 & 16035.9 & 17531.8942615017 & -1495.99426150171 \tabularnewline
67 & 15418.9 & 15365.2514343354 & 53.6485656646091 \tabularnewline
68 & 13763.9 & 13703.5238944533 & 60.3761055466694 \tabularnewline
69 & 15595.2 & 16367.0939159531 & -771.893915953135 \tabularnewline
70 & 15183.1 & 15752.4047381283 & -569.304738128343 \tabularnewline
71 & 15515.9 & 14930.5249260197 & 585.375073980333 \tabularnewline
72 & 14142.8 & 14316.8262304372 & -174.026230437215 \tabularnewline
73 & 15012.7 & 14733.8298337459 & 278.870166254115 \tabularnewline
74 & 16293.2 & 15558.2213930102 & 734.978606989824 \tabularnewline
75 & 17771.4 & 17665.8601056595 & 105.539894340487 \tabularnewline
76 & 15582.8 & 16324.9417102249 & -742.141710224914 \tabularnewline
77 & 16049.9 & 16341.218775882 & -291.318775881995 \tabularnewline
78 & 16105.8 & 16826.8555463431 & -721.055546343079 \tabularnewline
79 & 15623.6 & 15522.1294791316 & 101.470520868368 \tabularnewline
80 & 14254.9 & 13889.8125541897 & 365.087445810306 \tabularnewline
81 & 15266.8 & 16506.7058402655 & -1239.90584026549 \tabularnewline
82 & 16671 & 15675.9854866218 & 995.014513378248 \tabularnewline
83 & 15665.4 & 16066.1489821355 & -400.748982135463 \tabularnewline
84 & 13949.5 & 14679.9683332712 & -730.468333271157 \tabularnewline
85 & 15146.9 & 14896.8337135416 & 250.066286458421 \tabularnewline
86 & 15172.9 & 15826.5911009073 & -653.691100907339 \tabularnewline
87 & 16981.4 & 16964.0896352721 & 17.3103647278695 \tabularnewline
88 & 16553.8 & 15345.4982451766 & 1208.30175482341 \tabularnewline
89 & 16438.5 & 16608.4945921019 & -169.994592101946 \tabularnewline
90 & 15895.1 & 17049.238105812 & -1154.13810581196 \tabularnewline
91 & 16989 & 15714.4642506581 & 1274.53574934186 \tabularnewline
92 & 13803.5 & 14829.9556880089 & -1026.45568800893 \tabularnewline
93 & 16678.3 & 16214.1157484422 & 464.184251557823 \tabularnewline
94 & 17315.1 & 16965.073458028 & 350.026541972031 \tabularnewline
95 & 15895.4 & 16609.5089416235 & -714.108941623477 \tabularnewline
96 & 14912.1 & 14954.2113521131 & -42.1113521130701 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=278670&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]13820.5[/C][C]13355.603258547[/C][C]464.896741452987[/C][/ROW]
[ROW][C]14[/C][C]13644.7[/C][C]13409.1288104881[/C][C]235.571189511873[/C][/ROW]
[ROW][C]15[/C][C]15684.1[/C][C]15600.6976093603[/C][C]83.4023906396615[/C][/ROW]
[ROW][C]16[/C][C]13568.3[/C][C]13536.5121726997[/C][C]31.7878273002862[/C][/ROW]
[ROW][C]17[/C][C]14531.1[/C][C]14523.9132972209[/C][C]7.18670277905949[/C][/ROW]
[ROW][C]18[/C][C]15320.1[/C][C]15383.2645235232[/C][C]-63.1645235232227[/C][/ROW]
[ROW][C]19[/C][C]14344.2[/C][C]13689.5050707101[/C][C]654.694929289859[/C][/ROW]
[ROW][C]20[/C][C]12899.4[/C][C]12935.6527789494[/C][C]-36.2527789493688[/C][/ROW]
[ROW][C]21[/C][C]14462[/C][C]15496.0814843933[/C][C]-1034.08148439332[/C][/ROW]
[ROW][C]22[/C][C]16044.7[/C][C]15169.7642216832[/C][C]874.935778316794[/C][/ROW]
[ROW][C]23[/C][C]14731.2[/C][C]15743.7692394452[/C][C]-1012.56923944523[/C][/ROW]
[ROW][C]24[/C][C]12798.3[/C][C]13309.9517676222[/C][C]-511.651767622192[/C][/ROW]
[ROW][C]25[/C][C]14213.1[/C][C]14283.9817491619[/C][C]-70.8817491619102[/C][/ROW]
[ROW][C]26[/C][C]14683.3[/C][C]13966.824124655[/C][C]716.475875344966[/C][/ROW]
[ROW][C]27[/C][C]14652[/C][C]16395.3541165686[/C][C]-1743.35411656862[/C][/ROW]
[ROW][C]28[/C][C]15623.1[/C][C]13262.6403630086[/C][C]2360.45963699139[/C][/ROW]
[ROW][C]29[/C][C]14880.4[/C][C]15587.9773614457[/C][C]-707.577361445719[/C][/ROW]
[ROW][C]30[/C][C]15765.7[/C][C]16015.8249416456[/C][C]-250.124941645554[/C][/ROW]
[ROW][C]31[/C][C]15433.1[/C][C]14406.1269391077[/C][C]1026.97306089231[/C][/ROW]
[ROW][C]32[/C][C]12402.6[/C][C]13682.4090923433[/C][C]-1279.80909234325[/C][/ROW]
[ROW][C]33[/C][C]15639.8[/C][C]15257.948224171[/C][C]381.85177582902[/C][/ROW]
[ROW][C]34[/C][C]14861.7[/C][C]16259.764474986[/C][C]-1398.06447498602[/C][/ROW]
[ROW][C]35[/C][C]11699.4[/C][C]15016.5411846204[/C][C]-3317.14118462042[/C][/ROW]
[ROW][C]36[/C][C]10651.9[/C][C]11386.1040051208[/C][C]-734.204005120833[/C][/ROW]
[ROW][C]37[/C][C]10086.9[/C][C]12349.5318247514[/C][C]-2262.63182475142[/C][/ROW]
[ROW][C]38[/C][C]10676.9[/C][C]10977.5098353811[/C][C]-300.609835381123[/C][/ROW]
[ROW][C]39[/C][C]11332.1[/C][C]12160.8635170997[/C][C]-828.7635170997[/C][/ROW]
[ROW][C]40[/C][C]10756.1[/C][C]10653.8684168903[/C][C]102.231583109666[/C][/ROW]
[ROW][C]41[/C][C]10450.5[/C][C]10854.7463799449[/C][C]-404.246379944898[/C][/ROW]
[ROW][C]42[/C][C]11930.2[/C][C]11580.0855045021[/C][C]350.11449549789[/C][/ROW]
[ROW][C]43[/C][C]11419.9[/C][C]10658.5390919176[/C][C]761.360908082423[/C][/ROW]
[ROW][C]44[/C][C]9713.1[/C][C]9164.46277923354[/C][C]548.637220766464[/C][/ROW]
[ROW][C]45[/C][C]12608.5[/C][C]12240.148962072[/C][C]368.351037928031[/C][/ROW]
[ROW][C]46[/C][C]12357.2[/C][C]12758.0916101607[/C][C]-400.891610160699[/C][/ROW]
[ROW][C]47[/C][C]12107.9[/C][C]11577.3104094202[/C][C]530.589590579762[/C][/ROW]
[ROW][C]48[/C][C]11627.2[/C][C]10859.3199395343[/C][C]767.880060465741[/C][/ROW]
[ROW][C]49[/C][C]11105.9[/C][C]12281.200589349[/C][C]-1175.30058934899[/C][/ROW]
[ROW][C]50[/C][C]11841.6[/C][C]12061.7629506348[/C][C]-220.162950634825[/C][/ROW]
[ROW][C]51[/C][C]14290.8[/C][C]13150.2980450327[/C][C]1140.50195496733[/C][/ROW]
[ROW][C]52[/C][C]13271.7[/C][C]13029.3224167378[/C][C]242.377583262245[/C][/ROW]
[ROW][C]53[/C][C]12909.4[/C][C]13175.6482047495[/C][C]-266.248204749501[/C][/ROW]
[ROW][C]54[/C][C]14924.1[/C][C]14182.4347495813[/C][C]741.665250418662[/C][/ROW]
[ROW][C]55[/C][C]13257.4[/C][C]13596.956903894[/C][C]-339.556903893952[/C][/ROW]
[ROW][C]56[/C][C]12184.4[/C][C]11410.3408566357[/C][C]774.059143364329[/C][/ROW]
[ROW][C]57[/C][C]15035.5[/C][C]14567.9583430461[/C][C]467.541656953876[/C][/ROW]
[ROW][C]58[/C][C]14401[/C][C]14937.4198957583[/C][C]-536.419895758287[/C][/ROW]
[ROW][C]59[/C][C]14165[/C][C]13927.5336925533[/C][C]237.466307446657[/C][/ROW]
[ROW][C]60[/C][C]13375.6[/C][C]13103.7699500875[/C][C]271.830049912534[/C][/ROW]
[ROW][C]61[/C][C]14210.8[/C][C]13719.4965607575[/C][C]491.303439242518[/C][/ROW]
[ROW][C]62[/C][C]15017.5[/C][C]14717.7868232128[/C][C]299.713176787214[/C][/ROW]
[ROW][C]63[/C][C]17157.8[/C][C]16470.4256193389[/C][C]687.374380661135[/C][/ROW]
[ROW][C]64[/C][C]15106.2[/C][C]15847.6020748476[/C][C]-741.402074847607[/C][/ROW]
[ROW][C]65[/C][C]16696.1[/C][C]15289.8750555578[/C][C]1406.22494444223[/C][/ROW]
[ROW][C]66[/C][C]16035.9[/C][C]17531.8942615017[/C][C]-1495.99426150171[/C][/ROW]
[ROW][C]67[/C][C]15418.9[/C][C]15365.2514343354[/C][C]53.6485656646091[/C][/ROW]
[ROW][C]68[/C][C]13763.9[/C][C]13703.5238944533[/C][C]60.3761055466694[/C][/ROW]
[ROW][C]69[/C][C]15595.2[/C][C]16367.0939159531[/C][C]-771.893915953135[/C][/ROW]
[ROW][C]70[/C][C]15183.1[/C][C]15752.4047381283[/C][C]-569.304738128343[/C][/ROW]
[ROW][C]71[/C][C]15515.9[/C][C]14930.5249260197[/C][C]585.375073980333[/C][/ROW]
[ROW][C]72[/C][C]14142.8[/C][C]14316.8262304372[/C][C]-174.026230437215[/C][/ROW]
[ROW][C]73[/C][C]15012.7[/C][C]14733.8298337459[/C][C]278.870166254115[/C][/ROW]
[ROW][C]74[/C][C]16293.2[/C][C]15558.2213930102[/C][C]734.978606989824[/C][/ROW]
[ROW][C]75[/C][C]17771.4[/C][C]17665.8601056595[/C][C]105.539894340487[/C][/ROW]
[ROW][C]76[/C][C]15582.8[/C][C]16324.9417102249[/C][C]-742.141710224914[/C][/ROW]
[ROW][C]77[/C][C]16049.9[/C][C]16341.218775882[/C][C]-291.318775881995[/C][/ROW]
[ROW][C]78[/C][C]16105.8[/C][C]16826.8555463431[/C][C]-721.055546343079[/C][/ROW]
[ROW][C]79[/C][C]15623.6[/C][C]15522.1294791316[/C][C]101.470520868368[/C][/ROW]
[ROW][C]80[/C][C]14254.9[/C][C]13889.8125541897[/C][C]365.087445810306[/C][/ROW]
[ROW][C]81[/C][C]15266.8[/C][C]16506.7058402655[/C][C]-1239.90584026549[/C][/ROW]
[ROW][C]82[/C][C]16671[/C][C]15675.9854866218[/C][C]995.014513378248[/C][/ROW]
[ROW][C]83[/C][C]15665.4[/C][C]16066.1489821355[/C][C]-400.748982135463[/C][/ROW]
[ROW][C]84[/C][C]13949.5[/C][C]14679.9683332712[/C][C]-730.468333271157[/C][/ROW]
[ROW][C]85[/C][C]15146.9[/C][C]14896.8337135416[/C][C]250.066286458421[/C][/ROW]
[ROW][C]86[/C][C]15172.9[/C][C]15826.5911009073[/C][C]-653.691100907339[/C][/ROW]
[ROW][C]87[/C][C]16981.4[/C][C]16964.0896352721[/C][C]17.3103647278695[/C][/ROW]
[ROW][C]88[/C][C]16553.8[/C][C]15345.4982451766[/C][C]1208.30175482341[/C][/ROW]
[ROW][C]89[/C][C]16438.5[/C][C]16608.4945921019[/C][C]-169.994592101946[/C][/ROW]
[ROW][C]90[/C][C]15895.1[/C][C]17049.238105812[/C][C]-1154.13810581196[/C][/ROW]
[ROW][C]91[/C][C]16989[/C][C]15714.4642506581[/C][C]1274.53574934186[/C][/ROW]
[ROW][C]92[/C][C]13803.5[/C][C]14829.9556880089[/C][C]-1026.45568800893[/C][/ROW]
[ROW][C]93[/C][C]16678.3[/C][C]16214.1157484422[/C][C]464.184251557823[/C][/ROW]
[ROW][C]94[/C][C]17315.1[/C][C]16965.073458028[/C][C]350.026541972031[/C][/ROW]
[ROW][C]95[/C][C]15895.4[/C][C]16609.5089416235[/C][C]-714.108941623477[/C][/ROW]
[ROW][C]96[/C][C]14912.1[/C][C]14954.2113521131[/C][C]-42.1113521130701[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=278670&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=278670&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
1313820.513355.603258547464.896741452987
1413644.713409.1288104881235.571189511873
1515684.115600.697609360383.4023906396615
1613568.313536.512172699731.7878273002862
1714531.114523.91329722097.18670277905949
1815320.115383.2645235232-63.1645235232227
1914344.213689.5050707101654.694929289859
2012899.412935.6527789494-36.2527789493688
211446215496.0814843933-1034.08148439332
2216044.715169.7642216832874.935778316794
2314731.215743.7692394452-1012.56923944523
2412798.313309.9517676222-511.651767622192
2514213.114283.9817491619-70.8817491619102
2614683.313966.824124655716.475875344966
271465216395.3541165686-1743.35411656862
2815623.113262.64036300862360.45963699139
2914880.415587.9773614457-707.577361445719
3015765.716015.8249416456-250.124941645554
3115433.114406.12693910771026.97306089231
3212402.613682.4090923433-1279.80909234325
3315639.815257.948224171381.85177582902
3414861.716259.764474986-1398.06447498602
3511699.415016.5411846204-3317.14118462042
3610651.911386.1040051208-734.204005120833
3710086.912349.5318247514-2262.63182475142
3810676.910977.5098353811-300.609835381123
3911332.112160.8635170997-828.7635170997
4010756.110653.8684168903102.231583109666
4110450.510854.7463799449-404.246379944898
4211930.211580.0855045021350.11449549789
4311419.910658.5390919176761.360908082423
449713.19164.46277923354548.637220766464
4512608.512240.148962072368.351037928031
4612357.212758.0916101607-400.891610160699
4712107.911577.3104094202530.589590579762
4811627.210859.3199395343767.880060465741
4911105.912281.200589349-1175.30058934899
5011841.612061.7629506348-220.162950634825
5114290.813150.29804503271140.50195496733
5213271.713029.3224167378242.377583262245
5312909.413175.6482047495-266.248204749501
5414924.114182.4347495813741.665250418662
5513257.413596.956903894-339.556903893952
5612184.411410.3408566357774.059143364329
5715035.514567.9583430461467.541656953876
581440114937.4198957583-536.419895758287
591416513927.5336925533237.466307446657
6013375.613103.7699500875271.830049912534
6114210.813719.4965607575491.303439242518
6215017.514717.7868232128299.713176787214
6317157.816470.4256193389687.374380661135
6415106.215847.6020748476-741.402074847607
6516696.115289.87505555781406.22494444223
6616035.917531.8942615017-1495.99426150171
6715418.915365.251434335453.6485656646091
6813763.913703.523894453360.3761055466694
6915595.216367.0939159531-771.893915953135
7015183.115752.4047381283-569.304738128343
7115515.914930.5249260197585.375073980333
7214142.814316.8262304372-174.026230437215
7315012.714733.8298337459278.870166254115
7416293.215558.2213930102734.978606989824
7517771.417665.8601056595105.539894340487
7615582.816324.9417102249-742.141710224914
7716049.916341.218775882-291.318775881995
7816105.816826.8555463431-721.055546343079
7915623.615522.1294791316101.470520868368
8014254.913889.8125541897365.087445810306
8115266.816506.7058402655-1239.90584026549
821667115675.9854866218995.014513378248
8315665.416066.1489821355-400.748982135463
8413949.514679.9683332712-730.468333271157
8515146.914896.8337135416250.066286458421
8615172.915826.5911009073-653.691100907339
8716981.416964.089635272117.3103647278695
8816553.815345.49824517661208.30175482341
8916438.516608.4945921019-169.994592101946
9015895.117049.238105812-1154.13810581196
911698915714.46425065811274.53574934186
9213803.514829.9556880089-1026.45568800893
9316678.316214.1157484422464.184251557823
9417315.116965.073458028350.026541972031
9515895.416609.5089416235-714.108941623477
9614912.114954.2113521131-42.1113521130701






Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
9715830.782611298414147.846420920317513.7188016765
9816374.427839388914431.120024792718317.7356539852
9918068.825451953115896.127519966820241.5233839394
10016758.796921096214378.715547478119138.8782947144
10116955.494156901614384.704708807719526.2836049954
10217231.156924029614482.86119252319979.4526555362
10317212.356544137514297.343599191420127.3694890837
10414976.511496061911903.813738294218049.2092538295
10517352.026183843914129.34988114520574.7024865428
10617804.441642214614438.462795970421170.4204884588
10716962.153724505713458.729023623820465.5784253877
10815898.905376656412263.227217614119534.5835356986

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
97 & 15830.7826112984 & 14147.8464209203 & 17513.7188016765 \tabularnewline
98 & 16374.4278393889 & 14431.1200247927 & 18317.7356539852 \tabularnewline
99 & 18068.8254519531 & 15896.1275199668 & 20241.5233839394 \tabularnewline
100 & 16758.7969210962 & 14378.7155474781 & 19138.8782947144 \tabularnewline
101 & 16955.4941569016 & 14384.7047088077 & 19526.2836049954 \tabularnewline
102 & 17231.1569240296 & 14482.861192523 & 19979.4526555362 \tabularnewline
103 & 17212.3565441375 & 14297.3435991914 & 20127.3694890837 \tabularnewline
104 & 14976.5114960619 & 11903.8137382942 & 18049.2092538295 \tabularnewline
105 & 17352.0261838439 & 14129.349881145 & 20574.7024865428 \tabularnewline
106 & 17804.4416422146 & 14438.4627959704 & 21170.4204884588 \tabularnewline
107 & 16962.1537245057 & 13458.7290236238 & 20465.5784253877 \tabularnewline
108 & 15898.9053766564 & 12263.2272176141 & 19534.5835356986 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=278670&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]97[/C][C]15830.7826112984[/C][C]14147.8464209203[/C][C]17513.7188016765[/C][/ROW]
[ROW][C]98[/C][C]16374.4278393889[/C][C]14431.1200247927[/C][C]18317.7356539852[/C][/ROW]
[ROW][C]99[/C][C]18068.8254519531[/C][C]15896.1275199668[/C][C]20241.5233839394[/C][/ROW]
[ROW][C]100[/C][C]16758.7969210962[/C][C]14378.7155474781[/C][C]19138.8782947144[/C][/ROW]
[ROW][C]101[/C][C]16955.4941569016[/C][C]14384.7047088077[/C][C]19526.2836049954[/C][/ROW]
[ROW][C]102[/C][C]17231.1569240296[/C][C]14482.861192523[/C][C]19979.4526555362[/C][/ROW]
[ROW][C]103[/C][C]17212.3565441375[/C][C]14297.3435991914[/C][C]20127.3694890837[/C][/ROW]
[ROW][C]104[/C][C]14976.5114960619[/C][C]11903.8137382942[/C][C]18049.2092538295[/C][/ROW]
[ROW][C]105[/C][C]17352.0261838439[/C][C]14129.349881145[/C][C]20574.7024865428[/C][/ROW]
[ROW][C]106[/C][C]17804.4416422146[/C][C]14438.4627959704[/C][C]21170.4204884588[/C][/ROW]
[ROW][C]107[/C][C]16962.1537245057[/C][C]13458.7290236238[/C][C]20465.5784253877[/C][/ROW]
[ROW][C]108[/C][C]15898.9053766564[/C][C]12263.2272176141[/C][C]19534.5835356986[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=278670&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=278670&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
9715830.782611298414147.846420920317513.7188016765
9816374.427839388914431.120024792718317.7356539852
9918068.825451953115896.127519966820241.5233839394
10016758.796921096214378.715547478119138.8782947144
10116955.494156901614384.704708807719526.2836049954
10217231.156924029614482.86119252319979.4526555362
10317212.356544137514297.343599191420127.3694890837
10414976.511496061911903.813738294218049.2092538295
10517352.026183843914129.34988114520574.7024865428
10617804.441642214614438.462795970421170.4204884588
10716962.153724505713458.729023623820465.5784253877
10815898.905376656412263.227217614119534.5835356986


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):
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')