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Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationSat, 29 Nov 2014 11:41:46 +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/2014/Nov/29/t1417261353dgabpl2dlu9mo9v.htm/, Retrieved Sun, 19 May 2024 23:07:16 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=261089, Retrieved Sun, 19 May 2024 23:07:16 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact130
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [] [2014-11-29 11:41:46] [fa76cbd0c9542d7a6f5f3c5daec42b95] [Current]
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Dataseries X:
75
84,3
84
79,1
78,8
82,7
85,3
84,5
80,8
70,1
68,2
68,1
72,3
73,1
71,5
74,1
80,3
80,6
81,4
87,4
89,3
93,2
92,8
96,8
100,3
95,6
89
87,4
86,7
92,8
98,6
100,8
105,5
107,8
113,7
120,3
126,5
134,8
134,5
133,1
128,8
127,1
129,1
128,4
126,5
117,1
114,2
109,1
110,3
109,2
103,6
98,9
95,9
91,2
98,7
94,5
95,6
93,8
89,5
87,1
87,1
84,5
84,2
83,7
82,2
77,7
78,5
79,1
78,6
79
76,2
77,8




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'Sir Maurice George Kendall' @ kendall.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 Maurice George Kendall' @ kendall.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=261089&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 Maurice George Kendall' @ kendall.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=261089&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=261089&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 Maurice George Kendall' @ kendall.wessa.net







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.999927223879053
betaFALSE
gammaFALSE

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.999927223879053 \tabularnewline
beta & FALSE \tabularnewline
gamma & FALSE \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=261089&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]0.999927223879053[/C][/ROW]
[ROW][C]beta[/C][C]FALSE[/C][/ROW]
[ROW][C]gamma[/C][C]FALSE[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=261089&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=261089&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
alpha0.999927223879053
betaFALSE
gammaFALSE







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
284.3759.3
38484.2993231820752-0.299323182075184
479.184.0000217835801-4.90002178358012
578.879.100356604578-0.300356604577971
682.778.80002185878863.89997814121142
785.382.69971617471912.60028382528088
884.585.2998107614298-0.799810761429825
980.884.5000582071247-3.70005820712471
1070.180.8002692758836-10.7002692758836
1168.270.100778724091-1.90077872409098
1268.168.2001383313023-0.100138331302318
1372.368.10000728767934.19999271232069
1473.172.29969434082240.80030565917761
1571.573.0999417568585-1.59994175685854
1674.171.50011643755482.59988356244519
1780.374.09981079055946.20018920944059
1880.680.29954877428020.300451225719797
1981.480.59997813432530.800021865674751
2087.481.39994177751196.00005822248806
2189.387.39956333903711.90043666096288
2293.289.29986169359173.90013830640829
2392.893.1997161630629-0.399716163062919
2496.892.80002908979183.99997091020816
25100.396.79970889763333.50029110236675
2695.6100.299745262391-4.69974526239139
278995.6003420292296-6.60034202922964
2887.489.0004803472898-1.6004803472898
2986.787.4001164767513-0.700116476751333
3092.886.70005095176146.09994904823861
3198.692.79955606937035.8004439306297
32100.898.5995778661912.20042213380904
33105.5100.7998398618134.70016013818736
34107.8105.4996579405772.30034205942268
35113.7107.7998325900285.90016740997194
36120.3113.6995706087036.60042939129703
37126.5120.2995196463526.20048035364769
38134.8126.4995487530928.30045124690815
39134.5134.799395925356-0.299395925356151
40133.1134.500021788874-1.40002178887408
41128.8133.100101888155-4.30010188815501
42127.1128.800312944735-1.70031294473512
43129.1127.1001237421811.99987625781949
44128.4129.099854456764-0.699854456763575
45126.5128.400050932693-1.90005093269261
46117.1126.500138278336-9.4001382783365
47114.2117.1006841056-2.90068410560025
48109.1114.200211100537-5.10021110053731
49110.3109.100371173581.1996288264201
50109.2110.299912695667-1.09991269566744
51103.6109.200080047379-5.60008004737938
5298.9103.600407552103-4.70040755210282
5395.998.9003420774285-3.00034207742851
5491.295.9002183532579-4.70021835325791
5598.791.20034206365937.49965793634065
5694.598.699454203987-4.19945420398696
5795.694.50030561998711.09969438001293
5893.895.5999199685088-1.7999199685088
5989.593.8001309911933-4.30013099119331
6087.189.5003129468531-2.40031294685311
6187.187.1001746854653-0.000174685465324842
6284.587.1000000127129-2.60000001271293
6384.284.5001892179154-0.300189217915388
6483.784.2000218466068-0.500021846606828
6582.283.7000363896504-1.50003638965039
6677.782.2001091668297-4.50010916682972
6778.577.7003275004890.79967249951099
6879.178.49994180293750.600058197062538
6978.679.0999563300921-0.499956330092076
707978.60003638488230.399963615117656
7176.278.9999708921996-2.79997089219957
7277.876.20020377102031.5997962289797

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
2 & 84.3 & 75 & 9.3 \tabularnewline
3 & 84 & 84.2993231820752 & -0.299323182075184 \tabularnewline
4 & 79.1 & 84.0000217835801 & -4.90002178358012 \tabularnewline
5 & 78.8 & 79.100356604578 & -0.300356604577971 \tabularnewline
6 & 82.7 & 78.8000218587886 & 3.89997814121142 \tabularnewline
7 & 85.3 & 82.6997161747191 & 2.60028382528088 \tabularnewline
8 & 84.5 & 85.2998107614298 & -0.799810761429825 \tabularnewline
9 & 80.8 & 84.5000582071247 & -3.70005820712471 \tabularnewline
10 & 70.1 & 80.8002692758836 & -10.7002692758836 \tabularnewline
11 & 68.2 & 70.100778724091 & -1.90077872409098 \tabularnewline
12 & 68.1 & 68.2001383313023 & -0.100138331302318 \tabularnewline
13 & 72.3 & 68.1000072876793 & 4.19999271232069 \tabularnewline
14 & 73.1 & 72.2996943408224 & 0.80030565917761 \tabularnewline
15 & 71.5 & 73.0999417568585 & -1.59994175685854 \tabularnewline
16 & 74.1 & 71.5001164375548 & 2.59988356244519 \tabularnewline
17 & 80.3 & 74.0998107905594 & 6.20018920944059 \tabularnewline
18 & 80.6 & 80.2995487742802 & 0.300451225719797 \tabularnewline
19 & 81.4 & 80.5999781343253 & 0.800021865674751 \tabularnewline
20 & 87.4 & 81.3999417775119 & 6.00005822248806 \tabularnewline
21 & 89.3 & 87.3995633390371 & 1.90043666096288 \tabularnewline
22 & 93.2 & 89.2998616935917 & 3.90013830640829 \tabularnewline
23 & 92.8 & 93.1997161630629 & -0.399716163062919 \tabularnewline
24 & 96.8 & 92.8000290897918 & 3.99997091020816 \tabularnewline
25 & 100.3 & 96.7997088976333 & 3.50029110236675 \tabularnewline
26 & 95.6 & 100.299745262391 & -4.69974526239139 \tabularnewline
27 & 89 & 95.6003420292296 & -6.60034202922964 \tabularnewline
28 & 87.4 & 89.0004803472898 & -1.6004803472898 \tabularnewline
29 & 86.7 & 87.4001164767513 & -0.700116476751333 \tabularnewline
30 & 92.8 & 86.7000509517614 & 6.09994904823861 \tabularnewline
31 & 98.6 & 92.7995560693703 & 5.8004439306297 \tabularnewline
32 & 100.8 & 98.599577866191 & 2.20042213380904 \tabularnewline
33 & 105.5 & 100.799839861813 & 4.70016013818736 \tabularnewline
34 & 107.8 & 105.499657940577 & 2.30034205942268 \tabularnewline
35 & 113.7 & 107.799832590028 & 5.90016740997194 \tabularnewline
36 & 120.3 & 113.699570608703 & 6.60042939129703 \tabularnewline
37 & 126.5 & 120.299519646352 & 6.20048035364769 \tabularnewline
38 & 134.8 & 126.499548753092 & 8.30045124690815 \tabularnewline
39 & 134.5 & 134.799395925356 & -0.299395925356151 \tabularnewline
40 & 133.1 & 134.500021788874 & -1.40002178887408 \tabularnewline
41 & 128.8 & 133.100101888155 & -4.30010188815501 \tabularnewline
42 & 127.1 & 128.800312944735 & -1.70031294473512 \tabularnewline
43 & 129.1 & 127.100123742181 & 1.99987625781949 \tabularnewline
44 & 128.4 & 129.099854456764 & -0.699854456763575 \tabularnewline
45 & 126.5 & 128.400050932693 & -1.90005093269261 \tabularnewline
46 & 117.1 & 126.500138278336 & -9.4001382783365 \tabularnewline
47 & 114.2 & 117.1006841056 & -2.90068410560025 \tabularnewline
48 & 109.1 & 114.200211100537 & -5.10021110053731 \tabularnewline
49 & 110.3 & 109.10037117358 & 1.1996288264201 \tabularnewline
50 & 109.2 & 110.299912695667 & -1.09991269566744 \tabularnewline
51 & 103.6 & 109.200080047379 & -5.60008004737938 \tabularnewline
52 & 98.9 & 103.600407552103 & -4.70040755210282 \tabularnewline
53 & 95.9 & 98.9003420774285 & -3.00034207742851 \tabularnewline
54 & 91.2 & 95.9002183532579 & -4.70021835325791 \tabularnewline
55 & 98.7 & 91.2003420636593 & 7.49965793634065 \tabularnewline
56 & 94.5 & 98.699454203987 & -4.19945420398696 \tabularnewline
57 & 95.6 & 94.5003056199871 & 1.09969438001293 \tabularnewline
58 & 93.8 & 95.5999199685088 & -1.7999199685088 \tabularnewline
59 & 89.5 & 93.8001309911933 & -4.30013099119331 \tabularnewline
60 & 87.1 & 89.5003129468531 & -2.40031294685311 \tabularnewline
61 & 87.1 & 87.1001746854653 & -0.000174685465324842 \tabularnewline
62 & 84.5 & 87.1000000127129 & -2.60000001271293 \tabularnewline
63 & 84.2 & 84.5001892179154 & -0.300189217915388 \tabularnewline
64 & 83.7 & 84.2000218466068 & -0.500021846606828 \tabularnewline
65 & 82.2 & 83.7000363896504 & -1.50003638965039 \tabularnewline
66 & 77.7 & 82.2001091668297 & -4.50010916682972 \tabularnewline
67 & 78.5 & 77.700327500489 & 0.79967249951099 \tabularnewline
68 & 79.1 & 78.4999418029375 & 0.600058197062538 \tabularnewline
69 & 78.6 & 79.0999563300921 & -0.499956330092076 \tabularnewline
70 & 79 & 78.6000363848823 & 0.399963615117656 \tabularnewline
71 & 76.2 & 78.9999708921996 & -2.79997089219957 \tabularnewline
72 & 77.8 & 76.2002037710203 & 1.5997962289797 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=261089&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]2[/C][C]84.3[/C][C]75[/C][C]9.3[/C][/ROW]
[ROW][C]3[/C][C]84[/C][C]84.2993231820752[/C][C]-0.299323182075184[/C][/ROW]
[ROW][C]4[/C][C]79.1[/C][C]84.0000217835801[/C][C]-4.90002178358012[/C][/ROW]
[ROW][C]5[/C][C]78.8[/C][C]79.100356604578[/C][C]-0.300356604577971[/C][/ROW]
[ROW][C]6[/C][C]82.7[/C][C]78.8000218587886[/C][C]3.89997814121142[/C][/ROW]
[ROW][C]7[/C][C]85.3[/C][C]82.6997161747191[/C][C]2.60028382528088[/C][/ROW]
[ROW][C]8[/C][C]84.5[/C][C]85.2998107614298[/C][C]-0.799810761429825[/C][/ROW]
[ROW][C]9[/C][C]80.8[/C][C]84.5000582071247[/C][C]-3.70005820712471[/C][/ROW]
[ROW][C]10[/C][C]70.1[/C][C]80.8002692758836[/C][C]-10.7002692758836[/C][/ROW]
[ROW][C]11[/C][C]68.2[/C][C]70.100778724091[/C][C]-1.90077872409098[/C][/ROW]
[ROW][C]12[/C][C]68.1[/C][C]68.2001383313023[/C][C]-0.100138331302318[/C][/ROW]
[ROW][C]13[/C][C]72.3[/C][C]68.1000072876793[/C][C]4.19999271232069[/C][/ROW]
[ROW][C]14[/C][C]73.1[/C][C]72.2996943408224[/C][C]0.80030565917761[/C][/ROW]
[ROW][C]15[/C][C]71.5[/C][C]73.0999417568585[/C][C]-1.59994175685854[/C][/ROW]
[ROW][C]16[/C][C]74.1[/C][C]71.5001164375548[/C][C]2.59988356244519[/C][/ROW]
[ROW][C]17[/C][C]80.3[/C][C]74.0998107905594[/C][C]6.20018920944059[/C][/ROW]
[ROW][C]18[/C][C]80.6[/C][C]80.2995487742802[/C][C]0.300451225719797[/C][/ROW]
[ROW][C]19[/C][C]81.4[/C][C]80.5999781343253[/C][C]0.800021865674751[/C][/ROW]
[ROW][C]20[/C][C]87.4[/C][C]81.3999417775119[/C][C]6.00005822248806[/C][/ROW]
[ROW][C]21[/C][C]89.3[/C][C]87.3995633390371[/C][C]1.90043666096288[/C][/ROW]
[ROW][C]22[/C][C]93.2[/C][C]89.2998616935917[/C][C]3.90013830640829[/C][/ROW]
[ROW][C]23[/C][C]92.8[/C][C]93.1997161630629[/C][C]-0.399716163062919[/C][/ROW]
[ROW][C]24[/C][C]96.8[/C][C]92.8000290897918[/C][C]3.99997091020816[/C][/ROW]
[ROW][C]25[/C][C]100.3[/C][C]96.7997088976333[/C][C]3.50029110236675[/C][/ROW]
[ROW][C]26[/C][C]95.6[/C][C]100.299745262391[/C][C]-4.69974526239139[/C][/ROW]
[ROW][C]27[/C][C]89[/C][C]95.6003420292296[/C][C]-6.60034202922964[/C][/ROW]
[ROW][C]28[/C][C]87.4[/C][C]89.0004803472898[/C][C]-1.6004803472898[/C][/ROW]
[ROW][C]29[/C][C]86.7[/C][C]87.4001164767513[/C][C]-0.700116476751333[/C][/ROW]
[ROW][C]30[/C][C]92.8[/C][C]86.7000509517614[/C][C]6.09994904823861[/C][/ROW]
[ROW][C]31[/C][C]98.6[/C][C]92.7995560693703[/C][C]5.8004439306297[/C][/ROW]
[ROW][C]32[/C][C]100.8[/C][C]98.599577866191[/C][C]2.20042213380904[/C][/ROW]
[ROW][C]33[/C][C]105.5[/C][C]100.799839861813[/C][C]4.70016013818736[/C][/ROW]
[ROW][C]34[/C][C]107.8[/C][C]105.499657940577[/C][C]2.30034205942268[/C][/ROW]
[ROW][C]35[/C][C]113.7[/C][C]107.799832590028[/C][C]5.90016740997194[/C][/ROW]
[ROW][C]36[/C][C]120.3[/C][C]113.699570608703[/C][C]6.60042939129703[/C][/ROW]
[ROW][C]37[/C][C]126.5[/C][C]120.299519646352[/C][C]6.20048035364769[/C][/ROW]
[ROW][C]38[/C][C]134.8[/C][C]126.499548753092[/C][C]8.30045124690815[/C][/ROW]
[ROW][C]39[/C][C]134.5[/C][C]134.799395925356[/C][C]-0.299395925356151[/C][/ROW]
[ROW][C]40[/C][C]133.1[/C][C]134.500021788874[/C][C]-1.40002178887408[/C][/ROW]
[ROW][C]41[/C][C]128.8[/C][C]133.100101888155[/C][C]-4.30010188815501[/C][/ROW]
[ROW][C]42[/C][C]127.1[/C][C]128.800312944735[/C][C]-1.70031294473512[/C][/ROW]
[ROW][C]43[/C][C]129.1[/C][C]127.100123742181[/C][C]1.99987625781949[/C][/ROW]
[ROW][C]44[/C][C]128.4[/C][C]129.099854456764[/C][C]-0.699854456763575[/C][/ROW]
[ROW][C]45[/C][C]126.5[/C][C]128.400050932693[/C][C]-1.90005093269261[/C][/ROW]
[ROW][C]46[/C][C]117.1[/C][C]126.500138278336[/C][C]-9.4001382783365[/C][/ROW]
[ROW][C]47[/C][C]114.2[/C][C]117.1006841056[/C][C]-2.90068410560025[/C][/ROW]
[ROW][C]48[/C][C]109.1[/C][C]114.200211100537[/C][C]-5.10021110053731[/C][/ROW]
[ROW][C]49[/C][C]110.3[/C][C]109.10037117358[/C][C]1.1996288264201[/C][/ROW]
[ROW][C]50[/C][C]109.2[/C][C]110.299912695667[/C][C]-1.09991269566744[/C][/ROW]
[ROW][C]51[/C][C]103.6[/C][C]109.200080047379[/C][C]-5.60008004737938[/C][/ROW]
[ROW][C]52[/C][C]98.9[/C][C]103.600407552103[/C][C]-4.70040755210282[/C][/ROW]
[ROW][C]53[/C][C]95.9[/C][C]98.9003420774285[/C][C]-3.00034207742851[/C][/ROW]
[ROW][C]54[/C][C]91.2[/C][C]95.9002183532579[/C][C]-4.70021835325791[/C][/ROW]
[ROW][C]55[/C][C]98.7[/C][C]91.2003420636593[/C][C]7.49965793634065[/C][/ROW]
[ROW][C]56[/C][C]94.5[/C][C]98.699454203987[/C][C]-4.19945420398696[/C][/ROW]
[ROW][C]57[/C][C]95.6[/C][C]94.5003056199871[/C][C]1.09969438001293[/C][/ROW]
[ROW][C]58[/C][C]93.8[/C][C]95.5999199685088[/C][C]-1.7999199685088[/C][/ROW]
[ROW][C]59[/C][C]89.5[/C][C]93.8001309911933[/C][C]-4.30013099119331[/C][/ROW]
[ROW][C]60[/C][C]87.1[/C][C]89.5003129468531[/C][C]-2.40031294685311[/C][/ROW]
[ROW][C]61[/C][C]87.1[/C][C]87.1001746854653[/C][C]-0.000174685465324842[/C][/ROW]
[ROW][C]62[/C][C]84.5[/C][C]87.1000000127129[/C][C]-2.60000001271293[/C][/ROW]
[ROW][C]63[/C][C]84.2[/C][C]84.5001892179154[/C][C]-0.300189217915388[/C][/ROW]
[ROW][C]64[/C][C]83.7[/C][C]84.2000218466068[/C][C]-0.500021846606828[/C][/ROW]
[ROW][C]65[/C][C]82.2[/C][C]83.7000363896504[/C][C]-1.50003638965039[/C][/ROW]
[ROW][C]66[/C][C]77.7[/C][C]82.2001091668297[/C][C]-4.50010916682972[/C][/ROW]
[ROW][C]67[/C][C]78.5[/C][C]77.700327500489[/C][C]0.79967249951099[/C][/ROW]
[ROW][C]68[/C][C]79.1[/C][C]78.4999418029375[/C][C]0.600058197062538[/C][/ROW]
[ROW][C]69[/C][C]78.6[/C][C]79.0999563300921[/C][C]-0.499956330092076[/C][/ROW]
[ROW][C]70[/C][C]79[/C][C]78.6000363848823[/C][C]0.399963615117656[/C][/ROW]
[ROW][C]71[/C][C]76.2[/C][C]78.9999708921996[/C][C]-2.79997089219957[/C][/ROW]
[ROW][C]72[/C][C]77.8[/C][C]76.2002037710203[/C][C]1.5997962289797[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=261089&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=261089&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
284.3759.3
38484.2993231820752-0.299323182075184
479.184.0000217835801-4.90002178358012
578.879.100356604578-0.300356604577971
682.778.80002185878863.89997814121142
785.382.69971617471912.60028382528088
884.585.2998107614298-0.799810761429825
980.884.5000582071247-3.70005820712471
1070.180.8002692758836-10.7002692758836
1168.270.100778724091-1.90077872409098
1268.168.2001383313023-0.100138331302318
1372.368.10000728767934.19999271232069
1473.172.29969434082240.80030565917761
1571.573.0999417568585-1.59994175685854
1674.171.50011643755482.59988356244519
1780.374.09981079055946.20018920944059
1880.680.29954877428020.300451225719797
1981.480.59997813432530.800021865674751
2087.481.39994177751196.00005822248806
2189.387.39956333903711.90043666096288
2293.289.29986169359173.90013830640829
2392.893.1997161630629-0.399716163062919
2496.892.80002908979183.99997091020816
25100.396.79970889763333.50029110236675
2695.6100.299745262391-4.69974526239139
278995.6003420292296-6.60034202922964
2887.489.0004803472898-1.6004803472898
2986.787.4001164767513-0.700116476751333
3092.886.70005095176146.09994904823861
3198.692.79955606937035.8004439306297
32100.898.5995778661912.20042213380904
33105.5100.7998398618134.70016013818736
34107.8105.4996579405772.30034205942268
35113.7107.7998325900285.90016740997194
36120.3113.6995706087036.60042939129703
37126.5120.2995196463526.20048035364769
38134.8126.4995487530928.30045124690815
39134.5134.799395925356-0.299395925356151
40133.1134.500021788874-1.40002178887408
41128.8133.100101888155-4.30010188815501
42127.1128.800312944735-1.70031294473512
43129.1127.1001237421811.99987625781949
44128.4129.099854456764-0.699854456763575
45126.5128.400050932693-1.90005093269261
46117.1126.500138278336-9.4001382783365
47114.2117.1006841056-2.90068410560025
48109.1114.200211100537-5.10021110053731
49110.3109.100371173581.1996288264201
50109.2110.299912695667-1.09991269566744
51103.6109.200080047379-5.60008004737938
5298.9103.600407552103-4.70040755210282
5395.998.9003420774285-3.00034207742851
5491.295.9002183532579-4.70021835325791
5598.791.20034206365937.49965793634065
5694.598.699454203987-4.19945420398696
5795.694.50030561998711.09969438001293
5893.895.5999199685088-1.7999199685088
5989.593.8001309911933-4.30013099119331
6087.189.5003129468531-2.40031294685311
6187.187.1001746854653-0.000174685465324842
6284.587.1000000127129-2.60000001271293
6384.284.5001892179154-0.300189217915388
6483.784.2000218466068-0.500021846606828
6582.283.7000363896504-1.50003638965039
6677.782.2001091668297-4.50010916682972
6778.577.7003275004890.79967249951099
6879.178.49994180293750.600058197062538
6978.679.0999563300921-0.499956330092076
707978.60003638488230.399963615117656
7176.278.9999708921996-2.79997089219957
7277.876.20020377102031.5997962289797







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
7377.799883573036269.828101924115785.7716652219566
7477.799883573036266.526492073170789.0732750729016
7577.799883573036263.993022627824591.6067445182478
7677.799883573036261.857190500296493.7425766457759
7777.799883573036259.975475710143395.624291435929
7877.799883573036258.274270422255897.3254967238166
7977.799883573036256.709847485700998.8899196603714
8077.799883573036255.2537159293705100.346051216702
8177.799883573036253.8860857009405101.713681445132
8277.799883573036252.5925476979656103.007219448107
8377.799883573036251.3622241613221104.23754298475
8477.799883573036250.1866641225453105.413103023527

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
73 & 77.7998835730362 & 69.8281019241157 & 85.7716652219566 \tabularnewline
74 & 77.7998835730362 & 66.5264920731707 & 89.0732750729016 \tabularnewline
75 & 77.7998835730362 & 63.9930226278245 & 91.6067445182478 \tabularnewline
76 & 77.7998835730362 & 61.8571905002964 & 93.7425766457759 \tabularnewline
77 & 77.7998835730362 & 59.9754757101433 & 95.624291435929 \tabularnewline
78 & 77.7998835730362 & 58.2742704222558 & 97.3254967238166 \tabularnewline
79 & 77.7998835730362 & 56.7098474857009 & 98.8899196603714 \tabularnewline
80 & 77.7998835730362 & 55.2537159293705 & 100.346051216702 \tabularnewline
81 & 77.7998835730362 & 53.8860857009405 & 101.713681445132 \tabularnewline
82 & 77.7998835730362 & 52.5925476979656 & 103.007219448107 \tabularnewline
83 & 77.7998835730362 & 51.3622241613221 & 104.23754298475 \tabularnewline
84 & 77.7998835730362 & 50.1866641225453 & 105.413103023527 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=261089&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]73[/C][C]77.7998835730362[/C][C]69.8281019241157[/C][C]85.7716652219566[/C][/ROW]
[ROW][C]74[/C][C]77.7998835730362[/C][C]66.5264920731707[/C][C]89.0732750729016[/C][/ROW]
[ROW][C]75[/C][C]77.7998835730362[/C][C]63.9930226278245[/C][C]91.6067445182478[/C][/ROW]
[ROW][C]76[/C][C]77.7998835730362[/C][C]61.8571905002964[/C][C]93.7425766457759[/C][/ROW]
[ROW][C]77[/C][C]77.7998835730362[/C][C]59.9754757101433[/C][C]95.624291435929[/C][/ROW]
[ROW][C]78[/C][C]77.7998835730362[/C][C]58.2742704222558[/C][C]97.3254967238166[/C][/ROW]
[ROW][C]79[/C][C]77.7998835730362[/C][C]56.7098474857009[/C][C]98.8899196603714[/C][/ROW]
[ROW][C]80[/C][C]77.7998835730362[/C][C]55.2537159293705[/C][C]100.346051216702[/C][/ROW]
[ROW][C]81[/C][C]77.7998835730362[/C][C]53.8860857009405[/C][C]101.713681445132[/C][/ROW]
[ROW][C]82[/C][C]77.7998835730362[/C][C]52.5925476979656[/C][C]103.007219448107[/C][/ROW]
[ROW][C]83[/C][C]77.7998835730362[/C][C]51.3622241613221[/C][C]104.23754298475[/C][/ROW]
[ROW][C]84[/C][C]77.7998835730362[/C][C]50.1866641225453[/C][C]105.413103023527[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=261089&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=261089&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
7377.799883573036269.828101924115785.7716652219566
7477.799883573036266.526492073170789.0732750729016
7577.799883573036263.993022627824591.6067445182478
7677.799883573036261.857190500296493.7425766457759
7777.799883573036259.975475710143395.624291435929
7877.799883573036258.274270422255897.3254967238166
7977.799883573036256.709847485700998.8899196603714
8077.799883573036255.2537159293705100.346051216702
8177.799883573036253.8860857009405101.713681445132
8277.799883573036252.5925476979656103.007219448107
8377.799883573036251.3622241613221104.23754298475
8477.799883573036250.1866641225453105.413103023527



Parameters (Session):
par1 = 12 ; par2 = Single ; par3 = additive ;
Parameters (R input):
par1 = 12 ; par2 = Single ; 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')