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Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationSun, 22 May 2016 11:09:07 +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/2016/May/22/t1463911826lzp2eigds638nqc.htm/, Retrieved Mon, 06 May 2024 22:01:25 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=295479, Retrieved Mon, 06 May 2024 22:01:25 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact123
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [Exponential Smoot...] [2016-05-22 10:09:07] [544b481aaa38f6ceeb4c090a83033a19] [Current]
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Dataseries X:
1,9
2
2
1,8
1,6
1,4
0,2
0,3
0,4
0,7
1
1,1
0,8
0,8
1
1,1
1
0,8
1,6
1,5
1,6
1,6
1,6
1,9
2
1,9
2
2,1
2,3
2,3
2,6
2,6
2,7
2,6
2,6
2,4
2,5
2,5
2,5
2,4
2,1
2,1
2,3
2,3
2,3
2,9
2,8
2,9
3
3
2,9
2,6
2,8
2,9
3,1
2,8
2,4
1,6
1,5
1,7
1,4
1,1
0,8
1,2
0,8
0,9
0,9
1
0,9
1,1
1
0,7
0
0,2
0,4
0,6
1,1
1
1
0,8
0,6
0,6
0,7
0,7




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'Herman Ole Andreas Wold' @ wold.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 & 'Herman Ole Andreas Wold' @ wold.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=295479&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]'Herman Ole Andreas Wold' @ wold.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=295479&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=295479&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'Herman Ole Andreas Wold' @ wold.wessa.net







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha1
beta0.0388466063098428
gammaFALSE

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 1 \tabularnewline
beta & 0.0388466063098428 \tabularnewline
gamma & FALSE \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=295479&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]0.0388466063098428[/C][/ROW]
[ROW][C]gamma[/C][C]FALSE[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=295479&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=295479&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
alpha1
beta0.0388466063098428
gammaFALSE







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
322.1-0.1
41.82.09611533936902-0.296115339369016
51.61.88461226335824-0.284612263358242
61.41.67355604281261-0.273556042812611
70.21.46292931891379-1.26292931891379
80.30.2138688008647890.0861311991352107
90.40.3172147056485890.0827852943514106
100.70.4204306333865030.279569366613497
1110.731290954507630.26870904549237
121.11.041729389009770.0582706109902347
130.81.14399300449434-0.343993004494337
140.80.830630043675406-0.0306300436754057
1510.8294401704274940.170559829572506
161.11.036065840979170.0639341590208291
1711.1385494660844-0.138549466084404
180.81.03316728952098-0.233167289520984
191.60.8241095316206290.775890468379371
201.51.65425024318532-0.154250243185322
211.61.54825814471510.0517418552848956
221.61.6502681401971-0.0502681401970977
231.61.64831539354493-0.0483153935449332
241.91.646438504473190.253561495526812
2521.956288508065250.043711491934747
261.92.05798655118366-0.157986551183658
2721.951849309827580.0481506901724236
282.12.053719800732250.046280199267748
292.32.155517629413150.144482370586852
302.32.36113027918205-0.0611302791820476
312.62.358755575293050.241244424706949
322.62.66812710248409-0.068127102484087
332.72.665480595754860.0345194042451427
342.62.76682155746162-0.166821557461619
352.62.66034110609491-0.0603411060949126
362.42.65799705890214-0.257997058902143
372.52.447974748725870.0520252512741259
382.52.54999575318029-0.0499957531802906
392.52.54805358783933-0.0480535878393318
402.42.54618686903076-0.146186869030762
412.12.44050800528186-0.340508005281855
422.12.12728042485532-0.0272804248553213
432.32.1262206729310.173779327068998
442.32.33297141003444-0.03297141003444
452.32.33169058264935-0.0316905826493517
462.92.330459511061440.569540488938557
472.82.95258422621275-0.152584226212754
482.92.846656846847980.0533431531520248
4932.94872904731780.0512709526822022
5033.05072074983177-0.0507207498317741
512.93.04875042083132-0.148750420831319
522.62.94297197179486-0.342971971794861
532.82.629648674631240.170351325368764
542.92.83626624550220.0637337544978038
553.12.938742085571820.16125791442818
562.83.14500640828796-0.345006408287959
572.42.83160408017082-0.431604080170823
581.62.41483772638671-0.814837726386705
591.51.58318404602335-0.0831840460233537
601.71.479952628136220.220047371863775
611.41.68850072176053-0.288500721760532
621.11.3772934478022-0.277293447802195
630.81.06652153840312-0.266521538403125
641.20.7561680811276850.443831918872315
650.81.17340944494786-0.37340944494786
660.90.7589037552475930.141096244752407
670.90.8643848655192870.0356151344807129
6810.8657683926271320.134231607372868
690.90.970982835033083-0.0709828350330827
701.10.8682253927857960.231774607214204
7111.07722904970486-0.0772290497048647
720.70.974228963215297-0.274228963215297
7300.663576098642515-0.663576098642515
740.2-0.06220158081807170.262201580818072
750.40.1479840607657860.252015939234214
760.60.3577740247410230.242225975258977
771.10.5671836818399260.532816318160074
7811.08788178758695-0.0878817875869506
7910.9844678783827550.0155321216172448
800.80.985071248596377-0.185071248596377
810.60.777881858662882-0.177881858662882
820.60.5709717521297420.0290282478702577
830.70.5720994010466230.127900598953377
840.70.6770679052609580.0229320947390423

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
3 & 2 & 2.1 & -0.1 \tabularnewline
4 & 1.8 & 2.09611533936902 & -0.296115339369016 \tabularnewline
5 & 1.6 & 1.88461226335824 & -0.284612263358242 \tabularnewline
6 & 1.4 & 1.67355604281261 & -0.273556042812611 \tabularnewline
7 & 0.2 & 1.46292931891379 & -1.26292931891379 \tabularnewline
8 & 0.3 & 0.213868800864789 & 0.0861311991352107 \tabularnewline
9 & 0.4 & 0.317214705648589 & 0.0827852943514106 \tabularnewline
10 & 0.7 & 0.420430633386503 & 0.279569366613497 \tabularnewline
11 & 1 & 0.73129095450763 & 0.26870904549237 \tabularnewline
12 & 1.1 & 1.04172938900977 & 0.0582706109902347 \tabularnewline
13 & 0.8 & 1.14399300449434 & -0.343993004494337 \tabularnewline
14 & 0.8 & 0.830630043675406 & -0.0306300436754057 \tabularnewline
15 & 1 & 0.829440170427494 & 0.170559829572506 \tabularnewline
16 & 1.1 & 1.03606584097917 & 0.0639341590208291 \tabularnewline
17 & 1 & 1.1385494660844 & -0.138549466084404 \tabularnewline
18 & 0.8 & 1.03316728952098 & -0.233167289520984 \tabularnewline
19 & 1.6 & 0.824109531620629 & 0.775890468379371 \tabularnewline
20 & 1.5 & 1.65425024318532 & -0.154250243185322 \tabularnewline
21 & 1.6 & 1.5482581447151 & 0.0517418552848956 \tabularnewline
22 & 1.6 & 1.6502681401971 & -0.0502681401970977 \tabularnewline
23 & 1.6 & 1.64831539354493 & -0.0483153935449332 \tabularnewline
24 & 1.9 & 1.64643850447319 & 0.253561495526812 \tabularnewline
25 & 2 & 1.95628850806525 & 0.043711491934747 \tabularnewline
26 & 1.9 & 2.05798655118366 & -0.157986551183658 \tabularnewline
27 & 2 & 1.95184930982758 & 0.0481506901724236 \tabularnewline
28 & 2.1 & 2.05371980073225 & 0.046280199267748 \tabularnewline
29 & 2.3 & 2.15551762941315 & 0.144482370586852 \tabularnewline
30 & 2.3 & 2.36113027918205 & -0.0611302791820476 \tabularnewline
31 & 2.6 & 2.35875557529305 & 0.241244424706949 \tabularnewline
32 & 2.6 & 2.66812710248409 & -0.068127102484087 \tabularnewline
33 & 2.7 & 2.66548059575486 & 0.0345194042451427 \tabularnewline
34 & 2.6 & 2.76682155746162 & -0.166821557461619 \tabularnewline
35 & 2.6 & 2.66034110609491 & -0.0603411060949126 \tabularnewline
36 & 2.4 & 2.65799705890214 & -0.257997058902143 \tabularnewline
37 & 2.5 & 2.44797474872587 & 0.0520252512741259 \tabularnewline
38 & 2.5 & 2.54999575318029 & -0.0499957531802906 \tabularnewline
39 & 2.5 & 2.54805358783933 & -0.0480535878393318 \tabularnewline
40 & 2.4 & 2.54618686903076 & -0.146186869030762 \tabularnewline
41 & 2.1 & 2.44050800528186 & -0.340508005281855 \tabularnewline
42 & 2.1 & 2.12728042485532 & -0.0272804248553213 \tabularnewline
43 & 2.3 & 2.126220672931 & 0.173779327068998 \tabularnewline
44 & 2.3 & 2.33297141003444 & -0.03297141003444 \tabularnewline
45 & 2.3 & 2.33169058264935 & -0.0316905826493517 \tabularnewline
46 & 2.9 & 2.33045951106144 & 0.569540488938557 \tabularnewline
47 & 2.8 & 2.95258422621275 & -0.152584226212754 \tabularnewline
48 & 2.9 & 2.84665684684798 & 0.0533431531520248 \tabularnewline
49 & 3 & 2.9487290473178 & 0.0512709526822022 \tabularnewline
50 & 3 & 3.05072074983177 & -0.0507207498317741 \tabularnewline
51 & 2.9 & 3.04875042083132 & -0.148750420831319 \tabularnewline
52 & 2.6 & 2.94297197179486 & -0.342971971794861 \tabularnewline
53 & 2.8 & 2.62964867463124 & 0.170351325368764 \tabularnewline
54 & 2.9 & 2.8362662455022 & 0.0637337544978038 \tabularnewline
55 & 3.1 & 2.93874208557182 & 0.16125791442818 \tabularnewline
56 & 2.8 & 3.14500640828796 & -0.345006408287959 \tabularnewline
57 & 2.4 & 2.83160408017082 & -0.431604080170823 \tabularnewline
58 & 1.6 & 2.41483772638671 & -0.814837726386705 \tabularnewline
59 & 1.5 & 1.58318404602335 & -0.0831840460233537 \tabularnewline
60 & 1.7 & 1.47995262813622 & 0.220047371863775 \tabularnewline
61 & 1.4 & 1.68850072176053 & -0.288500721760532 \tabularnewline
62 & 1.1 & 1.3772934478022 & -0.277293447802195 \tabularnewline
63 & 0.8 & 1.06652153840312 & -0.266521538403125 \tabularnewline
64 & 1.2 & 0.756168081127685 & 0.443831918872315 \tabularnewline
65 & 0.8 & 1.17340944494786 & -0.37340944494786 \tabularnewline
66 & 0.9 & 0.758903755247593 & 0.141096244752407 \tabularnewline
67 & 0.9 & 0.864384865519287 & 0.0356151344807129 \tabularnewline
68 & 1 & 0.865768392627132 & 0.134231607372868 \tabularnewline
69 & 0.9 & 0.970982835033083 & -0.0709828350330827 \tabularnewline
70 & 1.1 & 0.868225392785796 & 0.231774607214204 \tabularnewline
71 & 1 & 1.07722904970486 & -0.0772290497048647 \tabularnewline
72 & 0.7 & 0.974228963215297 & -0.274228963215297 \tabularnewline
73 & 0 & 0.663576098642515 & -0.663576098642515 \tabularnewline
74 & 0.2 & -0.0622015808180717 & 0.262201580818072 \tabularnewline
75 & 0.4 & 0.147984060765786 & 0.252015939234214 \tabularnewline
76 & 0.6 & 0.357774024741023 & 0.242225975258977 \tabularnewline
77 & 1.1 & 0.567183681839926 & 0.532816318160074 \tabularnewline
78 & 1 & 1.08788178758695 & -0.0878817875869506 \tabularnewline
79 & 1 & 0.984467878382755 & 0.0155321216172448 \tabularnewline
80 & 0.8 & 0.985071248596377 & -0.185071248596377 \tabularnewline
81 & 0.6 & 0.777881858662882 & -0.177881858662882 \tabularnewline
82 & 0.6 & 0.570971752129742 & 0.0290282478702577 \tabularnewline
83 & 0.7 & 0.572099401046623 & 0.127900598953377 \tabularnewline
84 & 0.7 & 0.677067905260958 & 0.0229320947390423 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=295479&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]2[/C][C]2.1[/C][C]-0.1[/C][/ROW]
[ROW][C]4[/C][C]1.8[/C][C]2.09611533936902[/C][C]-0.296115339369016[/C][/ROW]
[ROW][C]5[/C][C]1.6[/C][C]1.88461226335824[/C][C]-0.284612263358242[/C][/ROW]
[ROW][C]6[/C][C]1.4[/C][C]1.67355604281261[/C][C]-0.273556042812611[/C][/ROW]
[ROW][C]7[/C][C]0.2[/C][C]1.46292931891379[/C][C]-1.26292931891379[/C][/ROW]
[ROW][C]8[/C][C]0.3[/C][C]0.213868800864789[/C][C]0.0861311991352107[/C][/ROW]
[ROW][C]9[/C][C]0.4[/C][C]0.317214705648589[/C][C]0.0827852943514106[/C][/ROW]
[ROW][C]10[/C][C]0.7[/C][C]0.420430633386503[/C][C]0.279569366613497[/C][/ROW]
[ROW][C]11[/C][C]1[/C][C]0.73129095450763[/C][C]0.26870904549237[/C][/ROW]
[ROW][C]12[/C][C]1.1[/C][C]1.04172938900977[/C][C]0.0582706109902347[/C][/ROW]
[ROW][C]13[/C][C]0.8[/C][C]1.14399300449434[/C][C]-0.343993004494337[/C][/ROW]
[ROW][C]14[/C][C]0.8[/C][C]0.830630043675406[/C][C]-0.0306300436754057[/C][/ROW]
[ROW][C]15[/C][C]1[/C][C]0.829440170427494[/C][C]0.170559829572506[/C][/ROW]
[ROW][C]16[/C][C]1.1[/C][C]1.03606584097917[/C][C]0.0639341590208291[/C][/ROW]
[ROW][C]17[/C][C]1[/C][C]1.1385494660844[/C][C]-0.138549466084404[/C][/ROW]
[ROW][C]18[/C][C]0.8[/C][C]1.03316728952098[/C][C]-0.233167289520984[/C][/ROW]
[ROW][C]19[/C][C]1.6[/C][C]0.824109531620629[/C][C]0.775890468379371[/C][/ROW]
[ROW][C]20[/C][C]1.5[/C][C]1.65425024318532[/C][C]-0.154250243185322[/C][/ROW]
[ROW][C]21[/C][C]1.6[/C][C]1.5482581447151[/C][C]0.0517418552848956[/C][/ROW]
[ROW][C]22[/C][C]1.6[/C][C]1.6502681401971[/C][C]-0.0502681401970977[/C][/ROW]
[ROW][C]23[/C][C]1.6[/C][C]1.64831539354493[/C][C]-0.0483153935449332[/C][/ROW]
[ROW][C]24[/C][C]1.9[/C][C]1.64643850447319[/C][C]0.253561495526812[/C][/ROW]
[ROW][C]25[/C][C]2[/C][C]1.95628850806525[/C][C]0.043711491934747[/C][/ROW]
[ROW][C]26[/C][C]1.9[/C][C]2.05798655118366[/C][C]-0.157986551183658[/C][/ROW]
[ROW][C]27[/C][C]2[/C][C]1.95184930982758[/C][C]0.0481506901724236[/C][/ROW]
[ROW][C]28[/C][C]2.1[/C][C]2.05371980073225[/C][C]0.046280199267748[/C][/ROW]
[ROW][C]29[/C][C]2.3[/C][C]2.15551762941315[/C][C]0.144482370586852[/C][/ROW]
[ROW][C]30[/C][C]2.3[/C][C]2.36113027918205[/C][C]-0.0611302791820476[/C][/ROW]
[ROW][C]31[/C][C]2.6[/C][C]2.35875557529305[/C][C]0.241244424706949[/C][/ROW]
[ROW][C]32[/C][C]2.6[/C][C]2.66812710248409[/C][C]-0.068127102484087[/C][/ROW]
[ROW][C]33[/C][C]2.7[/C][C]2.66548059575486[/C][C]0.0345194042451427[/C][/ROW]
[ROW][C]34[/C][C]2.6[/C][C]2.76682155746162[/C][C]-0.166821557461619[/C][/ROW]
[ROW][C]35[/C][C]2.6[/C][C]2.66034110609491[/C][C]-0.0603411060949126[/C][/ROW]
[ROW][C]36[/C][C]2.4[/C][C]2.65799705890214[/C][C]-0.257997058902143[/C][/ROW]
[ROW][C]37[/C][C]2.5[/C][C]2.44797474872587[/C][C]0.0520252512741259[/C][/ROW]
[ROW][C]38[/C][C]2.5[/C][C]2.54999575318029[/C][C]-0.0499957531802906[/C][/ROW]
[ROW][C]39[/C][C]2.5[/C][C]2.54805358783933[/C][C]-0.0480535878393318[/C][/ROW]
[ROW][C]40[/C][C]2.4[/C][C]2.54618686903076[/C][C]-0.146186869030762[/C][/ROW]
[ROW][C]41[/C][C]2.1[/C][C]2.44050800528186[/C][C]-0.340508005281855[/C][/ROW]
[ROW][C]42[/C][C]2.1[/C][C]2.12728042485532[/C][C]-0.0272804248553213[/C][/ROW]
[ROW][C]43[/C][C]2.3[/C][C]2.126220672931[/C][C]0.173779327068998[/C][/ROW]
[ROW][C]44[/C][C]2.3[/C][C]2.33297141003444[/C][C]-0.03297141003444[/C][/ROW]
[ROW][C]45[/C][C]2.3[/C][C]2.33169058264935[/C][C]-0.0316905826493517[/C][/ROW]
[ROW][C]46[/C][C]2.9[/C][C]2.33045951106144[/C][C]0.569540488938557[/C][/ROW]
[ROW][C]47[/C][C]2.8[/C][C]2.95258422621275[/C][C]-0.152584226212754[/C][/ROW]
[ROW][C]48[/C][C]2.9[/C][C]2.84665684684798[/C][C]0.0533431531520248[/C][/ROW]
[ROW][C]49[/C][C]3[/C][C]2.9487290473178[/C][C]0.0512709526822022[/C][/ROW]
[ROW][C]50[/C][C]3[/C][C]3.05072074983177[/C][C]-0.0507207498317741[/C][/ROW]
[ROW][C]51[/C][C]2.9[/C][C]3.04875042083132[/C][C]-0.148750420831319[/C][/ROW]
[ROW][C]52[/C][C]2.6[/C][C]2.94297197179486[/C][C]-0.342971971794861[/C][/ROW]
[ROW][C]53[/C][C]2.8[/C][C]2.62964867463124[/C][C]0.170351325368764[/C][/ROW]
[ROW][C]54[/C][C]2.9[/C][C]2.8362662455022[/C][C]0.0637337544978038[/C][/ROW]
[ROW][C]55[/C][C]3.1[/C][C]2.93874208557182[/C][C]0.16125791442818[/C][/ROW]
[ROW][C]56[/C][C]2.8[/C][C]3.14500640828796[/C][C]-0.345006408287959[/C][/ROW]
[ROW][C]57[/C][C]2.4[/C][C]2.83160408017082[/C][C]-0.431604080170823[/C][/ROW]
[ROW][C]58[/C][C]1.6[/C][C]2.41483772638671[/C][C]-0.814837726386705[/C][/ROW]
[ROW][C]59[/C][C]1.5[/C][C]1.58318404602335[/C][C]-0.0831840460233537[/C][/ROW]
[ROW][C]60[/C][C]1.7[/C][C]1.47995262813622[/C][C]0.220047371863775[/C][/ROW]
[ROW][C]61[/C][C]1.4[/C][C]1.68850072176053[/C][C]-0.288500721760532[/C][/ROW]
[ROW][C]62[/C][C]1.1[/C][C]1.3772934478022[/C][C]-0.277293447802195[/C][/ROW]
[ROW][C]63[/C][C]0.8[/C][C]1.06652153840312[/C][C]-0.266521538403125[/C][/ROW]
[ROW][C]64[/C][C]1.2[/C][C]0.756168081127685[/C][C]0.443831918872315[/C][/ROW]
[ROW][C]65[/C][C]0.8[/C][C]1.17340944494786[/C][C]-0.37340944494786[/C][/ROW]
[ROW][C]66[/C][C]0.9[/C][C]0.758903755247593[/C][C]0.141096244752407[/C][/ROW]
[ROW][C]67[/C][C]0.9[/C][C]0.864384865519287[/C][C]0.0356151344807129[/C][/ROW]
[ROW][C]68[/C][C]1[/C][C]0.865768392627132[/C][C]0.134231607372868[/C][/ROW]
[ROW][C]69[/C][C]0.9[/C][C]0.970982835033083[/C][C]-0.0709828350330827[/C][/ROW]
[ROW][C]70[/C][C]1.1[/C][C]0.868225392785796[/C][C]0.231774607214204[/C][/ROW]
[ROW][C]71[/C][C]1[/C][C]1.07722904970486[/C][C]-0.0772290497048647[/C][/ROW]
[ROW][C]72[/C][C]0.7[/C][C]0.974228963215297[/C][C]-0.274228963215297[/C][/ROW]
[ROW][C]73[/C][C]0[/C][C]0.663576098642515[/C][C]-0.663576098642515[/C][/ROW]
[ROW][C]74[/C][C]0.2[/C][C]-0.0622015808180717[/C][C]0.262201580818072[/C][/ROW]
[ROW][C]75[/C][C]0.4[/C][C]0.147984060765786[/C][C]0.252015939234214[/C][/ROW]
[ROW][C]76[/C][C]0.6[/C][C]0.357774024741023[/C][C]0.242225975258977[/C][/ROW]
[ROW][C]77[/C][C]1.1[/C][C]0.567183681839926[/C][C]0.532816318160074[/C][/ROW]
[ROW][C]78[/C][C]1[/C][C]1.08788178758695[/C][C]-0.0878817875869506[/C][/ROW]
[ROW][C]79[/C][C]1[/C][C]0.984467878382755[/C][C]0.0155321216172448[/C][/ROW]
[ROW][C]80[/C][C]0.8[/C][C]0.985071248596377[/C][C]-0.185071248596377[/C][/ROW]
[ROW][C]81[/C][C]0.6[/C][C]0.777881858662882[/C][C]-0.177881858662882[/C][/ROW]
[ROW][C]82[/C][C]0.6[/C][C]0.570971752129742[/C][C]0.0290282478702577[/C][/ROW]
[ROW][C]83[/C][C]0.7[/C][C]0.572099401046623[/C][C]0.127900598953377[/C][/ROW]
[ROW][C]84[/C][C]0.7[/C][C]0.677067905260958[/C][C]0.0229320947390423[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=295479&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=295479&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
322.1-0.1
41.82.09611533936902-0.296115339369016
51.61.88461226335824-0.284612263358242
61.41.67355604281261-0.273556042812611
70.21.46292931891379-1.26292931891379
80.30.2138688008647890.0861311991352107
90.40.3172147056485890.0827852943514106
100.70.4204306333865030.279569366613497
1110.731290954507630.26870904549237
121.11.041729389009770.0582706109902347
130.81.14399300449434-0.343993004494337
140.80.830630043675406-0.0306300436754057
1510.8294401704274940.170559829572506
161.11.036065840979170.0639341590208291
1711.1385494660844-0.138549466084404
180.81.03316728952098-0.233167289520984
191.60.8241095316206290.775890468379371
201.51.65425024318532-0.154250243185322
211.61.54825814471510.0517418552848956
221.61.6502681401971-0.0502681401970977
231.61.64831539354493-0.0483153935449332
241.91.646438504473190.253561495526812
2521.956288508065250.043711491934747
261.92.05798655118366-0.157986551183658
2721.951849309827580.0481506901724236
282.12.053719800732250.046280199267748
292.32.155517629413150.144482370586852
302.32.36113027918205-0.0611302791820476
312.62.358755575293050.241244424706949
322.62.66812710248409-0.068127102484087
332.72.665480595754860.0345194042451427
342.62.76682155746162-0.166821557461619
352.62.66034110609491-0.0603411060949126
362.42.65799705890214-0.257997058902143
372.52.447974748725870.0520252512741259
382.52.54999575318029-0.0499957531802906
392.52.54805358783933-0.0480535878393318
402.42.54618686903076-0.146186869030762
412.12.44050800528186-0.340508005281855
422.12.12728042485532-0.0272804248553213
432.32.1262206729310.173779327068998
442.32.33297141003444-0.03297141003444
452.32.33169058264935-0.0316905826493517
462.92.330459511061440.569540488938557
472.82.95258422621275-0.152584226212754
482.92.846656846847980.0533431531520248
4932.94872904731780.0512709526822022
5033.05072074983177-0.0507207498317741
512.93.04875042083132-0.148750420831319
522.62.94297197179486-0.342971971794861
532.82.629648674631240.170351325368764
542.92.83626624550220.0637337544978038
553.12.938742085571820.16125791442818
562.83.14500640828796-0.345006408287959
572.42.83160408017082-0.431604080170823
581.62.41483772638671-0.814837726386705
591.51.58318404602335-0.0831840460233537
601.71.479952628136220.220047371863775
611.41.68850072176053-0.288500721760532
621.11.3772934478022-0.277293447802195
630.81.06652153840312-0.266521538403125
641.20.7561680811276850.443831918872315
650.81.17340944494786-0.37340944494786
660.90.7589037552475930.141096244752407
670.90.8643848655192870.0356151344807129
6810.8657683926271320.134231607372868
690.90.970982835033083-0.0709828350330827
701.10.8682253927857960.231774607214204
7111.07722904970486-0.0772290497048647
720.70.974228963215297-0.274228963215297
7300.663576098642515-0.663576098642515
740.2-0.06220158081807170.262201580818072
750.40.1479840607657860.252015939234214
760.60.3577740247410230.242225975258977
771.10.5671836818399260.532816318160074
7811.08788178758695-0.0878817875869506
7910.9844678783827550.0155321216172448
800.80.985071248596377-0.185071248596377
810.60.777881858662882-0.177881858662882
820.60.5709717521297420.0290282478702577
830.70.5720994010466230.127900598953377
840.70.6770679052609580.0229320947390423







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
850.6779587393171450.1206833611969031.23523411743739
860.655917478634291-0.1476423651947971.45947732246338
870.633876217951436-0.3693161966670321.6370686325699
880.611834957268581-0.5686534736533831.79232338819055
890.589793696585726-0.75486962970591.93445702287735
900.567752435902871-0.9325914884786482.06809636028439
910.545711175220017-1.104509270867892.19593162130792
920.523669914537162-1.272337781139292.31967761021362
930.501628653854307-1.437241520303142.44049882801176
940.479587393171452-1.60004876315322.5592235494961
950.457546132488598-1.761369798405732.67646206338293
960.435504871805743-1.92166693851492.79267668212638

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
85 & 0.677958739317145 & 0.120683361196903 & 1.23523411743739 \tabularnewline
86 & 0.655917478634291 & -0.147642365194797 & 1.45947732246338 \tabularnewline
87 & 0.633876217951436 & -0.369316196667032 & 1.6370686325699 \tabularnewline
88 & 0.611834957268581 & -0.568653473653383 & 1.79232338819055 \tabularnewline
89 & 0.589793696585726 & -0.7548696297059 & 1.93445702287735 \tabularnewline
90 & 0.567752435902871 & -0.932591488478648 & 2.06809636028439 \tabularnewline
91 & 0.545711175220017 & -1.10450927086789 & 2.19593162130792 \tabularnewline
92 & 0.523669914537162 & -1.27233778113929 & 2.31967761021362 \tabularnewline
93 & 0.501628653854307 & -1.43724152030314 & 2.44049882801176 \tabularnewline
94 & 0.479587393171452 & -1.6000487631532 & 2.5592235494961 \tabularnewline
95 & 0.457546132488598 & -1.76136979840573 & 2.67646206338293 \tabularnewline
96 & 0.435504871805743 & -1.9216669385149 & 2.79267668212638 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=295479&T=3

[TABLE]
[ROW][C]Extrapolation Forecasts of Exponential Smoothing[/C][/ROW]
[ROW][C]t[/C][C]Forecast[/C][C]95% Lower Bound[/C][C]95% Upper Bound[/C][/ROW]
[ROW][C]85[/C][C]0.677958739317145[/C][C]0.120683361196903[/C][C]1.23523411743739[/C][/ROW]
[ROW][C]86[/C][C]0.655917478634291[/C][C]-0.147642365194797[/C][C]1.45947732246338[/C][/ROW]
[ROW][C]87[/C][C]0.633876217951436[/C][C]-0.369316196667032[/C][C]1.6370686325699[/C][/ROW]
[ROW][C]88[/C][C]0.611834957268581[/C][C]-0.568653473653383[/C][C]1.79232338819055[/C][/ROW]
[ROW][C]89[/C][C]0.589793696585726[/C][C]-0.7548696297059[/C][C]1.93445702287735[/C][/ROW]
[ROW][C]90[/C][C]0.567752435902871[/C][C]-0.932591488478648[/C][C]2.06809636028439[/C][/ROW]
[ROW][C]91[/C][C]0.545711175220017[/C][C]-1.10450927086789[/C][C]2.19593162130792[/C][/ROW]
[ROW][C]92[/C][C]0.523669914537162[/C][C]-1.27233778113929[/C][C]2.31967761021362[/C][/ROW]
[ROW][C]93[/C][C]0.501628653854307[/C][C]-1.43724152030314[/C][C]2.44049882801176[/C][/ROW]
[ROW][C]94[/C][C]0.479587393171452[/C][C]-1.6000487631532[/C][C]2.5592235494961[/C][/ROW]
[ROW][C]95[/C][C]0.457546132488598[/C][C]-1.76136979840573[/C][C]2.67646206338293[/C][/ROW]
[ROW][C]96[/C][C]0.435504871805743[/C][C]-1.9216669385149[/C][C]2.79267668212638[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=295479&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=295479&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
850.6779587393171450.1206833611969031.23523411743739
860.655917478634291-0.1476423651947971.45947732246338
870.633876217951436-0.3693161966670321.6370686325699
880.611834957268581-0.5686534736533831.79232338819055
890.589793696585726-0.75486962970591.93445702287735
900.567752435902871-0.9325914884786482.06809636028439
910.545711175220017-1.104509270867892.19593162130792
920.523669914537162-1.272337781139292.31967761021362
930.501628653854307-1.437241520303142.44049882801176
940.479587393171452-1.60004876315322.5592235494961
950.457546132488598-1.761369798405732.67646206338293
960.435504871805743-1.92166693851492.79267668212638



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