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Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationMon, 05 Jan 2015 14:54:36 +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/2015/Jan/05/t14204697707xugujhaj9g06sb.htm/, Retrieved Tue, 14 May 2024 11:21:23 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=271974, Retrieved Tue, 14 May 2024 11:21:23 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact96
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [] [2015-01-05 14:54:36] [cbda179e085b8c88f5d239d64a2141d3] [Current]
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Dataseries X:
1,4
1,5
1,8
1,8
1,8
1,7
1,5
1,1
1,3
1,6
1,9
1,9
2
2,2
2,2
2
2,3
2,6
3,2
3,2
3,1
2,8
2,3
1,9
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




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=271974&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=271974&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=271974&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
alpha0.999923097779756
betaFALSE
gammaFALSE

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.999923097779756 \tabularnewline
beta & FALSE \tabularnewline
gamma & FALSE \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=271974&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]0.999923097779756[/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=271974&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=271974&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
alpha0.999923097779756
betaFALSE
gammaFALSE







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
21.51.40.1
31.81.499992309777980.300007690222024
41.81.799976928742532.30712574682546e-05
51.81.799999998225771.77423076230809e-09
61.71.79999999999986-0.0999999999998638
71.51.70000769022202-0.200007690222024
81.11.50001538103544-0.400015381035444
91.31.100030762070930.199969237929067
101.61.299984621921620.300015378078377
111.91.599976928151320.300023071848681
121.91.899976927559652.3072440349603e-05
1321.899999998225680.100000001774322
142.21.999992309777840.200007690222161
152.22.199984618964561.53810354439621e-05
1622.19999999881716-0.199999998817164
172.32.000015380443960.299984619556042
182.62.299976930516720.300023069483283
193.22.599976927559830.600023072440168
203.23.199953856893534.61431064682216e-05
213.13.19999999645149-0.0999999964514924
222.83.10000769022175-0.300007690221752
232.32.80002307125747-0.500023071257468
241.92.30003845288435-0.400038452884353
251.91.90003076384521-3.07638452095027e-05
2621.900000002365810.0999999976341921
2721.999992309778167.69022184243795e-06
281.81.9999999994086-0.199999999408605
291.61.800015380444-0.200015380444003
301.41.60001538162684-0.200015381626839
310.21.40001538162693-1.20001538162693
320.30.2000922838471740.0999077161528263
330.40.2999923168748080.100007683125192
340.70.3999923091871260.300007690812874
3510.6999769287424860.300023071257514
361.10.9999769275596960.100023072440304
370.81.09999230800365-0.299992308003654
380.80.800023070074542-2.3070074541498e-05
3910.800000001774140.19999999822586
401.10.9999846195560880.100015380443912
4111.09999230859519-0.0999923085951855
420.81.00000768963054-0.200007689630538
431.60.8000153810353980.799984618964602
441.51.59993847940664-0.0999384794066409
451.61.500007685490950.0999923145090458
461.61.599992310369017.68963099306852e-06
471.61.599999999408655.91349857970158e-10
481.91.599999999999950.300000000000045
4921.899976929333930.100023070666073
501.91.99999230800379-0.0999923080037903
5121.900007689630490.0999923103695073
522.11.999992310369330.100007689630675
532.32.099992309186630.200007690813374
542.32.299984618964511.53810354897033e-05
552.62.299999998817160.300000001182836
562.62.599976929333842.30706661641378e-05
572.72.599999998225810.100000001774186
582.62.69999230977784-0.0999923097778392
592.62.60000768963063-7.68963062913741e-06
602.42.60000000059135-0.20000000059135
612.52.400015380444090.0999846195559058
622.52.499992310960777.68903923420439e-06
632.52.49999999940875.91304338826149e-10
642.42.49999999999995-0.0999999999999543
652.12.40000769022202-0.300007690222024
662.12.10002307125747-2.30712574684766e-05
672.32.100000001774230.199999998225769
682.32.299984619556091.53804439126937e-05
692.32.299999998817211.18279031013913e-09
702.92.299999999999910.600000000000091
712.82.89995385866785-0.0999538586678539
722.92.800007686673650.0999923133263465
7332.89999231036910.100007689630902
7432.999992309186637.69081337415045e-06
752.92.99999999940856-0.0999999994085594
762.62.90000769022198-0.300007690221979
772.82.600023071257470.199976928742532
782.92.799984621330180.100015378669818
793.12.899992308595320.200007691404679
802.83.09998461896447-0.299984618964465
812.42.80002306948324-0.400023069483237
821.62.40003076266219-0.800030762662192
831.51.60006152414191-0.100061524141912
841.71.500007694953370.199992305046632

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
2 & 1.5 & 1.4 & 0.1 \tabularnewline
3 & 1.8 & 1.49999230977798 & 0.300007690222024 \tabularnewline
4 & 1.8 & 1.79997692874253 & 2.30712574682546e-05 \tabularnewline
5 & 1.8 & 1.79999999822577 & 1.77423076230809e-09 \tabularnewline
6 & 1.7 & 1.79999999999986 & -0.0999999999998638 \tabularnewline
7 & 1.5 & 1.70000769022202 & -0.200007690222024 \tabularnewline
8 & 1.1 & 1.50001538103544 & -0.400015381035444 \tabularnewline
9 & 1.3 & 1.10003076207093 & 0.199969237929067 \tabularnewline
10 & 1.6 & 1.29998462192162 & 0.300015378078377 \tabularnewline
11 & 1.9 & 1.59997692815132 & 0.300023071848681 \tabularnewline
12 & 1.9 & 1.89997692755965 & 2.3072440349603e-05 \tabularnewline
13 & 2 & 1.89999999822568 & 0.100000001774322 \tabularnewline
14 & 2.2 & 1.99999230977784 & 0.200007690222161 \tabularnewline
15 & 2.2 & 2.19998461896456 & 1.53810354439621e-05 \tabularnewline
16 & 2 & 2.19999999881716 & -0.199999998817164 \tabularnewline
17 & 2.3 & 2.00001538044396 & 0.299984619556042 \tabularnewline
18 & 2.6 & 2.29997693051672 & 0.300023069483283 \tabularnewline
19 & 3.2 & 2.59997692755983 & 0.600023072440168 \tabularnewline
20 & 3.2 & 3.19995385689353 & 4.61431064682216e-05 \tabularnewline
21 & 3.1 & 3.19999999645149 & -0.0999999964514924 \tabularnewline
22 & 2.8 & 3.10000769022175 & -0.300007690221752 \tabularnewline
23 & 2.3 & 2.80002307125747 & -0.500023071257468 \tabularnewline
24 & 1.9 & 2.30003845288435 & -0.400038452884353 \tabularnewline
25 & 1.9 & 1.90003076384521 & -3.07638452095027e-05 \tabularnewline
26 & 2 & 1.90000000236581 & 0.0999999976341921 \tabularnewline
27 & 2 & 1.99999230977816 & 7.69022184243795e-06 \tabularnewline
28 & 1.8 & 1.9999999994086 & -0.199999999408605 \tabularnewline
29 & 1.6 & 1.800015380444 & -0.200015380444003 \tabularnewline
30 & 1.4 & 1.60001538162684 & -0.200015381626839 \tabularnewline
31 & 0.2 & 1.40001538162693 & -1.20001538162693 \tabularnewline
32 & 0.3 & 0.200092283847174 & 0.0999077161528263 \tabularnewline
33 & 0.4 & 0.299992316874808 & 0.100007683125192 \tabularnewline
34 & 0.7 & 0.399992309187126 & 0.300007690812874 \tabularnewline
35 & 1 & 0.699976928742486 & 0.300023071257514 \tabularnewline
36 & 1.1 & 0.999976927559696 & 0.100023072440304 \tabularnewline
37 & 0.8 & 1.09999230800365 & -0.299992308003654 \tabularnewline
38 & 0.8 & 0.800023070074542 & -2.3070074541498e-05 \tabularnewline
39 & 1 & 0.80000000177414 & 0.19999999822586 \tabularnewline
40 & 1.1 & 0.999984619556088 & 0.100015380443912 \tabularnewline
41 & 1 & 1.09999230859519 & -0.0999923085951855 \tabularnewline
42 & 0.8 & 1.00000768963054 & -0.200007689630538 \tabularnewline
43 & 1.6 & 0.800015381035398 & 0.799984618964602 \tabularnewline
44 & 1.5 & 1.59993847940664 & -0.0999384794066409 \tabularnewline
45 & 1.6 & 1.50000768549095 & 0.0999923145090458 \tabularnewline
46 & 1.6 & 1.59999231036901 & 7.68963099306852e-06 \tabularnewline
47 & 1.6 & 1.59999999940865 & 5.91349857970158e-10 \tabularnewline
48 & 1.9 & 1.59999999999995 & 0.300000000000045 \tabularnewline
49 & 2 & 1.89997692933393 & 0.100023070666073 \tabularnewline
50 & 1.9 & 1.99999230800379 & -0.0999923080037903 \tabularnewline
51 & 2 & 1.90000768963049 & 0.0999923103695073 \tabularnewline
52 & 2.1 & 1.99999231036933 & 0.100007689630675 \tabularnewline
53 & 2.3 & 2.09999230918663 & 0.200007690813374 \tabularnewline
54 & 2.3 & 2.29998461896451 & 1.53810354897033e-05 \tabularnewline
55 & 2.6 & 2.29999999881716 & 0.300000001182836 \tabularnewline
56 & 2.6 & 2.59997692933384 & 2.30706661641378e-05 \tabularnewline
57 & 2.7 & 2.59999999822581 & 0.100000001774186 \tabularnewline
58 & 2.6 & 2.69999230977784 & -0.0999923097778392 \tabularnewline
59 & 2.6 & 2.60000768963063 & -7.68963062913741e-06 \tabularnewline
60 & 2.4 & 2.60000000059135 & -0.20000000059135 \tabularnewline
61 & 2.5 & 2.40001538044409 & 0.0999846195559058 \tabularnewline
62 & 2.5 & 2.49999231096077 & 7.68903923420439e-06 \tabularnewline
63 & 2.5 & 2.4999999994087 & 5.91304338826149e-10 \tabularnewline
64 & 2.4 & 2.49999999999995 & -0.0999999999999543 \tabularnewline
65 & 2.1 & 2.40000769022202 & -0.300007690222024 \tabularnewline
66 & 2.1 & 2.10002307125747 & -2.30712574684766e-05 \tabularnewline
67 & 2.3 & 2.10000000177423 & 0.199999998225769 \tabularnewline
68 & 2.3 & 2.29998461955609 & 1.53804439126937e-05 \tabularnewline
69 & 2.3 & 2.29999999881721 & 1.18279031013913e-09 \tabularnewline
70 & 2.9 & 2.29999999999991 & 0.600000000000091 \tabularnewline
71 & 2.8 & 2.89995385866785 & -0.0999538586678539 \tabularnewline
72 & 2.9 & 2.80000768667365 & 0.0999923133263465 \tabularnewline
73 & 3 & 2.8999923103691 & 0.100007689630902 \tabularnewline
74 & 3 & 2.99999230918663 & 7.69081337415045e-06 \tabularnewline
75 & 2.9 & 2.99999999940856 & -0.0999999994085594 \tabularnewline
76 & 2.6 & 2.90000769022198 & -0.300007690221979 \tabularnewline
77 & 2.8 & 2.60002307125747 & 0.199976928742532 \tabularnewline
78 & 2.9 & 2.79998462133018 & 0.100015378669818 \tabularnewline
79 & 3.1 & 2.89999230859532 & 0.200007691404679 \tabularnewline
80 & 2.8 & 3.09998461896447 & -0.299984618964465 \tabularnewline
81 & 2.4 & 2.80002306948324 & -0.400023069483237 \tabularnewline
82 & 1.6 & 2.40003076266219 & -0.800030762662192 \tabularnewline
83 & 1.5 & 1.60006152414191 & -0.100061524141912 \tabularnewline
84 & 1.7 & 1.50000769495337 & 0.199992305046632 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=271974&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]1.5[/C][C]1.4[/C][C]0.1[/C][/ROW]
[ROW][C]3[/C][C]1.8[/C][C]1.49999230977798[/C][C]0.300007690222024[/C][/ROW]
[ROW][C]4[/C][C]1.8[/C][C]1.79997692874253[/C][C]2.30712574682546e-05[/C][/ROW]
[ROW][C]5[/C][C]1.8[/C][C]1.79999999822577[/C][C]1.77423076230809e-09[/C][/ROW]
[ROW][C]6[/C][C]1.7[/C][C]1.79999999999986[/C][C]-0.0999999999998638[/C][/ROW]
[ROW][C]7[/C][C]1.5[/C][C]1.70000769022202[/C][C]-0.200007690222024[/C][/ROW]
[ROW][C]8[/C][C]1.1[/C][C]1.50001538103544[/C][C]-0.400015381035444[/C][/ROW]
[ROW][C]9[/C][C]1.3[/C][C]1.10003076207093[/C][C]0.199969237929067[/C][/ROW]
[ROW][C]10[/C][C]1.6[/C][C]1.29998462192162[/C][C]0.300015378078377[/C][/ROW]
[ROW][C]11[/C][C]1.9[/C][C]1.59997692815132[/C][C]0.300023071848681[/C][/ROW]
[ROW][C]12[/C][C]1.9[/C][C]1.89997692755965[/C][C]2.3072440349603e-05[/C][/ROW]
[ROW][C]13[/C][C]2[/C][C]1.89999999822568[/C][C]0.100000001774322[/C][/ROW]
[ROW][C]14[/C][C]2.2[/C][C]1.99999230977784[/C][C]0.200007690222161[/C][/ROW]
[ROW][C]15[/C][C]2.2[/C][C]2.19998461896456[/C][C]1.53810354439621e-05[/C][/ROW]
[ROW][C]16[/C][C]2[/C][C]2.19999999881716[/C][C]-0.199999998817164[/C][/ROW]
[ROW][C]17[/C][C]2.3[/C][C]2.00001538044396[/C][C]0.299984619556042[/C][/ROW]
[ROW][C]18[/C][C]2.6[/C][C]2.29997693051672[/C][C]0.300023069483283[/C][/ROW]
[ROW][C]19[/C][C]3.2[/C][C]2.59997692755983[/C][C]0.600023072440168[/C][/ROW]
[ROW][C]20[/C][C]3.2[/C][C]3.19995385689353[/C][C]4.61431064682216e-05[/C][/ROW]
[ROW][C]21[/C][C]3.1[/C][C]3.19999999645149[/C][C]-0.0999999964514924[/C][/ROW]
[ROW][C]22[/C][C]2.8[/C][C]3.10000769022175[/C][C]-0.300007690221752[/C][/ROW]
[ROW][C]23[/C][C]2.3[/C][C]2.80002307125747[/C][C]-0.500023071257468[/C][/ROW]
[ROW][C]24[/C][C]1.9[/C][C]2.30003845288435[/C][C]-0.400038452884353[/C][/ROW]
[ROW][C]25[/C][C]1.9[/C][C]1.90003076384521[/C][C]-3.07638452095027e-05[/C][/ROW]
[ROW][C]26[/C][C]2[/C][C]1.90000000236581[/C][C]0.0999999976341921[/C][/ROW]
[ROW][C]27[/C][C]2[/C][C]1.99999230977816[/C][C]7.69022184243795e-06[/C][/ROW]
[ROW][C]28[/C][C]1.8[/C][C]1.9999999994086[/C][C]-0.199999999408605[/C][/ROW]
[ROW][C]29[/C][C]1.6[/C][C]1.800015380444[/C][C]-0.200015380444003[/C][/ROW]
[ROW][C]30[/C][C]1.4[/C][C]1.60001538162684[/C][C]-0.200015381626839[/C][/ROW]
[ROW][C]31[/C][C]0.2[/C][C]1.40001538162693[/C][C]-1.20001538162693[/C][/ROW]
[ROW][C]32[/C][C]0.3[/C][C]0.200092283847174[/C][C]0.0999077161528263[/C][/ROW]
[ROW][C]33[/C][C]0.4[/C][C]0.299992316874808[/C][C]0.100007683125192[/C][/ROW]
[ROW][C]34[/C][C]0.7[/C][C]0.399992309187126[/C][C]0.300007690812874[/C][/ROW]
[ROW][C]35[/C][C]1[/C][C]0.699976928742486[/C][C]0.300023071257514[/C][/ROW]
[ROW][C]36[/C][C]1.1[/C][C]0.999976927559696[/C][C]0.100023072440304[/C][/ROW]
[ROW][C]37[/C][C]0.8[/C][C]1.09999230800365[/C][C]-0.299992308003654[/C][/ROW]
[ROW][C]38[/C][C]0.8[/C][C]0.800023070074542[/C][C]-2.3070074541498e-05[/C][/ROW]
[ROW][C]39[/C][C]1[/C][C]0.80000000177414[/C][C]0.19999999822586[/C][/ROW]
[ROW][C]40[/C][C]1.1[/C][C]0.999984619556088[/C][C]0.100015380443912[/C][/ROW]
[ROW][C]41[/C][C]1[/C][C]1.09999230859519[/C][C]-0.0999923085951855[/C][/ROW]
[ROW][C]42[/C][C]0.8[/C][C]1.00000768963054[/C][C]-0.200007689630538[/C][/ROW]
[ROW][C]43[/C][C]1.6[/C][C]0.800015381035398[/C][C]0.799984618964602[/C][/ROW]
[ROW][C]44[/C][C]1.5[/C][C]1.59993847940664[/C][C]-0.0999384794066409[/C][/ROW]
[ROW][C]45[/C][C]1.6[/C][C]1.50000768549095[/C][C]0.0999923145090458[/C][/ROW]
[ROW][C]46[/C][C]1.6[/C][C]1.59999231036901[/C][C]7.68963099306852e-06[/C][/ROW]
[ROW][C]47[/C][C]1.6[/C][C]1.59999999940865[/C][C]5.91349857970158e-10[/C][/ROW]
[ROW][C]48[/C][C]1.9[/C][C]1.59999999999995[/C][C]0.300000000000045[/C][/ROW]
[ROW][C]49[/C][C]2[/C][C]1.89997692933393[/C][C]0.100023070666073[/C][/ROW]
[ROW][C]50[/C][C]1.9[/C][C]1.99999230800379[/C][C]-0.0999923080037903[/C][/ROW]
[ROW][C]51[/C][C]2[/C][C]1.90000768963049[/C][C]0.0999923103695073[/C][/ROW]
[ROW][C]52[/C][C]2.1[/C][C]1.99999231036933[/C][C]0.100007689630675[/C][/ROW]
[ROW][C]53[/C][C]2.3[/C][C]2.09999230918663[/C][C]0.200007690813374[/C][/ROW]
[ROW][C]54[/C][C]2.3[/C][C]2.29998461896451[/C][C]1.53810354897033e-05[/C][/ROW]
[ROW][C]55[/C][C]2.6[/C][C]2.29999999881716[/C][C]0.300000001182836[/C][/ROW]
[ROW][C]56[/C][C]2.6[/C][C]2.59997692933384[/C][C]2.30706661641378e-05[/C][/ROW]
[ROW][C]57[/C][C]2.7[/C][C]2.59999999822581[/C][C]0.100000001774186[/C][/ROW]
[ROW][C]58[/C][C]2.6[/C][C]2.69999230977784[/C][C]-0.0999923097778392[/C][/ROW]
[ROW][C]59[/C][C]2.6[/C][C]2.60000768963063[/C][C]-7.68963062913741e-06[/C][/ROW]
[ROW][C]60[/C][C]2.4[/C][C]2.60000000059135[/C][C]-0.20000000059135[/C][/ROW]
[ROW][C]61[/C][C]2.5[/C][C]2.40001538044409[/C][C]0.0999846195559058[/C][/ROW]
[ROW][C]62[/C][C]2.5[/C][C]2.49999231096077[/C][C]7.68903923420439e-06[/C][/ROW]
[ROW][C]63[/C][C]2.5[/C][C]2.4999999994087[/C][C]5.91304338826149e-10[/C][/ROW]
[ROW][C]64[/C][C]2.4[/C][C]2.49999999999995[/C][C]-0.0999999999999543[/C][/ROW]
[ROW][C]65[/C][C]2.1[/C][C]2.40000769022202[/C][C]-0.300007690222024[/C][/ROW]
[ROW][C]66[/C][C]2.1[/C][C]2.10002307125747[/C][C]-2.30712574684766e-05[/C][/ROW]
[ROW][C]67[/C][C]2.3[/C][C]2.10000000177423[/C][C]0.199999998225769[/C][/ROW]
[ROW][C]68[/C][C]2.3[/C][C]2.29998461955609[/C][C]1.53804439126937e-05[/C][/ROW]
[ROW][C]69[/C][C]2.3[/C][C]2.29999999881721[/C][C]1.18279031013913e-09[/C][/ROW]
[ROW][C]70[/C][C]2.9[/C][C]2.29999999999991[/C][C]0.600000000000091[/C][/ROW]
[ROW][C]71[/C][C]2.8[/C][C]2.89995385866785[/C][C]-0.0999538586678539[/C][/ROW]
[ROW][C]72[/C][C]2.9[/C][C]2.80000768667365[/C][C]0.0999923133263465[/C][/ROW]
[ROW][C]73[/C][C]3[/C][C]2.8999923103691[/C][C]0.100007689630902[/C][/ROW]
[ROW][C]74[/C][C]3[/C][C]2.99999230918663[/C][C]7.69081337415045e-06[/C][/ROW]
[ROW][C]75[/C][C]2.9[/C][C]2.99999999940856[/C][C]-0.0999999994085594[/C][/ROW]
[ROW][C]76[/C][C]2.6[/C][C]2.90000769022198[/C][C]-0.300007690221979[/C][/ROW]
[ROW][C]77[/C][C]2.8[/C][C]2.60002307125747[/C][C]0.199976928742532[/C][/ROW]
[ROW][C]78[/C][C]2.9[/C][C]2.79998462133018[/C][C]0.100015378669818[/C][/ROW]
[ROW][C]79[/C][C]3.1[/C][C]2.89999230859532[/C][C]0.200007691404679[/C][/ROW]
[ROW][C]80[/C][C]2.8[/C][C]3.09998461896447[/C][C]-0.299984618964465[/C][/ROW]
[ROW][C]81[/C][C]2.4[/C][C]2.80002306948324[/C][C]-0.400023069483237[/C][/ROW]
[ROW][C]82[/C][C]1.6[/C][C]2.40003076266219[/C][C]-0.800030762662192[/C][/ROW]
[ROW][C]83[/C][C]1.5[/C][C]1.60006152414191[/C][C]-0.100061524141912[/C][/ROW]
[ROW][C]84[/C][C]1.7[/C][C]1.50000769495337[/C][C]0.199992305046632[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=271974&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=271974&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
21.51.40.1
31.81.499992309777980.300007690222024
41.81.799976928742532.30712574682546e-05
51.81.799999998225771.77423076230809e-09
61.71.79999999999986-0.0999999999998638
71.51.70000769022202-0.200007690222024
81.11.50001538103544-0.400015381035444
91.31.100030762070930.199969237929067
101.61.299984621921620.300015378078377
111.91.599976928151320.300023071848681
121.91.899976927559652.3072440349603e-05
1321.899999998225680.100000001774322
142.21.999992309777840.200007690222161
152.22.199984618964561.53810354439621e-05
1622.19999999881716-0.199999998817164
172.32.000015380443960.299984619556042
182.62.299976930516720.300023069483283
193.22.599976927559830.600023072440168
203.23.199953856893534.61431064682216e-05
213.13.19999999645149-0.0999999964514924
222.83.10000769022175-0.300007690221752
232.32.80002307125747-0.500023071257468
241.92.30003845288435-0.400038452884353
251.91.90003076384521-3.07638452095027e-05
2621.900000002365810.0999999976341921
2721.999992309778167.69022184243795e-06
281.81.9999999994086-0.199999999408605
291.61.800015380444-0.200015380444003
301.41.60001538162684-0.200015381626839
310.21.40001538162693-1.20001538162693
320.30.2000922838471740.0999077161528263
330.40.2999923168748080.100007683125192
340.70.3999923091871260.300007690812874
3510.6999769287424860.300023071257514
361.10.9999769275596960.100023072440304
370.81.09999230800365-0.299992308003654
380.80.800023070074542-2.3070074541498e-05
3910.800000001774140.19999999822586
401.10.9999846195560880.100015380443912
4111.09999230859519-0.0999923085951855
420.81.00000768963054-0.200007689630538
431.60.8000153810353980.799984618964602
441.51.59993847940664-0.0999384794066409
451.61.500007685490950.0999923145090458
461.61.599992310369017.68963099306852e-06
471.61.599999999408655.91349857970158e-10
481.91.599999999999950.300000000000045
4921.899976929333930.100023070666073
501.91.99999230800379-0.0999923080037903
5121.900007689630490.0999923103695073
522.11.999992310369330.100007689630675
532.32.099992309186630.200007690813374
542.32.299984618964511.53810354897033e-05
552.62.299999998817160.300000001182836
562.62.599976929333842.30706661641378e-05
572.72.599999998225810.100000001774186
582.62.69999230977784-0.0999923097778392
592.62.60000768963063-7.68963062913741e-06
602.42.60000000059135-0.20000000059135
612.52.400015380444090.0999846195559058
622.52.499992310960777.68903923420439e-06
632.52.49999999940875.91304338826149e-10
642.42.49999999999995-0.0999999999999543
652.12.40000769022202-0.300007690222024
662.12.10002307125747-2.30712574684766e-05
672.32.100000001774230.199999998225769
682.32.299984619556091.53804439126937e-05
692.32.299999998817211.18279031013913e-09
702.92.299999999999910.600000000000091
712.82.89995385866785-0.0999538586678539
722.92.800007686673650.0999923133263465
7332.89999231036910.100007689630902
7432.999992309186637.69081337415045e-06
752.92.99999999940856-0.0999999994085594
762.62.90000769022198-0.300007690221979
772.82.600023071257470.199976928742532
782.92.799984621330180.100015378669818
793.12.899992308595320.200007691404679
802.83.09998461896447-0.299984618964465
812.42.80002306948324-0.400023069483237
821.62.40003076266219-0.800030762662192
831.51.60006152414191-0.100061524141912
841.71.500007694953370.199992305046632







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
851.699984620147711.157189144703762.24278009559166
861.699984620147710.9323854127891922.46758382750623
871.699984620147710.7598834776569552.64008576263847
881.699984620147710.6144562819236812.78551295837174
891.699984620147710.4863317092780412.91363753101738
901.699984620147710.370497875934963.02947136436046
911.699984620147710.2639774411919723.13599179910345
921.699984620147710.1648304803339213.2351387599615
931.699984620147710.07170950581278523.32825973448264
941.69998462014771-0.01636658602700843.41633582632243
951.69998462014771-0.1001384528426923.50010769313811
961.69998462014771-0.180181514237073.58015075453249

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
85 & 1.69998462014771 & 1.15718914470376 & 2.24278009559166 \tabularnewline
86 & 1.69998462014771 & 0.932385412789192 & 2.46758382750623 \tabularnewline
87 & 1.69998462014771 & 0.759883477656955 & 2.64008576263847 \tabularnewline
88 & 1.69998462014771 & 0.614456281923681 & 2.78551295837174 \tabularnewline
89 & 1.69998462014771 & 0.486331709278041 & 2.91363753101738 \tabularnewline
90 & 1.69998462014771 & 0.37049787593496 & 3.02947136436046 \tabularnewline
91 & 1.69998462014771 & 0.263977441191972 & 3.13599179910345 \tabularnewline
92 & 1.69998462014771 & 0.164830480333921 & 3.2351387599615 \tabularnewline
93 & 1.69998462014771 & 0.0717095058127852 & 3.32825973448264 \tabularnewline
94 & 1.69998462014771 & -0.0163665860270084 & 3.41633582632243 \tabularnewline
95 & 1.69998462014771 & -0.100138452842692 & 3.50010769313811 \tabularnewline
96 & 1.69998462014771 & -0.18018151423707 & 3.58015075453249 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=271974&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]1.69998462014771[/C][C]1.15718914470376[/C][C]2.24278009559166[/C][/ROW]
[ROW][C]86[/C][C]1.69998462014771[/C][C]0.932385412789192[/C][C]2.46758382750623[/C][/ROW]
[ROW][C]87[/C][C]1.69998462014771[/C][C]0.759883477656955[/C][C]2.64008576263847[/C][/ROW]
[ROW][C]88[/C][C]1.69998462014771[/C][C]0.614456281923681[/C][C]2.78551295837174[/C][/ROW]
[ROW][C]89[/C][C]1.69998462014771[/C][C]0.486331709278041[/C][C]2.91363753101738[/C][/ROW]
[ROW][C]90[/C][C]1.69998462014771[/C][C]0.37049787593496[/C][C]3.02947136436046[/C][/ROW]
[ROW][C]91[/C][C]1.69998462014771[/C][C]0.263977441191972[/C][C]3.13599179910345[/C][/ROW]
[ROW][C]92[/C][C]1.69998462014771[/C][C]0.164830480333921[/C][C]3.2351387599615[/C][/ROW]
[ROW][C]93[/C][C]1.69998462014771[/C][C]0.0717095058127852[/C][C]3.32825973448264[/C][/ROW]
[ROW][C]94[/C][C]1.69998462014771[/C][C]-0.0163665860270084[/C][C]3.41633582632243[/C][/ROW]
[ROW][C]95[/C][C]1.69998462014771[/C][C]-0.100138452842692[/C][C]3.50010769313811[/C][/ROW]
[ROW][C]96[/C][C]1.69998462014771[/C][C]-0.18018151423707[/C][C]3.58015075453249[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=271974&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=271974&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
851.699984620147711.157189144703762.24278009559166
861.699984620147710.9323854127891922.46758382750623
871.699984620147710.7598834776569552.64008576263847
881.699984620147710.6144562819236812.78551295837174
891.699984620147710.4863317092780412.91363753101738
901.699984620147710.370497875934963.02947136436046
911.699984620147710.2639774411919723.13599179910345
921.699984620147710.1648304803339213.2351387599615
931.699984620147710.07170950581278523.32825973448264
941.69998462014771-0.01636658602700843.41633582632243
951.69998462014771-0.1001384528426923.50010769313811
961.69998462014771-0.180181514237073.58015075453249



Parameters (Session):
par1 = grey ;
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')