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Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationThu, 12 Dec 2013 06:27:45 -0500
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2013/Dec/12/t1386847682q9k7sj6the3uz33.htm/, Retrieved Tue, 07 Dec 2021 12:47:06 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=232245, Retrieved Tue, 07 Dec 2021 12:47:06 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact69
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [] [2013-12-12 11:27:45] [a77fefb2f58fa7cd2e34999d4ef06758] [Current]
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Dataseries X:
-2,5
4,4
13,7
12,3
13,4
2,2
1,7
-7,2
-4,8
-2,9
-2,4
-2,5
-5,3
-7,1
-8
-8,9
-7,7
-1,1
4
9,6
10,9
13
14,9
20,1
10,8
11
3,8
10,8
7,6
10,2
2,2
-0,1
-1,7
-4,8
-9,9
-13,5
-18,1
-18
-15,7
-15,2
-15,1
-17,9
-14,5
-9,4
-4,2
-2,2
4,5
12,4
15,8
11,5
14,1
18,8
26,1
27,9
25,4
23,4
11,5
9,9
8,1
12,6
8,2
5,4
1
-2,9
-3,7
-7
-7,2
-11,8
-2,1
1,2
2,5
4,8
-6,6
-16
-22,7
-17,7
-18,2
-18,9
-16
-12,2
-17,1
-18,6
-17,5
-24,9




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time4 seconds
R Server'Gertrude Mary Cox' @ cox.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 & 4 seconds \tabularnewline
R Server & 'Gertrude Mary Cox' @ cox.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=232245&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]4 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Gertrude Mary Cox' @ cox.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=232245&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=232245&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 time4 seconds
R Server'Gertrude Mary Cox' @ cox.wessa.net







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.860966419321329
beta0
gamma1

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.860966419321329 \tabularnewline
beta & 0 \tabularnewline
gamma & 1 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=232245&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]0.860966419321329[/C][/ROW]
[ROW][C]beta[/C][C]0[/C][/ROW]
[ROW][C]gamma[/C][C]1[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=232245&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=232245&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
alpha0.860966419321329
beta0
gamma1







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
13-5.31.72398504273504-7.02398504273504
14-7.1-7.00064466108957-0.0993553389104278
15-8-9.421734057019531.42173405701953
16-8.9-10.4957165622681.59571656226802
17-7.7-9.386572639614841.68657263961483
18-1.1-3.078371352041451.97837135204145
1941.268558828132462.73144117186754
209.6-4.7653098320856714.3653098320857
2110.911.3046917509388-0.404691750938829
221314.562384624323-1.56238462432303
2314.915.3983428098358-0.49834280983581
2420.115.80457193304254.29542806695751
2510.815.6865070119639-4.88650701196391
26119.764930177266941.23506982273306
273.88.70421853985796-4.90421853985796
2810.82.207992689159538.59200731084047
297.69.35334005190203-1.75334005190203
3010.212.7404618465082-2.54046184650824
312.213.3015303817679-11.1015303817679
32-0.1-3.024563848582042.92456384858204
33-1.71.14181342394293-2.84181342394293
34-4.82.1402681915576-6.9402681915576
35-9.9-1.5060132378786-8.3939867621214
36-13.5-7.23117328655365-6.26882671344635
37-18.1-17.7213041302963-0.378695869703684
38-18-18.91070220013720.910702200137184
39-15.7-21.10425071198625.40425071198623
40-15.2-16.84880209656971.6488020965697
41-15.1-17.11967195297782.01967195297782
42-17.9-10.5935498840081-7.30645011599186
43-14.5-15.32611321654590.826113216545874
44-9.4-19.432808743332610.0328087433326
45-4.2-9.948191395858385.74819139585838
46-2.2-2.12385377817746-0.0761462218225444
474.5-0.06247239171055564.56247239171056
4812.45.662912415454716.73708758454529
4915.87.189363016725418.6106369832746
5011.513.918748295971-2.41874829597098
5114.19.483408851735754.61659114826425
5218.812.53857556487426.26142443512575
5326.116.29058201107659.80941798892349
5427.928.2267696869416-0.326769686941635
5525.430.6341762216292-5.23417622162922
5623.422.58981484251340.810185157486561
5711.523.5383572928761-12.0383572928761
589.915.2392952598652-5.33929525986515
598.113.4142058199362-5.31420581993625
6012.610.9384468892891.66155311071098
618.28.35551902996433-0.15551902996433
625.46.00408342722131-0.604083427221314
6314.10925793152361-3.10925793152361
64-2.90.741415087711989-3.64141508771199
65-3.7-3.53930050316776-0.160699496832241
66-7-1.59631964623326-5.40368035376673
67-7.2-4.24225701193987-2.95774298806013
68-11.8-9.48631661567126-2.31368338432874
69-2.1-13.013698941561710.9136989415617
701.2-0.6204167207088981.8204167207089
712.53.7222537013196-1.2222537013196
724.85.73939287635117-0.939392876351175
73-6.60.664503817627854-7.26450381762785
74-16-7.86989447707523-8.13010552292477
75-22.7-16.592675649802-6.10732435019799
76-17.7-22.61574071789594.91574071789588
77-18.2-19.04509616332260.845096163322612
78-18.9-16.965109420265-1.93489057973501
79-16-16.28446784477510.284467844775115
80-12.2-18.64754688419836.44754688419826
81-17.1-12.7927538291711-4.30724617082894
82-18.6-14.7684658077066-3.83153419229343
83-17.5-15.7149686890253-1.78503131097469
84-24.9-14.1430349841236-10.7569650158764

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & -5.3 & 1.72398504273504 & -7.02398504273504 \tabularnewline
14 & -7.1 & -7.00064466108957 & -0.0993553389104278 \tabularnewline
15 & -8 & -9.42173405701953 & 1.42173405701953 \tabularnewline
16 & -8.9 & -10.495716562268 & 1.59571656226802 \tabularnewline
17 & -7.7 & -9.38657263961484 & 1.68657263961483 \tabularnewline
18 & -1.1 & -3.07837135204145 & 1.97837135204145 \tabularnewline
19 & 4 & 1.26855882813246 & 2.73144117186754 \tabularnewline
20 & 9.6 & -4.76530983208567 & 14.3653098320857 \tabularnewline
21 & 10.9 & 11.3046917509388 & -0.404691750938829 \tabularnewline
22 & 13 & 14.562384624323 & -1.56238462432303 \tabularnewline
23 & 14.9 & 15.3983428098358 & -0.49834280983581 \tabularnewline
24 & 20.1 & 15.8045719330425 & 4.29542806695751 \tabularnewline
25 & 10.8 & 15.6865070119639 & -4.88650701196391 \tabularnewline
26 & 11 & 9.76493017726694 & 1.23506982273306 \tabularnewline
27 & 3.8 & 8.70421853985796 & -4.90421853985796 \tabularnewline
28 & 10.8 & 2.20799268915953 & 8.59200731084047 \tabularnewline
29 & 7.6 & 9.35334005190203 & -1.75334005190203 \tabularnewline
30 & 10.2 & 12.7404618465082 & -2.54046184650824 \tabularnewline
31 & 2.2 & 13.3015303817679 & -11.1015303817679 \tabularnewline
32 & -0.1 & -3.02456384858204 & 2.92456384858204 \tabularnewline
33 & -1.7 & 1.14181342394293 & -2.84181342394293 \tabularnewline
34 & -4.8 & 2.1402681915576 & -6.9402681915576 \tabularnewline
35 & -9.9 & -1.5060132378786 & -8.3939867621214 \tabularnewline
36 & -13.5 & -7.23117328655365 & -6.26882671344635 \tabularnewline
37 & -18.1 & -17.7213041302963 & -0.378695869703684 \tabularnewline
38 & -18 & -18.9107022001372 & 0.910702200137184 \tabularnewline
39 & -15.7 & -21.1042507119862 & 5.40425071198623 \tabularnewline
40 & -15.2 & -16.8488020965697 & 1.6488020965697 \tabularnewline
41 & -15.1 & -17.1196719529778 & 2.01967195297782 \tabularnewline
42 & -17.9 & -10.5935498840081 & -7.30645011599186 \tabularnewline
43 & -14.5 & -15.3261132165459 & 0.826113216545874 \tabularnewline
44 & -9.4 & -19.4328087433326 & 10.0328087433326 \tabularnewline
45 & -4.2 & -9.94819139585838 & 5.74819139585838 \tabularnewline
46 & -2.2 & -2.12385377817746 & -0.0761462218225444 \tabularnewline
47 & 4.5 & -0.0624723917105556 & 4.56247239171056 \tabularnewline
48 & 12.4 & 5.66291241545471 & 6.73708758454529 \tabularnewline
49 & 15.8 & 7.18936301672541 & 8.6106369832746 \tabularnewline
50 & 11.5 & 13.918748295971 & -2.41874829597098 \tabularnewline
51 & 14.1 & 9.48340885173575 & 4.61659114826425 \tabularnewline
52 & 18.8 & 12.5385755648742 & 6.26142443512575 \tabularnewline
53 & 26.1 & 16.2905820110765 & 9.80941798892349 \tabularnewline
54 & 27.9 & 28.2267696869416 & -0.326769686941635 \tabularnewline
55 & 25.4 & 30.6341762216292 & -5.23417622162922 \tabularnewline
56 & 23.4 & 22.5898148425134 & 0.810185157486561 \tabularnewline
57 & 11.5 & 23.5383572928761 & -12.0383572928761 \tabularnewline
58 & 9.9 & 15.2392952598652 & -5.33929525986515 \tabularnewline
59 & 8.1 & 13.4142058199362 & -5.31420581993625 \tabularnewline
60 & 12.6 & 10.938446889289 & 1.66155311071098 \tabularnewline
61 & 8.2 & 8.35551902996433 & -0.15551902996433 \tabularnewline
62 & 5.4 & 6.00408342722131 & -0.604083427221314 \tabularnewline
63 & 1 & 4.10925793152361 & -3.10925793152361 \tabularnewline
64 & -2.9 & 0.741415087711989 & -3.64141508771199 \tabularnewline
65 & -3.7 & -3.53930050316776 & -0.160699496832241 \tabularnewline
66 & -7 & -1.59631964623326 & -5.40368035376673 \tabularnewline
67 & -7.2 & -4.24225701193987 & -2.95774298806013 \tabularnewline
68 & -11.8 & -9.48631661567126 & -2.31368338432874 \tabularnewline
69 & -2.1 & -13.0136989415617 & 10.9136989415617 \tabularnewline
70 & 1.2 & -0.620416720708898 & 1.8204167207089 \tabularnewline
71 & 2.5 & 3.7222537013196 & -1.2222537013196 \tabularnewline
72 & 4.8 & 5.73939287635117 & -0.939392876351175 \tabularnewline
73 & -6.6 & 0.664503817627854 & -7.26450381762785 \tabularnewline
74 & -16 & -7.86989447707523 & -8.13010552292477 \tabularnewline
75 & -22.7 & -16.592675649802 & -6.10732435019799 \tabularnewline
76 & -17.7 & -22.6157407178959 & 4.91574071789588 \tabularnewline
77 & -18.2 & -19.0450961633226 & 0.845096163322612 \tabularnewline
78 & -18.9 & -16.965109420265 & -1.93489057973501 \tabularnewline
79 & -16 & -16.2844678447751 & 0.284467844775115 \tabularnewline
80 & -12.2 & -18.6475468841983 & 6.44754688419826 \tabularnewline
81 & -17.1 & -12.7927538291711 & -4.30724617082894 \tabularnewline
82 & -18.6 & -14.7684658077066 & -3.83153419229343 \tabularnewline
83 & -17.5 & -15.7149686890253 & -1.78503131097469 \tabularnewline
84 & -24.9 & -14.1430349841236 & -10.7569650158764 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=232245&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]-5.3[/C][C]1.72398504273504[/C][C]-7.02398504273504[/C][/ROW]
[ROW][C]14[/C][C]-7.1[/C][C]-7.00064466108957[/C][C]-0.0993553389104278[/C][/ROW]
[ROW][C]15[/C][C]-8[/C][C]-9.42173405701953[/C][C]1.42173405701953[/C][/ROW]
[ROW][C]16[/C][C]-8.9[/C][C]-10.495716562268[/C][C]1.59571656226802[/C][/ROW]
[ROW][C]17[/C][C]-7.7[/C][C]-9.38657263961484[/C][C]1.68657263961483[/C][/ROW]
[ROW][C]18[/C][C]-1.1[/C][C]-3.07837135204145[/C][C]1.97837135204145[/C][/ROW]
[ROW][C]19[/C][C]4[/C][C]1.26855882813246[/C][C]2.73144117186754[/C][/ROW]
[ROW][C]20[/C][C]9.6[/C][C]-4.76530983208567[/C][C]14.3653098320857[/C][/ROW]
[ROW][C]21[/C][C]10.9[/C][C]11.3046917509388[/C][C]-0.404691750938829[/C][/ROW]
[ROW][C]22[/C][C]13[/C][C]14.562384624323[/C][C]-1.56238462432303[/C][/ROW]
[ROW][C]23[/C][C]14.9[/C][C]15.3983428098358[/C][C]-0.49834280983581[/C][/ROW]
[ROW][C]24[/C][C]20.1[/C][C]15.8045719330425[/C][C]4.29542806695751[/C][/ROW]
[ROW][C]25[/C][C]10.8[/C][C]15.6865070119639[/C][C]-4.88650701196391[/C][/ROW]
[ROW][C]26[/C][C]11[/C][C]9.76493017726694[/C][C]1.23506982273306[/C][/ROW]
[ROW][C]27[/C][C]3.8[/C][C]8.70421853985796[/C][C]-4.90421853985796[/C][/ROW]
[ROW][C]28[/C][C]10.8[/C][C]2.20799268915953[/C][C]8.59200731084047[/C][/ROW]
[ROW][C]29[/C][C]7.6[/C][C]9.35334005190203[/C][C]-1.75334005190203[/C][/ROW]
[ROW][C]30[/C][C]10.2[/C][C]12.7404618465082[/C][C]-2.54046184650824[/C][/ROW]
[ROW][C]31[/C][C]2.2[/C][C]13.3015303817679[/C][C]-11.1015303817679[/C][/ROW]
[ROW][C]32[/C][C]-0.1[/C][C]-3.02456384858204[/C][C]2.92456384858204[/C][/ROW]
[ROW][C]33[/C][C]-1.7[/C][C]1.14181342394293[/C][C]-2.84181342394293[/C][/ROW]
[ROW][C]34[/C][C]-4.8[/C][C]2.1402681915576[/C][C]-6.9402681915576[/C][/ROW]
[ROW][C]35[/C][C]-9.9[/C][C]-1.5060132378786[/C][C]-8.3939867621214[/C][/ROW]
[ROW][C]36[/C][C]-13.5[/C][C]-7.23117328655365[/C][C]-6.26882671344635[/C][/ROW]
[ROW][C]37[/C][C]-18.1[/C][C]-17.7213041302963[/C][C]-0.378695869703684[/C][/ROW]
[ROW][C]38[/C][C]-18[/C][C]-18.9107022001372[/C][C]0.910702200137184[/C][/ROW]
[ROW][C]39[/C][C]-15.7[/C][C]-21.1042507119862[/C][C]5.40425071198623[/C][/ROW]
[ROW][C]40[/C][C]-15.2[/C][C]-16.8488020965697[/C][C]1.6488020965697[/C][/ROW]
[ROW][C]41[/C][C]-15.1[/C][C]-17.1196719529778[/C][C]2.01967195297782[/C][/ROW]
[ROW][C]42[/C][C]-17.9[/C][C]-10.5935498840081[/C][C]-7.30645011599186[/C][/ROW]
[ROW][C]43[/C][C]-14.5[/C][C]-15.3261132165459[/C][C]0.826113216545874[/C][/ROW]
[ROW][C]44[/C][C]-9.4[/C][C]-19.4328087433326[/C][C]10.0328087433326[/C][/ROW]
[ROW][C]45[/C][C]-4.2[/C][C]-9.94819139585838[/C][C]5.74819139585838[/C][/ROW]
[ROW][C]46[/C][C]-2.2[/C][C]-2.12385377817746[/C][C]-0.0761462218225444[/C][/ROW]
[ROW][C]47[/C][C]4.5[/C][C]-0.0624723917105556[/C][C]4.56247239171056[/C][/ROW]
[ROW][C]48[/C][C]12.4[/C][C]5.66291241545471[/C][C]6.73708758454529[/C][/ROW]
[ROW][C]49[/C][C]15.8[/C][C]7.18936301672541[/C][C]8.6106369832746[/C][/ROW]
[ROW][C]50[/C][C]11.5[/C][C]13.918748295971[/C][C]-2.41874829597098[/C][/ROW]
[ROW][C]51[/C][C]14.1[/C][C]9.48340885173575[/C][C]4.61659114826425[/C][/ROW]
[ROW][C]52[/C][C]18.8[/C][C]12.5385755648742[/C][C]6.26142443512575[/C][/ROW]
[ROW][C]53[/C][C]26.1[/C][C]16.2905820110765[/C][C]9.80941798892349[/C][/ROW]
[ROW][C]54[/C][C]27.9[/C][C]28.2267696869416[/C][C]-0.326769686941635[/C][/ROW]
[ROW][C]55[/C][C]25.4[/C][C]30.6341762216292[/C][C]-5.23417622162922[/C][/ROW]
[ROW][C]56[/C][C]23.4[/C][C]22.5898148425134[/C][C]0.810185157486561[/C][/ROW]
[ROW][C]57[/C][C]11.5[/C][C]23.5383572928761[/C][C]-12.0383572928761[/C][/ROW]
[ROW][C]58[/C][C]9.9[/C][C]15.2392952598652[/C][C]-5.33929525986515[/C][/ROW]
[ROW][C]59[/C][C]8.1[/C][C]13.4142058199362[/C][C]-5.31420581993625[/C][/ROW]
[ROW][C]60[/C][C]12.6[/C][C]10.938446889289[/C][C]1.66155311071098[/C][/ROW]
[ROW][C]61[/C][C]8.2[/C][C]8.35551902996433[/C][C]-0.15551902996433[/C][/ROW]
[ROW][C]62[/C][C]5.4[/C][C]6.00408342722131[/C][C]-0.604083427221314[/C][/ROW]
[ROW][C]63[/C][C]1[/C][C]4.10925793152361[/C][C]-3.10925793152361[/C][/ROW]
[ROW][C]64[/C][C]-2.9[/C][C]0.741415087711989[/C][C]-3.64141508771199[/C][/ROW]
[ROW][C]65[/C][C]-3.7[/C][C]-3.53930050316776[/C][C]-0.160699496832241[/C][/ROW]
[ROW][C]66[/C][C]-7[/C][C]-1.59631964623326[/C][C]-5.40368035376673[/C][/ROW]
[ROW][C]67[/C][C]-7.2[/C][C]-4.24225701193987[/C][C]-2.95774298806013[/C][/ROW]
[ROW][C]68[/C][C]-11.8[/C][C]-9.48631661567126[/C][C]-2.31368338432874[/C][/ROW]
[ROW][C]69[/C][C]-2.1[/C][C]-13.0136989415617[/C][C]10.9136989415617[/C][/ROW]
[ROW][C]70[/C][C]1.2[/C][C]-0.620416720708898[/C][C]1.8204167207089[/C][/ROW]
[ROW][C]71[/C][C]2.5[/C][C]3.7222537013196[/C][C]-1.2222537013196[/C][/ROW]
[ROW][C]72[/C][C]4.8[/C][C]5.73939287635117[/C][C]-0.939392876351175[/C][/ROW]
[ROW][C]73[/C][C]-6.6[/C][C]0.664503817627854[/C][C]-7.26450381762785[/C][/ROW]
[ROW][C]74[/C][C]-16[/C][C]-7.86989447707523[/C][C]-8.13010552292477[/C][/ROW]
[ROW][C]75[/C][C]-22.7[/C][C]-16.592675649802[/C][C]-6.10732435019799[/C][/ROW]
[ROW][C]76[/C][C]-17.7[/C][C]-22.6157407178959[/C][C]4.91574071789588[/C][/ROW]
[ROW][C]77[/C][C]-18.2[/C][C]-19.0450961633226[/C][C]0.845096163322612[/C][/ROW]
[ROW][C]78[/C][C]-18.9[/C][C]-16.965109420265[/C][C]-1.93489057973501[/C][/ROW]
[ROW][C]79[/C][C]-16[/C][C]-16.2844678447751[/C][C]0.284467844775115[/C][/ROW]
[ROW][C]80[/C][C]-12.2[/C][C]-18.6475468841983[/C][C]6.44754688419826[/C][/ROW]
[ROW][C]81[/C][C]-17.1[/C][C]-12.7927538291711[/C][C]-4.30724617082894[/C][/ROW]
[ROW][C]82[/C][C]-18.6[/C][C]-14.7684658077066[/C][C]-3.83153419229343[/C][/ROW]
[ROW][C]83[/C][C]-17.5[/C][C]-15.7149686890253[/C][C]-1.78503131097469[/C][/ROW]
[ROW][C]84[/C][C]-24.9[/C][C]-14.1430349841236[/C][C]-10.7569650158764[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=232245&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=232245&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
13-5.31.72398504273504-7.02398504273504
14-7.1-7.00064466108957-0.0993553389104278
15-8-9.421734057019531.42173405701953
16-8.9-10.4957165622681.59571656226802
17-7.7-9.386572639614841.68657263961483
18-1.1-3.078371352041451.97837135204145
1941.268558828132462.73144117186754
209.6-4.7653098320856714.3653098320857
2110.911.3046917509388-0.404691750938829
221314.562384624323-1.56238462432303
2314.915.3983428098358-0.49834280983581
2420.115.80457193304254.29542806695751
2510.815.6865070119639-4.88650701196391
26119.764930177266941.23506982273306
273.88.70421853985796-4.90421853985796
2810.82.207992689159538.59200731084047
297.69.35334005190203-1.75334005190203
3010.212.7404618465082-2.54046184650824
312.213.3015303817679-11.1015303817679
32-0.1-3.024563848582042.92456384858204
33-1.71.14181342394293-2.84181342394293
34-4.82.1402681915576-6.9402681915576
35-9.9-1.5060132378786-8.3939867621214
36-13.5-7.23117328655365-6.26882671344635
37-18.1-17.7213041302963-0.378695869703684
38-18-18.91070220013720.910702200137184
39-15.7-21.10425071198625.40425071198623
40-15.2-16.84880209656971.6488020965697
41-15.1-17.11967195297782.01967195297782
42-17.9-10.5935498840081-7.30645011599186
43-14.5-15.32611321654590.826113216545874
44-9.4-19.432808743332610.0328087433326
45-4.2-9.948191395858385.74819139585838
46-2.2-2.12385377817746-0.0761462218225444
474.5-0.06247239171055564.56247239171056
4812.45.662912415454716.73708758454529
4915.87.189363016725418.6106369832746
5011.513.918748295971-2.41874829597098
5114.19.483408851735754.61659114826425
5218.812.53857556487426.26142443512575
5326.116.29058201107659.80941798892349
5427.928.2267696869416-0.326769686941635
5525.430.6341762216292-5.23417622162922
5623.422.58981484251340.810185157486561
5711.523.5383572928761-12.0383572928761
589.915.2392952598652-5.33929525986515
598.113.4142058199362-5.31420581993625
6012.610.9384468892891.66155311071098
618.28.35551902996433-0.15551902996433
625.46.00408342722131-0.604083427221314
6314.10925793152361-3.10925793152361
64-2.90.741415087711989-3.64141508771199
65-3.7-3.53930050316776-0.160699496832241
66-7-1.59631964623326-5.40368035376673
67-7.2-4.24225701193987-2.95774298806013
68-11.8-9.48631661567126-2.31368338432874
69-2.1-13.013698941561710.9136989415617
701.2-0.6204167207088981.8204167207089
712.53.7222537013196-1.2222537013196
724.85.73939287635117-0.939392876351175
73-6.60.664503817627854-7.26450381762785
74-16-7.86989447707523-8.13010552292477
75-22.7-16.592675649802-6.10732435019799
76-17.7-22.61574071789594.91574071789588
77-18.2-19.04509616332260.845096163322612
78-18.9-16.965109420265-1.93489057973501
79-16-16.28446784477510.284467844775115
80-12.2-18.64754688419836.44754688419826
81-17.1-12.7927538291711-4.30724617082894
82-18.6-14.7684658077066-3.83153419229343
83-17.5-15.7149686890253-1.78503131097469
84-24.9-14.1430349841236-10.7569650158764







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
85-28.5499267965983-39.0735983187005-18.0262552744962
86-30.9501789558212-44.8368929699878-17.0634649416547
87-32.3919777783973-48.9731113318488-15.8108442249458
88-31.6242654625962-50.519427640348-12.7291032848444
89-32.8518648803142-53.80706274456-11.8966670160685
90-31.8859890661012-54.716089401751-9.05588873045144
91-29.2309063278293-53.7932076276257-4.66860502803286
92-30.9820276821239-57.1621691818967-4.80188618235103
93-32.1736333692898-59.8772968951535-4.469969843426
94-30.3748110952437-59.5224720058626-1.22715018462475
95-27.7379590790573-58.26138123920462.78546308108992
96-25.8765734265734-57.71636714721045.96322029406356

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
85 & -28.5499267965983 & -39.0735983187005 & -18.0262552744962 \tabularnewline
86 & -30.9501789558212 & -44.8368929699878 & -17.0634649416547 \tabularnewline
87 & -32.3919777783973 & -48.9731113318488 & -15.8108442249458 \tabularnewline
88 & -31.6242654625962 & -50.519427640348 & -12.7291032848444 \tabularnewline
89 & -32.8518648803142 & -53.80706274456 & -11.8966670160685 \tabularnewline
90 & -31.8859890661012 & -54.716089401751 & -9.05588873045144 \tabularnewline
91 & -29.2309063278293 & -53.7932076276257 & -4.66860502803286 \tabularnewline
92 & -30.9820276821239 & -57.1621691818967 & -4.80188618235103 \tabularnewline
93 & -32.1736333692898 & -59.8772968951535 & -4.469969843426 \tabularnewline
94 & -30.3748110952437 & -59.5224720058626 & -1.22715018462475 \tabularnewline
95 & -27.7379590790573 & -58.2613812392046 & 2.78546308108992 \tabularnewline
96 & -25.8765734265734 & -57.7163671472104 & 5.96322029406356 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=232245&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]-28.5499267965983[/C][C]-39.0735983187005[/C][C]-18.0262552744962[/C][/ROW]
[ROW][C]86[/C][C]-30.9501789558212[/C][C]-44.8368929699878[/C][C]-17.0634649416547[/C][/ROW]
[ROW][C]87[/C][C]-32.3919777783973[/C][C]-48.9731113318488[/C][C]-15.8108442249458[/C][/ROW]
[ROW][C]88[/C][C]-31.6242654625962[/C][C]-50.519427640348[/C][C]-12.7291032848444[/C][/ROW]
[ROW][C]89[/C][C]-32.8518648803142[/C][C]-53.80706274456[/C][C]-11.8966670160685[/C][/ROW]
[ROW][C]90[/C][C]-31.8859890661012[/C][C]-54.716089401751[/C][C]-9.05588873045144[/C][/ROW]
[ROW][C]91[/C][C]-29.2309063278293[/C][C]-53.7932076276257[/C][C]-4.66860502803286[/C][/ROW]
[ROW][C]92[/C][C]-30.9820276821239[/C][C]-57.1621691818967[/C][C]-4.80188618235103[/C][/ROW]
[ROW][C]93[/C][C]-32.1736333692898[/C][C]-59.8772968951535[/C][C]-4.469969843426[/C][/ROW]
[ROW][C]94[/C][C]-30.3748110952437[/C][C]-59.5224720058626[/C][C]-1.22715018462475[/C][/ROW]
[ROW][C]95[/C][C]-27.7379590790573[/C][C]-58.2613812392046[/C][C]2.78546308108992[/C][/ROW]
[ROW][C]96[/C][C]-25.8765734265734[/C][C]-57.7163671472104[/C][C]5.96322029406356[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=232245&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=232245&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
85-28.5499267965983-39.0735983187005-18.0262552744962
86-30.9501789558212-44.8368929699878-17.0634649416547
87-32.3919777783973-48.9731113318488-15.8108442249458
88-31.6242654625962-50.519427640348-12.7291032848444
89-32.8518648803142-53.80706274456-11.8966670160685
90-31.8859890661012-54.716089401751-9.05588873045144
91-29.2309063278293-53.7932076276257-4.66860502803286
92-30.9820276821239-57.1621691818967-4.80188618235103
93-32.1736333692898-59.8772968951535-4.469969843426
94-30.3748110952437-59.5224720058626-1.22715018462475
95-27.7379590790573-58.26138123920462.78546308108992
96-25.8765734265734-57.71636714721045.96322029406356



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')