Free Statistics

of Irreproducible Research!

Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationSun, 06 Dec 2015 14:31:28 +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/Dec/06/t1449412322khrsrq3eu6b7bo7.htm/, Retrieved Thu, 16 May 2024 12:23:52 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=285291, Retrieved Thu, 16 May 2024 12:23:52 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact103
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [] [2015-12-06 14:31:28] [9de61432ca342460988ae3c030b81fa6] [Current]
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Dataseries X:
-12
-12
-8
-6
-2
4
3
5
8
5
3
6
15
12
11
12
14
18
15
16
-1
-5
-6
-5
-2
-9
-9
-12
-16
-19
-30
-26
-22
-31
-33
-31
-27
-29
-33
-27
-22
-23
-23
-15
-15
-24
-18
-14
-7
-12
-12
-15
-16
-17
-13
-8
-13
-13
-11
-16
-34
-35
-38
-32
-37
-39
-31
-30
-29
-36
-41
-42
-33
-43
-41
-34
-32
-36
-37
-30
-32
-30
-21
-19
-6
-11
-11




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'George Udny Yule' @ yule.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 & 'George Udny Yule' @ yule.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=285291&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]'George Udny Yule' @ yule.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=285291&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=285291&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'George Udny Yule' @ yule.wessa.net







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.258899343719628
beta0
gamma0.194833586503249

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.258899343719628 \tabularnewline
beta & 0 \tabularnewline
gamma & 0.194833586503249 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=285291&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]0.258899343719628[/C][/ROW]
[ROW][C]beta[/C][C]0[/C][/ROW]
[ROW][C]gamma[/C][C]0.194833586503249[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=285291&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=285291&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
alpha0.258899343719628
beta0
gamma0.194833586503249







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
13153.1793507010976311.8206492989024
14125.09248263765556.9075173623445
15116.75394391690654.2460560830935
16129.822020579754732.17797942024527
171413.88638474993770.113615250062296
181820.6955786371283-2.69557863712835
191547.4541778593089-32.4541778593089
201615.68184776343480.318152236565185
21-116.1342381321913-17.1342381321913
22-55.86059029101266-10.8605902910127
23-61.67943355364188-7.67943355364188
24-5-0.193847922502815-4.80615207749718
25-2-3.124015103221351.12401510322135
26-9-1.23377561594877-7.76622438405123
27-9-2.24540886420511-6.75459113579489
28-12-3.89121423270845-8.10878576729155
29-16-6.63225794455716-9.36774205544284
30-19-11.5081704552055-7.49182954479448
31-30-25.1558309394689-4.84416906053114
32-26-10.5089354434341-15.4910645565659
33-22-10.3799931193988-11.6200068806012
34-31-3.65231869615293-27.3476813038471
35-33-48.481276372496815.4812763724968
36-31-24.1211338919418-6.87886610805816
37-27-45.766396263642218.7663962636422
38-29-37.42933582878568.42933582878565
39-33-27.2495274105779-5.75047258942211
40-27-30.33066106865643.33066106865641
41-22-34.008520951803112.0085209518031
42-23-39.077173208520216.0771732085202
43-23-65.027038570543942.0270385705439
44-15-25.24999962299710.249999622997
45-15-16.0183200530551.01832005305496
46-24-5.23658767731425-18.7634123226857
47-18-31.392016381594613.3920163815946
48-14-16.3838096304052.38380963040503
49-7-24.70597219711217.705972197112
50-12-18.65317140593866.65317140593861
51-12-13.60584187452591.60584187452589
52-15-12.9184878124498-2.08151218755024
53-16-14.473531802793-1.526468197207
54-17-18.09242840842861.09242840842865
55-13-30.695419239193617.6954192391936
56-8-12.37702129535474.37702129535466
57-13-8.09553607931732-4.90446392068268
58-13-3.85002376961532-9.14997623038468
59-11-13.78328828870282.78328828870284
60-16-7.80319221803678-8.19680778196322
61-34-13.6194236024414-20.3805763975586
62-35-18.9854488460509-16.0145511539491
63-38-19.6616797623935-18.3383202376065
64-32-25.5153614736846-6.48463852631536
65-37-29.8262413653936-7.17375863460638
66-39-38.7755297205332-0.224470279466765
67-31-62.960915809411231.9609158094112
68-30-28.3149024680874-1.68509753191257
69-29-24.9849972577928-4.01500274220718
70-36-12.7099576921541-23.2900423078459
71-41-34.3455412601667-6.65445873983329
72-42-25.9259675749501-16.0740324250499
73-33-44.07374786945511.073747869455
74-43-40.148675764488-2.85132423551196
75-41-35.473859138336-5.526140861664
76-34-36.27112390668322.27112390668324
77-32-39.29625497245677.29625497245668
78-36-44.51448110608288.5144811060828
79-37-62.893947888945725.8939478889457
80-30-32.15573802517482.15573802517483
81-32-27.9094839272204-4.09051607277961
82-30-16.3660661913846-13.6339338086154
83-21-31.661173258344510.6611732583445
84-19-21.66225339089332.6622533908933
85-6-27.12910742514621.129107425146
86-11-21.791327604098910.7913276040989
87-11-16.26061186599835.26061186599831

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 15 & 3.17935070109763 & 11.8206492989024 \tabularnewline
14 & 12 & 5.0924826376555 & 6.9075173623445 \tabularnewline
15 & 11 & 6.7539439169065 & 4.2460560830935 \tabularnewline
16 & 12 & 9.82202057975473 & 2.17797942024527 \tabularnewline
17 & 14 & 13.8863847499377 & 0.113615250062296 \tabularnewline
18 & 18 & 20.6955786371283 & -2.69557863712835 \tabularnewline
19 & 15 & 47.4541778593089 & -32.4541778593089 \tabularnewline
20 & 16 & 15.6818477634348 & 0.318152236565185 \tabularnewline
21 & -1 & 16.1342381321913 & -17.1342381321913 \tabularnewline
22 & -5 & 5.86059029101266 & -10.8605902910127 \tabularnewline
23 & -6 & 1.67943355364188 & -7.67943355364188 \tabularnewline
24 & -5 & -0.193847922502815 & -4.80615207749718 \tabularnewline
25 & -2 & -3.12401510322135 & 1.12401510322135 \tabularnewline
26 & -9 & -1.23377561594877 & -7.76622438405123 \tabularnewline
27 & -9 & -2.24540886420511 & -6.75459113579489 \tabularnewline
28 & -12 & -3.89121423270845 & -8.10878576729155 \tabularnewline
29 & -16 & -6.63225794455716 & -9.36774205544284 \tabularnewline
30 & -19 & -11.5081704552055 & -7.49182954479448 \tabularnewline
31 & -30 & -25.1558309394689 & -4.84416906053114 \tabularnewline
32 & -26 & -10.5089354434341 & -15.4910645565659 \tabularnewline
33 & -22 & -10.3799931193988 & -11.6200068806012 \tabularnewline
34 & -31 & -3.65231869615293 & -27.3476813038471 \tabularnewline
35 & -33 & -48.4812763724968 & 15.4812763724968 \tabularnewline
36 & -31 & -24.1211338919418 & -6.87886610805816 \tabularnewline
37 & -27 & -45.7663962636422 & 18.7663962636422 \tabularnewline
38 & -29 & -37.4293358287856 & 8.42933582878565 \tabularnewline
39 & -33 & -27.2495274105779 & -5.75047258942211 \tabularnewline
40 & -27 & -30.3306610686564 & 3.33066106865641 \tabularnewline
41 & -22 & -34.0085209518031 & 12.0085209518031 \tabularnewline
42 & -23 & -39.0771732085202 & 16.0771732085202 \tabularnewline
43 & -23 & -65.0270385705439 & 42.0270385705439 \tabularnewline
44 & -15 & -25.249999622997 & 10.249999622997 \tabularnewline
45 & -15 & -16.018320053055 & 1.01832005305496 \tabularnewline
46 & -24 & -5.23658767731425 & -18.7634123226857 \tabularnewline
47 & -18 & -31.3920163815946 & 13.3920163815946 \tabularnewline
48 & -14 & -16.383809630405 & 2.38380963040503 \tabularnewline
49 & -7 & -24.705972197112 & 17.705972197112 \tabularnewline
50 & -12 & -18.6531714059386 & 6.65317140593861 \tabularnewline
51 & -12 & -13.6058418745259 & 1.60584187452589 \tabularnewline
52 & -15 & -12.9184878124498 & -2.08151218755024 \tabularnewline
53 & -16 & -14.473531802793 & -1.526468197207 \tabularnewline
54 & -17 & -18.0924284084286 & 1.09242840842865 \tabularnewline
55 & -13 & -30.6954192391936 & 17.6954192391936 \tabularnewline
56 & -8 & -12.3770212953547 & 4.37702129535466 \tabularnewline
57 & -13 & -8.09553607931732 & -4.90446392068268 \tabularnewline
58 & -13 & -3.85002376961532 & -9.14997623038468 \tabularnewline
59 & -11 & -13.7832882887028 & 2.78328828870284 \tabularnewline
60 & -16 & -7.80319221803678 & -8.19680778196322 \tabularnewline
61 & -34 & -13.6194236024414 & -20.3805763975586 \tabularnewline
62 & -35 & -18.9854488460509 & -16.0145511539491 \tabularnewline
63 & -38 & -19.6616797623935 & -18.3383202376065 \tabularnewline
64 & -32 & -25.5153614736846 & -6.48463852631536 \tabularnewline
65 & -37 & -29.8262413653936 & -7.17375863460638 \tabularnewline
66 & -39 & -38.7755297205332 & -0.224470279466765 \tabularnewline
67 & -31 & -62.9609158094112 & 31.9609158094112 \tabularnewline
68 & -30 & -28.3149024680874 & -1.68509753191257 \tabularnewline
69 & -29 & -24.9849972577928 & -4.01500274220718 \tabularnewline
70 & -36 & -12.7099576921541 & -23.2900423078459 \tabularnewline
71 & -41 & -34.3455412601667 & -6.65445873983329 \tabularnewline
72 & -42 & -25.9259675749501 & -16.0740324250499 \tabularnewline
73 & -33 & -44.073747869455 & 11.073747869455 \tabularnewline
74 & -43 & -40.148675764488 & -2.85132423551196 \tabularnewline
75 & -41 & -35.473859138336 & -5.526140861664 \tabularnewline
76 & -34 & -36.2711239066832 & 2.27112390668324 \tabularnewline
77 & -32 & -39.2962549724567 & 7.29625497245668 \tabularnewline
78 & -36 & -44.5144811060828 & 8.5144811060828 \tabularnewline
79 & -37 & -62.8939478889457 & 25.8939478889457 \tabularnewline
80 & -30 & -32.1557380251748 & 2.15573802517483 \tabularnewline
81 & -32 & -27.9094839272204 & -4.09051607277961 \tabularnewline
82 & -30 & -16.3660661913846 & -13.6339338086154 \tabularnewline
83 & -21 & -31.6611732583445 & 10.6611732583445 \tabularnewline
84 & -19 & -21.6622533908933 & 2.6622533908933 \tabularnewline
85 & -6 & -27.129107425146 & 21.129107425146 \tabularnewline
86 & -11 & -21.7913276040989 & 10.7913276040989 \tabularnewline
87 & -11 & -16.2606118659983 & 5.26061186599831 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=285291&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]15[/C][C]3.17935070109763[/C][C]11.8206492989024[/C][/ROW]
[ROW][C]14[/C][C]12[/C][C]5.0924826376555[/C][C]6.9075173623445[/C][/ROW]
[ROW][C]15[/C][C]11[/C][C]6.7539439169065[/C][C]4.2460560830935[/C][/ROW]
[ROW][C]16[/C][C]12[/C][C]9.82202057975473[/C][C]2.17797942024527[/C][/ROW]
[ROW][C]17[/C][C]14[/C][C]13.8863847499377[/C][C]0.113615250062296[/C][/ROW]
[ROW][C]18[/C][C]18[/C][C]20.6955786371283[/C][C]-2.69557863712835[/C][/ROW]
[ROW][C]19[/C][C]15[/C][C]47.4541778593089[/C][C]-32.4541778593089[/C][/ROW]
[ROW][C]20[/C][C]16[/C][C]15.6818477634348[/C][C]0.318152236565185[/C][/ROW]
[ROW][C]21[/C][C]-1[/C][C]16.1342381321913[/C][C]-17.1342381321913[/C][/ROW]
[ROW][C]22[/C][C]-5[/C][C]5.86059029101266[/C][C]-10.8605902910127[/C][/ROW]
[ROW][C]23[/C][C]-6[/C][C]1.67943355364188[/C][C]-7.67943355364188[/C][/ROW]
[ROW][C]24[/C][C]-5[/C][C]-0.193847922502815[/C][C]-4.80615207749718[/C][/ROW]
[ROW][C]25[/C][C]-2[/C][C]-3.12401510322135[/C][C]1.12401510322135[/C][/ROW]
[ROW][C]26[/C][C]-9[/C][C]-1.23377561594877[/C][C]-7.76622438405123[/C][/ROW]
[ROW][C]27[/C][C]-9[/C][C]-2.24540886420511[/C][C]-6.75459113579489[/C][/ROW]
[ROW][C]28[/C][C]-12[/C][C]-3.89121423270845[/C][C]-8.10878576729155[/C][/ROW]
[ROW][C]29[/C][C]-16[/C][C]-6.63225794455716[/C][C]-9.36774205544284[/C][/ROW]
[ROW][C]30[/C][C]-19[/C][C]-11.5081704552055[/C][C]-7.49182954479448[/C][/ROW]
[ROW][C]31[/C][C]-30[/C][C]-25.1558309394689[/C][C]-4.84416906053114[/C][/ROW]
[ROW][C]32[/C][C]-26[/C][C]-10.5089354434341[/C][C]-15.4910645565659[/C][/ROW]
[ROW][C]33[/C][C]-22[/C][C]-10.3799931193988[/C][C]-11.6200068806012[/C][/ROW]
[ROW][C]34[/C][C]-31[/C][C]-3.65231869615293[/C][C]-27.3476813038471[/C][/ROW]
[ROW][C]35[/C][C]-33[/C][C]-48.4812763724968[/C][C]15.4812763724968[/C][/ROW]
[ROW][C]36[/C][C]-31[/C][C]-24.1211338919418[/C][C]-6.87886610805816[/C][/ROW]
[ROW][C]37[/C][C]-27[/C][C]-45.7663962636422[/C][C]18.7663962636422[/C][/ROW]
[ROW][C]38[/C][C]-29[/C][C]-37.4293358287856[/C][C]8.42933582878565[/C][/ROW]
[ROW][C]39[/C][C]-33[/C][C]-27.2495274105779[/C][C]-5.75047258942211[/C][/ROW]
[ROW][C]40[/C][C]-27[/C][C]-30.3306610686564[/C][C]3.33066106865641[/C][/ROW]
[ROW][C]41[/C][C]-22[/C][C]-34.0085209518031[/C][C]12.0085209518031[/C][/ROW]
[ROW][C]42[/C][C]-23[/C][C]-39.0771732085202[/C][C]16.0771732085202[/C][/ROW]
[ROW][C]43[/C][C]-23[/C][C]-65.0270385705439[/C][C]42.0270385705439[/C][/ROW]
[ROW][C]44[/C][C]-15[/C][C]-25.249999622997[/C][C]10.249999622997[/C][/ROW]
[ROW][C]45[/C][C]-15[/C][C]-16.018320053055[/C][C]1.01832005305496[/C][/ROW]
[ROW][C]46[/C][C]-24[/C][C]-5.23658767731425[/C][C]-18.7634123226857[/C][/ROW]
[ROW][C]47[/C][C]-18[/C][C]-31.3920163815946[/C][C]13.3920163815946[/C][/ROW]
[ROW][C]48[/C][C]-14[/C][C]-16.383809630405[/C][C]2.38380963040503[/C][/ROW]
[ROW][C]49[/C][C]-7[/C][C]-24.705972197112[/C][C]17.705972197112[/C][/ROW]
[ROW][C]50[/C][C]-12[/C][C]-18.6531714059386[/C][C]6.65317140593861[/C][/ROW]
[ROW][C]51[/C][C]-12[/C][C]-13.6058418745259[/C][C]1.60584187452589[/C][/ROW]
[ROW][C]52[/C][C]-15[/C][C]-12.9184878124498[/C][C]-2.08151218755024[/C][/ROW]
[ROW][C]53[/C][C]-16[/C][C]-14.473531802793[/C][C]-1.526468197207[/C][/ROW]
[ROW][C]54[/C][C]-17[/C][C]-18.0924284084286[/C][C]1.09242840842865[/C][/ROW]
[ROW][C]55[/C][C]-13[/C][C]-30.6954192391936[/C][C]17.6954192391936[/C][/ROW]
[ROW][C]56[/C][C]-8[/C][C]-12.3770212953547[/C][C]4.37702129535466[/C][/ROW]
[ROW][C]57[/C][C]-13[/C][C]-8.09553607931732[/C][C]-4.90446392068268[/C][/ROW]
[ROW][C]58[/C][C]-13[/C][C]-3.85002376961532[/C][C]-9.14997623038468[/C][/ROW]
[ROW][C]59[/C][C]-11[/C][C]-13.7832882887028[/C][C]2.78328828870284[/C][/ROW]
[ROW][C]60[/C][C]-16[/C][C]-7.80319221803678[/C][C]-8.19680778196322[/C][/ROW]
[ROW][C]61[/C][C]-34[/C][C]-13.6194236024414[/C][C]-20.3805763975586[/C][/ROW]
[ROW][C]62[/C][C]-35[/C][C]-18.9854488460509[/C][C]-16.0145511539491[/C][/ROW]
[ROW][C]63[/C][C]-38[/C][C]-19.6616797623935[/C][C]-18.3383202376065[/C][/ROW]
[ROW][C]64[/C][C]-32[/C][C]-25.5153614736846[/C][C]-6.48463852631536[/C][/ROW]
[ROW][C]65[/C][C]-37[/C][C]-29.8262413653936[/C][C]-7.17375863460638[/C][/ROW]
[ROW][C]66[/C][C]-39[/C][C]-38.7755297205332[/C][C]-0.224470279466765[/C][/ROW]
[ROW][C]67[/C][C]-31[/C][C]-62.9609158094112[/C][C]31.9609158094112[/C][/ROW]
[ROW][C]68[/C][C]-30[/C][C]-28.3149024680874[/C][C]-1.68509753191257[/C][/ROW]
[ROW][C]69[/C][C]-29[/C][C]-24.9849972577928[/C][C]-4.01500274220718[/C][/ROW]
[ROW][C]70[/C][C]-36[/C][C]-12.7099576921541[/C][C]-23.2900423078459[/C][/ROW]
[ROW][C]71[/C][C]-41[/C][C]-34.3455412601667[/C][C]-6.65445873983329[/C][/ROW]
[ROW][C]72[/C][C]-42[/C][C]-25.9259675749501[/C][C]-16.0740324250499[/C][/ROW]
[ROW][C]73[/C][C]-33[/C][C]-44.073747869455[/C][C]11.073747869455[/C][/ROW]
[ROW][C]74[/C][C]-43[/C][C]-40.148675764488[/C][C]-2.85132423551196[/C][/ROW]
[ROW][C]75[/C][C]-41[/C][C]-35.473859138336[/C][C]-5.526140861664[/C][/ROW]
[ROW][C]76[/C][C]-34[/C][C]-36.2711239066832[/C][C]2.27112390668324[/C][/ROW]
[ROW][C]77[/C][C]-32[/C][C]-39.2962549724567[/C][C]7.29625497245668[/C][/ROW]
[ROW][C]78[/C][C]-36[/C][C]-44.5144811060828[/C][C]8.5144811060828[/C][/ROW]
[ROW][C]79[/C][C]-37[/C][C]-62.8939478889457[/C][C]25.8939478889457[/C][/ROW]
[ROW][C]80[/C][C]-30[/C][C]-32.1557380251748[/C][C]2.15573802517483[/C][/ROW]
[ROW][C]81[/C][C]-32[/C][C]-27.9094839272204[/C][C]-4.09051607277961[/C][/ROW]
[ROW][C]82[/C][C]-30[/C][C]-16.3660661913846[/C][C]-13.6339338086154[/C][/ROW]
[ROW][C]83[/C][C]-21[/C][C]-31.6611732583445[/C][C]10.6611732583445[/C][/ROW]
[ROW][C]84[/C][C]-19[/C][C]-21.6622533908933[/C][C]2.6622533908933[/C][/ROW]
[ROW][C]85[/C][C]-6[/C][C]-27.129107425146[/C][C]21.129107425146[/C][/ROW]
[ROW][C]86[/C][C]-11[/C][C]-21.7913276040989[/C][C]10.7913276040989[/C][/ROW]
[ROW][C]87[/C][C]-11[/C][C]-16.2606118659983[/C][C]5.26061186599831[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=285291&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=285291&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
13153.1793507010976311.8206492989024
14125.09248263765556.9075173623445
15116.75394391690654.2460560830935
16129.822020579754732.17797942024527
171413.88638474993770.113615250062296
181820.6955786371283-2.69557863712835
191547.4541778593089-32.4541778593089
201615.68184776343480.318152236565185
21-116.1342381321913-17.1342381321913
22-55.86059029101266-10.8605902910127
23-61.67943355364188-7.67943355364188
24-5-0.193847922502815-4.80615207749718
25-2-3.124015103221351.12401510322135
26-9-1.23377561594877-7.76622438405123
27-9-2.24540886420511-6.75459113579489
28-12-3.89121423270845-8.10878576729155
29-16-6.63225794455716-9.36774205544284
30-19-11.5081704552055-7.49182954479448
31-30-25.1558309394689-4.84416906053114
32-26-10.5089354434341-15.4910645565659
33-22-10.3799931193988-11.6200068806012
34-31-3.65231869615293-27.3476813038471
35-33-48.481276372496815.4812763724968
36-31-24.1211338919418-6.87886610805816
37-27-45.766396263642218.7663962636422
38-29-37.42933582878568.42933582878565
39-33-27.2495274105779-5.75047258942211
40-27-30.33066106865643.33066106865641
41-22-34.008520951803112.0085209518031
42-23-39.077173208520216.0771732085202
43-23-65.027038570543942.0270385705439
44-15-25.24999962299710.249999622997
45-15-16.0183200530551.01832005305496
46-24-5.23658767731425-18.7634123226857
47-18-31.392016381594613.3920163815946
48-14-16.3838096304052.38380963040503
49-7-24.70597219711217.705972197112
50-12-18.65317140593866.65317140593861
51-12-13.60584187452591.60584187452589
52-15-12.9184878124498-2.08151218755024
53-16-14.473531802793-1.526468197207
54-17-18.09242840842861.09242840842865
55-13-30.695419239193617.6954192391936
56-8-12.37702129535474.37702129535466
57-13-8.09553607931732-4.90446392068268
58-13-3.85002376961532-9.14997623038468
59-11-13.78328828870282.78328828870284
60-16-7.80319221803678-8.19680778196322
61-34-13.6194236024414-20.3805763975586
62-35-18.9854488460509-16.0145511539491
63-38-19.6616797623935-18.3383202376065
64-32-25.5153614736846-6.48463852631536
65-37-29.8262413653936-7.17375863460638
66-39-38.7755297205332-0.224470279466765
67-31-62.960915809411231.9609158094112
68-30-28.3149024680874-1.68509753191257
69-29-24.9849972577928-4.01500274220718
70-36-12.7099576921541-23.2900423078459
71-41-34.3455412601667-6.65445873983329
72-42-25.9259675749501-16.0740324250499
73-33-44.07374786945511.073747869455
74-43-40.148675764488-2.85132423551196
75-41-35.473859138336-5.526140861664
76-34-36.27112390668322.27112390668324
77-32-39.29625497245677.29625497245668
78-36-44.51448110608288.5144811060828
79-37-62.893947888945725.8939478889457
80-30-32.15573802517482.15573802517483
81-32-27.9094839272204-4.09051607277961
82-30-16.3660661913846-13.6339338086154
83-21-31.661173258344510.6611732583445
84-19-21.66225339089332.6622533908933
85-6-27.12910742514621.129107425146
86-11-21.791327604098910.7913276040989
87-11-16.26061186599835.26061186599831







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
88-13.7542555652172-24.0447701266223-3.4637410038122
89-14.3587124000146-26.96869100018-1.74873379984932
90-16.4710973821013-32.2511281068893-0.691066657313291
91-22.6690996756717-45.1729652744376-0.165234076905836
92-13.2458135521326-29.94954036914463.45791326487929
93-11.5669633048975-28.78251284828185.64858623848676
94-6.7138848510802-20.77727296005557.34950325789508
95-8.68584983552664-28.011578053100610.6398783820474
96-6.34251858643271-23.795446200412211.1104090275468
97-6.69787109670824-27.56271698762914.1669747942125
98-6.70211607045419-30.603522188037117.1992900471287
99-5.4865995849671-29.931418368367318.9582191984331

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
88 & -13.7542555652172 & -24.0447701266223 & -3.4637410038122 \tabularnewline
89 & -14.3587124000146 & -26.96869100018 & -1.74873379984932 \tabularnewline
90 & -16.4710973821013 & -32.2511281068893 & -0.691066657313291 \tabularnewline
91 & -22.6690996756717 & -45.1729652744376 & -0.165234076905836 \tabularnewline
92 & -13.2458135521326 & -29.9495403691446 & 3.45791326487929 \tabularnewline
93 & -11.5669633048975 & -28.7825128482818 & 5.64858623848676 \tabularnewline
94 & -6.7138848510802 & -20.7772729600555 & 7.34950325789508 \tabularnewline
95 & -8.68584983552664 & -28.0115780531006 & 10.6398783820474 \tabularnewline
96 & -6.34251858643271 & -23.7954462004122 & 11.1104090275468 \tabularnewline
97 & -6.69787109670824 & -27.562716987629 & 14.1669747942125 \tabularnewline
98 & -6.70211607045419 & -30.6035221880371 & 17.1992900471287 \tabularnewline
99 & -5.4865995849671 & -29.9314183683673 & 18.9582191984331 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=285291&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]88[/C][C]-13.7542555652172[/C][C]-24.0447701266223[/C][C]-3.4637410038122[/C][/ROW]
[ROW][C]89[/C][C]-14.3587124000146[/C][C]-26.96869100018[/C][C]-1.74873379984932[/C][/ROW]
[ROW][C]90[/C][C]-16.4710973821013[/C][C]-32.2511281068893[/C][C]-0.691066657313291[/C][/ROW]
[ROW][C]91[/C][C]-22.6690996756717[/C][C]-45.1729652744376[/C][C]-0.165234076905836[/C][/ROW]
[ROW][C]92[/C][C]-13.2458135521326[/C][C]-29.9495403691446[/C][C]3.45791326487929[/C][/ROW]
[ROW][C]93[/C][C]-11.5669633048975[/C][C]-28.7825128482818[/C][C]5.64858623848676[/C][/ROW]
[ROW][C]94[/C][C]-6.7138848510802[/C][C]-20.7772729600555[/C][C]7.34950325789508[/C][/ROW]
[ROW][C]95[/C][C]-8.68584983552664[/C][C]-28.0115780531006[/C][C]10.6398783820474[/C][/ROW]
[ROW][C]96[/C][C]-6.34251858643271[/C][C]-23.7954462004122[/C][C]11.1104090275468[/C][/ROW]
[ROW][C]97[/C][C]-6.69787109670824[/C][C]-27.562716987629[/C][C]14.1669747942125[/C][/ROW]
[ROW][C]98[/C][C]-6.70211607045419[/C][C]-30.6035221880371[/C][C]17.1992900471287[/C][/ROW]
[ROW][C]99[/C][C]-5.4865995849671[/C][C]-29.9314183683673[/C][C]18.9582191984331[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=285291&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=285291&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
88-13.7542555652172-24.0447701266223-3.4637410038122
89-14.3587124000146-26.96869100018-1.74873379984932
90-16.4710973821013-32.2511281068893-0.691066657313291
91-22.6690996756717-45.1729652744376-0.165234076905836
92-13.2458135521326-29.94954036914463.45791326487929
93-11.5669633048975-28.78251284828185.64858623848676
94-6.7138848510802-20.77727296005557.34950325789508
95-8.68584983552664-28.011578053100610.6398783820474
96-6.34251858643271-23.795446200412211.1104090275468
97-6.69787109670824-27.56271698762914.1669747942125
98-6.70211607045419-30.603522188037117.1992900471287
99-5.4865995849671-29.931418368367318.9582191984331



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