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of Irreproducible Research!

Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationWed, 17 Aug 2011 13:19:50 -0400
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2011/Aug/17/t13136017233clt5dqs1f2wmtg.htm/, Retrieved Wed, 15 May 2024 15:38:45 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=123973, Retrieved Wed, 15 May 2024 15:38:45 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywordsMorel sarah
Estimated Impact123
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [exponential smoot...] [2011-08-17 17:19:50] [d41d8cd98f00b204e9800998ecf8427e] [Current]
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Dataseries X:
240
150
290
210
240
240
310
310
190
230
260
320
270
250
240
250
230
230
240
300
190
270
300
330
230
260
300
330
190
260
240
270
170
230
270
320
190
300
310
360
170
280
270
260
280
300
320
370
210
310
290
450
190
290
280
310
340
220
390
410
250
310
280
450
210
390
300
310
370
250
440
360
290
300
340
600
220
410
360
250
410
290
470
350
330
250
270
580
260
450
320
240
420
380
400
370
300
310
280
560
280
480
320
170
420
310
470
420




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'AstonUniversity' @ aston.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 & 'AstonUniversity' @ aston.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=123973&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]'AstonUniversity' @ aston.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=123973&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=123973&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'AstonUniversity' @ aston.wessa.net







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.27720363493774
beta0.406306720105381
gammaFALSE

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.27720363493774 \tabularnewline
beta & 0.406306720105381 \tabularnewline
gamma & FALSE \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=123973&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]0.27720363493774[/C][/ROW]
[ROW][C]beta[/C][C]0.406306720105381[/C][/ROW]
[ROW][C]gamma[/C][C]FALSE[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=123973&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=123973&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
alpha0.27720363493774
beta0.406306720105381
gammaFALSE







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
329060230
421059.661666969634150.338333030366
524054.1733915946251185.826608405375
624079.4521902545936160.547809745406
7310115.806065640339194.193934359661
8310183.358773583708126.641226416292
9190246.449188637821-56.4491886378211
10230252.428419951363-22.4284199513629
11260265.312225804011-5.31222580401146
12320282.34238849349337.6576115065068
13270315.525311754015-45.5253117540147
14250320.522124129784-70.5221241297843
15240310.646843589285-70.6468435892846
16250292.780057582143-42.7800575821425
17230277.819740911038-47.8197409110376
18230256.076482643072-26.0764826430718
19240237.423548192722.57645180728022
20300227.00349631701772.9965036829832
21190244.325713083665-54.3257130836646
22270220.23505980296849.7649401970324
23300230.60372424534369.3962757546568
24330254.23034796241175.7696520375887
25230288.157607908274-58.1576079082744
26260278.409470665166-18.4094706651664
27300277.60620839496222.393791605038
28330290.63596476728439.3640352327163
29190312.803493826723-122.803493826723
30260276.186273728623-16.186273728623
31240267.300679439148-27.3006794391484
32270252.25926415935617.7407358406444
33170251.701626668278-81.7016266682783
34230214.37617514523215.6238248547678
35270205.7893992580964.2106007419102
36320217.903074936711102.096925063289
37190252.018123443132-62.0181234431317
38300233.65480133543566.345198664565
39310258.34669851165551.6533014883454
40360284.78364422230475.2163557776962
41170326.223949796933-156.223949796933
42280285.91270484159-5.91270484159043
43270286.602337189087-16.6023371890871
44260282.458848341571-22.4588483415714
45280274.1623799699265.83762003007382
46300274.36728487782725.6327151221734
47320282.94646710623137.0535328937694
48370298.86486981800871.1351301819923
49210332.242743533996-122.242743533996
50310298.24740424307311.7525957569267
51290302.719751399259-12.7197513992592
52450298.975653187772151.024346812228
53190357.6318410309-167.6318410309
54290309.075051390889-19.0750513908887
55280299.550326523607-19.5503265236069
56310287.69190625629822.3080937437017
57340289.94934613935850.0506538606418
58220305.534314644068-85.5343146440682
59390273.900932862848116.099067137152
60410311.2372605047798.7627394952297
61250354.891512800045-104.891512800045
62310330.278166499448-20.2781664994476
63280326.836023554062-46.8360235540616
64450310.756818828342139.243181171658
65210361.942363721341-151.942363721341
66390315.29699432907974.7030056709206
67300339.892322270522-39.8923222705224
68310328.228348481538-18.2283484815381
69370320.5166535583249.4833464416805
70250337.148181046125-87.1481810461254
71440306.08947900547133.91052099453
72360351.3913544731088.60864552689225
73290362.928683757228-72.9286837572283
74300343.649633228646-43.6496332286457
75340327.57059685099412.4294031490062
76600328.436793145315271.563206854685
77220431.721904203193-211.721904203193
78410377.19245127150132.8075487284987
79360394.142555903417-34.1425559034165
80250388.688382353072-138.688382353072
81410338.63329483522771.3667051647732
82290354.844251686697-64.8442516866965
83470325.993647585015144.006352414985
84350371.256582328503-21.2565823285033
85330368.313908356038-38.3139083560378
86250356.327597613456-106.327597613456
87270313.5119995928-43.5119995928001
88580283.208370226216296.791629773784
89260380.66569604126-120.66569604126
90450348.811792598218101.188207401782
91320389.853395028857-69.8533950288567
92240375.614076634124-135.614076634124
93420327.87148553429292.128514465708
94380353.63637543673626.3636245632642
95400364.14032592484435.8596740751555
96370381.315480178083-11.3154801780834
97300384.139051059012-84.1390510590117
98310357.299107327701-47.2991073277005
99280335.344045654606-55.3440456546062
100560304.925514591472255.074485408528
101280389.285091387042-109.285091387042
102480360.334122044491119.665877955509
103320408.327125526216-88.3271255262162
104170388.715454776673-218.715454776673
105420308.32580921139111.67419078861
106310332.099204916791-22.0992049167909
107470316.301102261019153.698897738981
108420366.54593337512253.4540666248783

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
3 & 290 & 60 & 230 \tabularnewline
4 & 210 & 59.661666969634 & 150.338333030366 \tabularnewline
5 & 240 & 54.1733915946251 & 185.826608405375 \tabularnewline
6 & 240 & 79.4521902545936 & 160.547809745406 \tabularnewline
7 & 310 & 115.806065640339 & 194.193934359661 \tabularnewline
8 & 310 & 183.358773583708 & 126.641226416292 \tabularnewline
9 & 190 & 246.449188637821 & -56.4491886378211 \tabularnewline
10 & 230 & 252.428419951363 & -22.4284199513629 \tabularnewline
11 & 260 & 265.312225804011 & -5.31222580401146 \tabularnewline
12 & 320 & 282.342388493493 & 37.6576115065068 \tabularnewline
13 & 270 & 315.525311754015 & -45.5253117540147 \tabularnewline
14 & 250 & 320.522124129784 & -70.5221241297843 \tabularnewline
15 & 240 & 310.646843589285 & -70.6468435892846 \tabularnewline
16 & 250 & 292.780057582143 & -42.7800575821425 \tabularnewline
17 & 230 & 277.819740911038 & -47.8197409110376 \tabularnewline
18 & 230 & 256.076482643072 & -26.0764826430718 \tabularnewline
19 & 240 & 237.42354819272 & 2.57645180728022 \tabularnewline
20 & 300 & 227.003496317017 & 72.9965036829832 \tabularnewline
21 & 190 & 244.325713083665 & -54.3257130836646 \tabularnewline
22 & 270 & 220.235059802968 & 49.7649401970324 \tabularnewline
23 & 300 & 230.603724245343 & 69.3962757546568 \tabularnewline
24 & 330 & 254.230347962411 & 75.7696520375887 \tabularnewline
25 & 230 & 288.157607908274 & -58.1576079082744 \tabularnewline
26 & 260 & 278.409470665166 & -18.4094706651664 \tabularnewline
27 & 300 & 277.606208394962 & 22.393791605038 \tabularnewline
28 & 330 & 290.635964767284 & 39.3640352327163 \tabularnewline
29 & 190 & 312.803493826723 & -122.803493826723 \tabularnewline
30 & 260 & 276.186273728623 & -16.186273728623 \tabularnewline
31 & 240 & 267.300679439148 & -27.3006794391484 \tabularnewline
32 & 270 & 252.259264159356 & 17.7407358406444 \tabularnewline
33 & 170 & 251.701626668278 & -81.7016266682783 \tabularnewline
34 & 230 & 214.376175145232 & 15.6238248547678 \tabularnewline
35 & 270 & 205.78939925809 & 64.2106007419102 \tabularnewline
36 & 320 & 217.903074936711 & 102.096925063289 \tabularnewline
37 & 190 & 252.018123443132 & -62.0181234431317 \tabularnewline
38 & 300 & 233.654801335435 & 66.345198664565 \tabularnewline
39 & 310 & 258.346698511655 & 51.6533014883454 \tabularnewline
40 & 360 & 284.783644222304 & 75.2163557776962 \tabularnewline
41 & 170 & 326.223949796933 & -156.223949796933 \tabularnewline
42 & 280 & 285.91270484159 & -5.91270484159043 \tabularnewline
43 & 270 & 286.602337189087 & -16.6023371890871 \tabularnewline
44 & 260 & 282.458848341571 & -22.4588483415714 \tabularnewline
45 & 280 & 274.162379969926 & 5.83762003007382 \tabularnewline
46 & 300 & 274.367284877827 & 25.6327151221734 \tabularnewline
47 & 320 & 282.946467106231 & 37.0535328937694 \tabularnewline
48 & 370 & 298.864869818008 & 71.1351301819923 \tabularnewline
49 & 210 & 332.242743533996 & -122.242743533996 \tabularnewline
50 & 310 & 298.247404243073 & 11.7525957569267 \tabularnewline
51 & 290 & 302.719751399259 & -12.7197513992592 \tabularnewline
52 & 450 & 298.975653187772 & 151.024346812228 \tabularnewline
53 & 190 & 357.6318410309 & -167.6318410309 \tabularnewline
54 & 290 & 309.075051390889 & -19.0750513908887 \tabularnewline
55 & 280 & 299.550326523607 & -19.5503265236069 \tabularnewline
56 & 310 & 287.691906256298 & 22.3080937437017 \tabularnewline
57 & 340 & 289.949346139358 & 50.0506538606418 \tabularnewline
58 & 220 & 305.534314644068 & -85.5343146440682 \tabularnewline
59 & 390 & 273.900932862848 & 116.099067137152 \tabularnewline
60 & 410 & 311.23726050477 & 98.7627394952297 \tabularnewline
61 & 250 & 354.891512800045 & -104.891512800045 \tabularnewline
62 & 310 & 330.278166499448 & -20.2781664994476 \tabularnewline
63 & 280 & 326.836023554062 & -46.8360235540616 \tabularnewline
64 & 450 & 310.756818828342 & 139.243181171658 \tabularnewline
65 & 210 & 361.942363721341 & -151.942363721341 \tabularnewline
66 & 390 & 315.296994329079 & 74.7030056709206 \tabularnewline
67 & 300 & 339.892322270522 & -39.8923222705224 \tabularnewline
68 & 310 & 328.228348481538 & -18.2283484815381 \tabularnewline
69 & 370 & 320.51665355832 & 49.4833464416805 \tabularnewline
70 & 250 & 337.148181046125 & -87.1481810461254 \tabularnewline
71 & 440 & 306.08947900547 & 133.91052099453 \tabularnewline
72 & 360 & 351.391354473108 & 8.60864552689225 \tabularnewline
73 & 290 & 362.928683757228 & -72.9286837572283 \tabularnewline
74 & 300 & 343.649633228646 & -43.6496332286457 \tabularnewline
75 & 340 & 327.570596850994 & 12.4294031490062 \tabularnewline
76 & 600 & 328.436793145315 & 271.563206854685 \tabularnewline
77 & 220 & 431.721904203193 & -211.721904203193 \tabularnewline
78 & 410 & 377.192451271501 & 32.8075487284987 \tabularnewline
79 & 360 & 394.142555903417 & -34.1425559034165 \tabularnewline
80 & 250 & 388.688382353072 & -138.688382353072 \tabularnewline
81 & 410 & 338.633294835227 & 71.3667051647732 \tabularnewline
82 & 290 & 354.844251686697 & -64.8442516866965 \tabularnewline
83 & 470 & 325.993647585015 & 144.006352414985 \tabularnewline
84 & 350 & 371.256582328503 & -21.2565823285033 \tabularnewline
85 & 330 & 368.313908356038 & -38.3139083560378 \tabularnewline
86 & 250 & 356.327597613456 & -106.327597613456 \tabularnewline
87 & 270 & 313.5119995928 & -43.5119995928001 \tabularnewline
88 & 580 & 283.208370226216 & 296.791629773784 \tabularnewline
89 & 260 & 380.66569604126 & -120.66569604126 \tabularnewline
90 & 450 & 348.811792598218 & 101.188207401782 \tabularnewline
91 & 320 & 389.853395028857 & -69.8533950288567 \tabularnewline
92 & 240 & 375.614076634124 & -135.614076634124 \tabularnewline
93 & 420 & 327.871485534292 & 92.128514465708 \tabularnewline
94 & 380 & 353.636375436736 & 26.3636245632642 \tabularnewline
95 & 400 & 364.140325924844 & 35.8596740751555 \tabularnewline
96 & 370 & 381.315480178083 & -11.3154801780834 \tabularnewline
97 & 300 & 384.139051059012 & -84.1390510590117 \tabularnewline
98 & 310 & 357.299107327701 & -47.2991073277005 \tabularnewline
99 & 280 & 335.344045654606 & -55.3440456546062 \tabularnewline
100 & 560 & 304.925514591472 & 255.074485408528 \tabularnewline
101 & 280 & 389.285091387042 & -109.285091387042 \tabularnewline
102 & 480 & 360.334122044491 & 119.665877955509 \tabularnewline
103 & 320 & 408.327125526216 & -88.3271255262162 \tabularnewline
104 & 170 & 388.715454776673 & -218.715454776673 \tabularnewline
105 & 420 & 308.32580921139 & 111.67419078861 \tabularnewline
106 & 310 & 332.099204916791 & -22.0992049167909 \tabularnewline
107 & 470 & 316.301102261019 & 153.698897738981 \tabularnewline
108 & 420 & 366.545933375122 & 53.4540666248783 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=123973&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]290[/C][C]60[/C][C]230[/C][/ROW]
[ROW][C]4[/C][C]210[/C][C]59.661666969634[/C][C]150.338333030366[/C][/ROW]
[ROW][C]5[/C][C]240[/C][C]54.1733915946251[/C][C]185.826608405375[/C][/ROW]
[ROW][C]6[/C][C]240[/C][C]79.4521902545936[/C][C]160.547809745406[/C][/ROW]
[ROW][C]7[/C][C]310[/C][C]115.806065640339[/C][C]194.193934359661[/C][/ROW]
[ROW][C]8[/C][C]310[/C][C]183.358773583708[/C][C]126.641226416292[/C][/ROW]
[ROW][C]9[/C][C]190[/C][C]246.449188637821[/C][C]-56.4491886378211[/C][/ROW]
[ROW][C]10[/C][C]230[/C][C]252.428419951363[/C][C]-22.4284199513629[/C][/ROW]
[ROW][C]11[/C][C]260[/C][C]265.312225804011[/C][C]-5.31222580401146[/C][/ROW]
[ROW][C]12[/C][C]320[/C][C]282.342388493493[/C][C]37.6576115065068[/C][/ROW]
[ROW][C]13[/C][C]270[/C][C]315.525311754015[/C][C]-45.5253117540147[/C][/ROW]
[ROW][C]14[/C][C]250[/C][C]320.522124129784[/C][C]-70.5221241297843[/C][/ROW]
[ROW][C]15[/C][C]240[/C][C]310.646843589285[/C][C]-70.6468435892846[/C][/ROW]
[ROW][C]16[/C][C]250[/C][C]292.780057582143[/C][C]-42.7800575821425[/C][/ROW]
[ROW][C]17[/C][C]230[/C][C]277.819740911038[/C][C]-47.8197409110376[/C][/ROW]
[ROW][C]18[/C][C]230[/C][C]256.076482643072[/C][C]-26.0764826430718[/C][/ROW]
[ROW][C]19[/C][C]240[/C][C]237.42354819272[/C][C]2.57645180728022[/C][/ROW]
[ROW][C]20[/C][C]300[/C][C]227.003496317017[/C][C]72.9965036829832[/C][/ROW]
[ROW][C]21[/C][C]190[/C][C]244.325713083665[/C][C]-54.3257130836646[/C][/ROW]
[ROW][C]22[/C][C]270[/C][C]220.235059802968[/C][C]49.7649401970324[/C][/ROW]
[ROW][C]23[/C][C]300[/C][C]230.603724245343[/C][C]69.3962757546568[/C][/ROW]
[ROW][C]24[/C][C]330[/C][C]254.230347962411[/C][C]75.7696520375887[/C][/ROW]
[ROW][C]25[/C][C]230[/C][C]288.157607908274[/C][C]-58.1576079082744[/C][/ROW]
[ROW][C]26[/C][C]260[/C][C]278.409470665166[/C][C]-18.4094706651664[/C][/ROW]
[ROW][C]27[/C][C]300[/C][C]277.606208394962[/C][C]22.393791605038[/C][/ROW]
[ROW][C]28[/C][C]330[/C][C]290.635964767284[/C][C]39.3640352327163[/C][/ROW]
[ROW][C]29[/C][C]190[/C][C]312.803493826723[/C][C]-122.803493826723[/C][/ROW]
[ROW][C]30[/C][C]260[/C][C]276.186273728623[/C][C]-16.186273728623[/C][/ROW]
[ROW][C]31[/C][C]240[/C][C]267.300679439148[/C][C]-27.3006794391484[/C][/ROW]
[ROW][C]32[/C][C]270[/C][C]252.259264159356[/C][C]17.7407358406444[/C][/ROW]
[ROW][C]33[/C][C]170[/C][C]251.701626668278[/C][C]-81.7016266682783[/C][/ROW]
[ROW][C]34[/C][C]230[/C][C]214.376175145232[/C][C]15.6238248547678[/C][/ROW]
[ROW][C]35[/C][C]270[/C][C]205.78939925809[/C][C]64.2106007419102[/C][/ROW]
[ROW][C]36[/C][C]320[/C][C]217.903074936711[/C][C]102.096925063289[/C][/ROW]
[ROW][C]37[/C][C]190[/C][C]252.018123443132[/C][C]-62.0181234431317[/C][/ROW]
[ROW][C]38[/C][C]300[/C][C]233.654801335435[/C][C]66.345198664565[/C][/ROW]
[ROW][C]39[/C][C]310[/C][C]258.346698511655[/C][C]51.6533014883454[/C][/ROW]
[ROW][C]40[/C][C]360[/C][C]284.783644222304[/C][C]75.2163557776962[/C][/ROW]
[ROW][C]41[/C][C]170[/C][C]326.223949796933[/C][C]-156.223949796933[/C][/ROW]
[ROW][C]42[/C][C]280[/C][C]285.91270484159[/C][C]-5.91270484159043[/C][/ROW]
[ROW][C]43[/C][C]270[/C][C]286.602337189087[/C][C]-16.6023371890871[/C][/ROW]
[ROW][C]44[/C][C]260[/C][C]282.458848341571[/C][C]-22.4588483415714[/C][/ROW]
[ROW][C]45[/C][C]280[/C][C]274.162379969926[/C][C]5.83762003007382[/C][/ROW]
[ROW][C]46[/C][C]300[/C][C]274.367284877827[/C][C]25.6327151221734[/C][/ROW]
[ROW][C]47[/C][C]320[/C][C]282.946467106231[/C][C]37.0535328937694[/C][/ROW]
[ROW][C]48[/C][C]370[/C][C]298.864869818008[/C][C]71.1351301819923[/C][/ROW]
[ROW][C]49[/C][C]210[/C][C]332.242743533996[/C][C]-122.242743533996[/C][/ROW]
[ROW][C]50[/C][C]310[/C][C]298.247404243073[/C][C]11.7525957569267[/C][/ROW]
[ROW][C]51[/C][C]290[/C][C]302.719751399259[/C][C]-12.7197513992592[/C][/ROW]
[ROW][C]52[/C][C]450[/C][C]298.975653187772[/C][C]151.024346812228[/C][/ROW]
[ROW][C]53[/C][C]190[/C][C]357.6318410309[/C][C]-167.6318410309[/C][/ROW]
[ROW][C]54[/C][C]290[/C][C]309.075051390889[/C][C]-19.0750513908887[/C][/ROW]
[ROW][C]55[/C][C]280[/C][C]299.550326523607[/C][C]-19.5503265236069[/C][/ROW]
[ROW][C]56[/C][C]310[/C][C]287.691906256298[/C][C]22.3080937437017[/C][/ROW]
[ROW][C]57[/C][C]340[/C][C]289.949346139358[/C][C]50.0506538606418[/C][/ROW]
[ROW][C]58[/C][C]220[/C][C]305.534314644068[/C][C]-85.5343146440682[/C][/ROW]
[ROW][C]59[/C][C]390[/C][C]273.900932862848[/C][C]116.099067137152[/C][/ROW]
[ROW][C]60[/C][C]410[/C][C]311.23726050477[/C][C]98.7627394952297[/C][/ROW]
[ROW][C]61[/C][C]250[/C][C]354.891512800045[/C][C]-104.891512800045[/C][/ROW]
[ROW][C]62[/C][C]310[/C][C]330.278166499448[/C][C]-20.2781664994476[/C][/ROW]
[ROW][C]63[/C][C]280[/C][C]326.836023554062[/C][C]-46.8360235540616[/C][/ROW]
[ROW][C]64[/C][C]450[/C][C]310.756818828342[/C][C]139.243181171658[/C][/ROW]
[ROW][C]65[/C][C]210[/C][C]361.942363721341[/C][C]-151.942363721341[/C][/ROW]
[ROW][C]66[/C][C]390[/C][C]315.296994329079[/C][C]74.7030056709206[/C][/ROW]
[ROW][C]67[/C][C]300[/C][C]339.892322270522[/C][C]-39.8923222705224[/C][/ROW]
[ROW][C]68[/C][C]310[/C][C]328.228348481538[/C][C]-18.2283484815381[/C][/ROW]
[ROW][C]69[/C][C]370[/C][C]320.51665355832[/C][C]49.4833464416805[/C][/ROW]
[ROW][C]70[/C][C]250[/C][C]337.148181046125[/C][C]-87.1481810461254[/C][/ROW]
[ROW][C]71[/C][C]440[/C][C]306.08947900547[/C][C]133.91052099453[/C][/ROW]
[ROW][C]72[/C][C]360[/C][C]351.391354473108[/C][C]8.60864552689225[/C][/ROW]
[ROW][C]73[/C][C]290[/C][C]362.928683757228[/C][C]-72.9286837572283[/C][/ROW]
[ROW][C]74[/C][C]300[/C][C]343.649633228646[/C][C]-43.6496332286457[/C][/ROW]
[ROW][C]75[/C][C]340[/C][C]327.570596850994[/C][C]12.4294031490062[/C][/ROW]
[ROW][C]76[/C][C]600[/C][C]328.436793145315[/C][C]271.563206854685[/C][/ROW]
[ROW][C]77[/C][C]220[/C][C]431.721904203193[/C][C]-211.721904203193[/C][/ROW]
[ROW][C]78[/C][C]410[/C][C]377.192451271501[/C][C]32.8075487284987[/C][/ROW]
[ROW][C]79[/C][C]360[/C][C]394.142555903417[/C][C]-34.1425559034165[/C][/ROW]
[ROW][C]80[/C][C]250[/C][C]388.688382353072[/C][C]-138.688382353072[/C][/ROW]
[ROW][C]81[/C][C]410[/C][C]338.633294835227[/C][C]71.3667051647732[/C][/ROW]
[ROW][C]82[/C][C]290[/C][C]354.844251686697[/C][C]-64.8442516866965[/C][/ROW]
[ROW][C]83[/C][C]470[/C][C]325.993647585015[/C][C]144.006352414985[/C][/ROW]
[ROW][C]84[/C][C]350[/C][C]371.256582328503[/C][C]-21.2565823285033[/C][/ROW]
[ROW][C]85[/C][C]330[/C][C]368.313908356038[/C][C]-38.3139083560378[/C][/ROW]
[ROW][C]86[/C][C]250[/C][C]356.327597613456[/C][C]-106.327597613456[/C][/ROW]
[ROW][C]87[/C][C]270[/C][C]313.5119995928[/C][C]-43.5119995928001[/C][/ROW]
[ROW][C]88[/C][C]580[/C][C]283.208370226216[/C][C]296.791629773784[/C][/ROW]
[ROW][C]89[/C][C]260[/C][C]380.66569604126[/C][C]-120.66569604126[/C][/ROW]
[ROW][C]90[/C][C]450[/C][C]348.811792598218[/C][C]101.188207401782[/C][/ROW]
[ROW][C]91[/C][C]320[/C][C]389.853395028857[/C][C]-69.8533950288567[/C][/ROW]
[ROW][C]92[/C][C]240[/C][C]375.614076634124[/C][C]-135.614076634124[/C][/ROW]
[ROW][C]93[/C][C]420[/C][C]327.871485534292[/C][C]92.128514465708[/C][/ROW]
[ROW][C]94[/C][C]380[/C][C]353.636375436736[/C][C]26.3636245632642[/C][/ROW]
[ROW][C]95[/C][C]400[/C][C]364.140325924844[/C][C]35.8596740751555[/C][/ROW]
[ROW][C]96[/C][C]370[/C][C]381.315480178083[/C][C]-11.3154801780834[/C][/ROW]
[ROW][C]97[/C][C]300[/C][C]384.139051059012[/C][C]-84.1390510590117[/C][/ROW]
[ROW][C]98[/C][C]310[/C][C]357.299107327701[/C][C]-47.2991073277005[/C][/ROW]
[ROW][C]99[/C][C]280[/C][C]335.344045654606[/C][C]-55.3440456546062[/C][/ROW]
[ROW][C]100[/C][C]560[/C][C]304.925514591472[/C][C]255.074485408528[/C][/ROW]
[ROW][C]101[/C][C]280[/C][C]389.285091387042[/C][C]-109.285091387042[/C][/ROW]
[ROW][C]102[/C][C]480[/C][C]360.334122044491[/C][C]119.665877955509[/C][/ROW]
[ROW][C]103[/C][C]320[/C][C]408.327125526216[/C][C]-88.3271255262162[/C][/ROW]
[ROW][C]104[/C][C]170[/C][C]388.715454776673[/C][C]-218.715454776673[/C][/ROW]
[ROW][C]105[/C][C]420[/C][C]308.32580921139[/C][C]111.67419078861[/C][/ROW]
[ROW][C]106[/C][C]310[/C][C]332.099204916791[/C][C]-22.0992049167909[/C][/ROW]
[ROW][C]107[/C][C]470[/C][C]316.301102261019[/C][C]153.698897738981[/C][/ROW]
[ROW][C]108[/C][C]420[/C][C]366.545933375122[/C][C]53.4540666248783[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=123973&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=123973&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
329060230
421059.661666969634150.338333030366
524054.1733915946251185.826608405375
624079.4521902545936160.547809745406
7310115.806065640339194.193934359661
8310183.358773583708126.641226416292
9190246.449188637821-56.4491886378211
10230252.428419951363-22.4284199513629
11260265.312225804011-5.31222580401146
12320282.34238849349337.6576115065068
13270315.525311754015-45.5253117540147
14250320.522124129784-70.5221241297843
15240310.646843589285-70.6468435892846
16250292.780057582143-42.7800575821425
17230277.819740911038-47.8197409110376
18230256.076482643072-26.0764826430718
19240237.423548192722.57645180728022
20300227.00349631701772.9965036829832
21190244.325713083665-54.3257130836646
22270220.23505980296849.7649401970324
23300230.60372424534369.3962757546568
24330254.23034796241175.7696520375887
25230288.157607908274-58.1576079082744
26260278.409470665166-18.4094706651664
27300277.60620839496222.393791605038
28330290.63596476728439.3640352327163
29190312.803493826723-122.803493826723
30260276.186273728623-16.186273728623
31240267.300679439148-27.3006794391484
32270252.25926415935617.7407358406444
33170251.701626668278-81.7016266682783
34230214.37617514523215.6238248547678
35270205.7893992580964.2106007419102
36320217.903074936711102.096925063289
37190252.018123443132-62.0181234431317
38300233.65480133543566.345198664565
39310258.34669851165551.6533014883454
40360284.78364422230475.2163557776962
41170326.223949796933-156.223949796933
42280285.91270484159-5.91270484159043
43270286.602337189087-16.6023371890871
44260282.458848341571-22.4588483415714
45280274.1623799699265.83762003007382
46300274.36728487782725.6327151221734
47320282.94646710623137.0535328937694
48370298.86486981800871.1351301819923
49210332.242743533996-122.242743533996
50310298.24740424307311.7525957569267
51290302.719751399259-12.7197513992592
52450298.975653187772151.024346812228
53190357.6318410309-167.6318410309
54290309.075051390889-19.0750513908887
55280299.550326523607-19.5503265236069
56310287.69190625629822.3080937437017
57340289.94934613935850.0506538606418
58220305.534314644068-85.5343146440682
59390273.900932862848116.099067137152
60410311.2372605047798.7627394952297
61250354.891512800045-104.891512800045
62310330.278166499448-20.2781664994476
63280326.836023554062-46.8360235540616
64450310.756818828342139.243181171658
65210361.942363721341-151.942363721341
66390315.29699432907974.7030056709206
67300339.892322270522-39.8923222705224
68310328.228348481538-18.2283484815381
69370320.5166535583249.4833464416805
70250337.148181046125-87.1481810461254
71440306.08947900547133.91052099453
72360351.3913544731088.60864552689225
73290362.928683757228-72.9286837572283
74300343.649633228646-43.6496332286457
75340327.57059685099412.4294031490062
76600328.436793145315271.563206854685
77220431.721904203193-211.721904203193
78410377.19245127150132.8075487284987
79360394.142555903417-34.1425559034165
80250388.688382353072-138.688382353072
81410338.63329483522771.3667051647732
82290354.844251686697-64.8442516866965
83470325.993647585015144.006352414985
84350371.256582328503-21.2565823285033
85330368.313908356038-38.3139083560378
86250356.327597613456-106.327597613456
87270313.5119995928-43.5119995928001
88580283.208370226216296.791629773784
89260380.66569604126-120.66569604126
90450348.811792598218101.188207401782
91320389.853395028857-69.8533950288567
92240375.614076634124-135.614076634124
93420327.87148553429292.128514465708
94380353.63637543673626.3636245632642
95400364.14032592484435.8596740751555
96370381.315480178083-11.3154801780834
97300384.139051059012-84.1390510590117
98310357.299107327701-47.2991073277005
99280335.344045654606-55.3440456546062
100560304.925514591472255.074485408528
101280389.285091387042-109.285091387042
102480360.334122044491119.665877955509
103320408.327125526216-88.3271255262162
104170388.715454776673-218.715454776673
105420308.32580921139111.67419078861
106310332.099204916791-22.0992049167909
107470316.301102261019153.698897738981
108420366.54593337512253.4540666248783







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
109395.023048393065199.248904830442590.797191955689
110408.682501840389198.55837450142618.806629179358
111422.341955287712190.331907629341654.352002946083
112436.001408735035174.602367493878697.400449976193
113449.660862182359151.958087535024747.363636829694
114463.320315629682123.182820595829803.457810663535
115476.97976907700689.0344343350689864.925103818942
116490.63922252432950.1581818497089931.120263198949
117504.2986759716527.074569188923651001.52278275438
118517.958129418976-39.80416920381561075.72042804177
119531.617582866299-90.15155346307621153.38671919567
120545.277036313622-143.7065971980621234.26066982531

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
109 & 395.023048393065 & 199.248904830442 & 590.797191955689 \tabularnewline
110 & 408.682501840389 & 198.55837450142 & 618.806629179358 \tabularnewline
111 & 422.341955287712 & 190.331907629341 & 654.352002946083 \tabularnewline
112 & 436.001408735035 & 174.602367493878 & 697.400449976193 \tabularnewline
113 & 449.660862182359 & 151.958087535024 & 747.363636829694 \tabularnewline
114 & 463.320315629682 & 123.182820595829 & 803.457810663535 \tabularnewline
115 & 476.979769077006 & 89.0344343350689 & 864.925103818942 \tabularnewline
116 & 490.639222524329 & 50.1581818497089 & 931.120263198949 \tabularnewline
117 & 504.298675971652 & 7.07456918892365 & 1001.52278275438 \tabularnewline
118 & 517.958129418976 & -39.8041692038156 & 1075.72042804177 \tabularnewline
119 & 531.617582866299 & -90.1515534630762 & 1153.38671919567 \tabularnewline
120 & 545.277036313622 & -143.706597198062 & 1234.26066982531 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=123973&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]109[/C][C]395.023048393065[/C][C]199.248904830442[/C][C]590.797191955689[/C][/ROW]
[ROW][C]110[/C][C]408.682501840389[/C][C]198.55837450142[/C][C]618.806629179358[/C][/ROW]
[ROW][C]111[/C][C]422.341955287712[/C][C]190.331907629341[/C][C]654.352002946083[/C][/ROW]
[ROW][C]112[/C][C]436.001408735035[/C][C]174.602367493878[/C][C]697.400449976193[/C][/ROW]
[ROW][C]113[/C][C]449.660862182359[/C][C]151.958087535024[/C][C]747.363636829694[/C][/ROW]
[ROW][C]114[/C][C]463.320315629682[/C][C]123.182820595829[/C][C]803.457810663535[/C][/ROW]
[ROW][C]115[/C][C]476.979769077006[/C][C]89.0344343350689[/C][C]864.925103818942[/C][/ROW]
[ROW][C]116[/C][C]490.639222524329[/C][C]50.1581818497089[/C][C]931.120263198949[/C][/ROW]
[ROW][C]117[/C][C]504.298675971652[/C][C]7.07456918892365[/C][C]1001.52278275438[/C][/ROW]
[ROW][C]118[/C][C]517.958129418976[/C][C]-39.8041692038156[/C][C]1075.72042804177[/C][/ROW]
[ROW][C]119[/C][C]531.617582866299[/C][C]-90.1515534630762[/C][C]1153.38671919567[/C][/ROW]
[ROW][C]120[/C][C]545.277036313622[/C][C]-143.706597198062[/C][C]1234.26066982531[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=123973&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=123973&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
109395.023048393065199.248904830442590.797191955689
110408.682501840389198.55837450142618.806629179358
111422.341955287712190.331907629341654.352002946083
112436.001408735035174.602367493878697.400449976193
113449.660862182359151.958087535024747.363636829694
114463.320315629682123.182820595829803.457810663535
115476.97976907700689.0344343350689864.925103818942
116490.63922252432950.1581818497089931.120263198949
117504.2986759716527.074569188923651001.52278275438
118517.958129418976-39.80416920381561075.72042804177
119531.617582866299-90.15155346307621153.38671919567
120545.277036313622-143.7065971980621234.26066982531



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')