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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, 10 Aug 2011 13:17:49 -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/10/t1312996690y1h9pzoxhswpux1.htm/, Retrieved Tue, 14 May 2024 12:17:53 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=123543, Retrieved Tue, 14 May 2024 12:17:53 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywordsVan Boxel Dieter
Estimated Impact240
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [Tijdreeks B - Sta...] [2011-08-10 17:17:49] [f91e4cd4d3d1892f3fcf702e4827e40c] [Current]
- RM      [Exponential Smoothing] [Tijdreeks B - Sta...] [2011-08-18 17:50:56] [74be16979710d4c4e7c6647856088456]
- R P     [Exponential Smoothing] [Tijdreeks B - sta...] [2011-08-18 17:53:55] [74be16979710d4c4e7c6647856088456]
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Dataseries X:
500
510
590
490
540
530
550
510
390
480
530
690
570
460
540
510
520
520
580
480
410
530
540
670
570
400
510
570
470
640
650
500
340
450
600
680
630
480
400
520
470
610
670
500
290
470
660
650
570
500
400
500
340
530
680
480
340
460
630
650
550
470
240
430
390
570
700
620
280
480
560
560
560
550
140
380
390
500
750
680
280
360
590
580
490
610
170
320
440
510
770
660
300
350
580
620
490
640
150
290
370
560
780
690
310
280
590
590




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'Gwilym Jenkins' @ jenkins.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 & 'Gwilym Jenkins' @ jenkins.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=123543&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]'Gwilym Jenkins' @ jenkins.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=123543&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=123543&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'Gwilym Jenkins' @ jenkins.wessa.net







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha6.61069613518961e-05
betaFALSE
gammaFALSE

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 6.61069613518961e-05 \tabularnewline
beta & FALSE \tabularnewline
gamma & FALSE \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=123543&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]6.61069613518961e-05[/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=123543&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=123543&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
alpha6.61069613518961e-05
betaFALSE
gammaFALSE







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
251050010
3590500.00066106961389.9993389303865
4490500.006610652434-10.0066106524339
5540500.0059491458139.9940508541898
6530500.00859303098429.9914069690157
7550500.01057567176649.9894243282343
8510500.0138803207089.98611967929224
9390500.014540472735-110.014540472735
10480500.00726774576-20.0072677457603
11530500.00594512608529.9940548739154
12690500.007927941911189.992072058089
13570500.02048774047669.9795122595243
14460500.025113873388-40.0251138733881
15540500.02246793473239.9775320652678
16510500.0251107278999.97488927210065
17520500.02577013751919.9742298624811
18520500.0270905731619.9729094268395
19580500.02841092151279.971589078488
20480500.03369760026-20.0336976002605
21410500.032373233387-90.0323732333875
22530500.0264214667729.9735785332303
23540500.02840292896739.9715970710326
24670500.03104532979169.96895467021
25570500.04228146090869.9577185390925
26400500.046906153103-100.046906153103
27510500.0402923561459.95970764385521
28570500.04095076215369.9590492378469
29470500.045575542317-30.0455755423173
30640500.043589320616139.956410679384
31650500.052841413648149.947158586352
32500500.062753964665-0.0627539646653759
33340500.062749816191-160.062749816191
34450500.052168554175-50.0521685541755
35600500.04885975740399.9511402425968
36680500.055467223568179.944532776432
37630500.067362809842129.932637190158
38480500.075952261667-20.0759522616672
39400500.074625101467-100.074625101467
40520500.06800947209319.931990527907
41470500.06932711542-30.0693271154205
42610500.067339323575109.932660676425
43670500.074606637726169.925393362274
44500500.085839889137-0.0858398891372758
45290500.085834214523-210.085834214523
46470500.0719460784-30.0719460784001
47660500.069958113423159.930041886577
48650500.080530602521149.919469397479
49570500.0904413230969.9095586769097
50500500.095062831584-0.0950628315838458
51400500.095056547269-100.095056547269
52500500.088439567234-0.0884395672342748
53340500.088433720763-160.088433720763
54530500.07785076086229.9221492391376
55680500.079828823226179.920171176774
56480500.091722799028-20.0917227990281
57340500.090394596286-160.090394596286
58460500.079811506757-40.0798115067572
59630500.077161952207129.922838047793
60650500.08575075624149.91424924376
61550500.09566113172149.9043388682787
62470500.098960155922-30.0989601559222
63240500.096970405126-260.096970405126
64430500.079776184756-70.0797761847561
65390500.0751434237-110.0751434237
66570500.06786669044869.9321333095518
67700500.072489691282199.927510308718
68620500.085706291479119.914293708521
69280500.093633461059-220.093633461059
70480500.079083739738-20.0790837397379
71560500.07775637252559.9222436274748
72560500.08171764996959.9182823500312
73560500.08567866554459.9143213344556
74550500.08963941926949.9103605807308
75140500.092938841547-360.092938841547
76380500.069134191556-120.069134191556
77390500.061196785943-110.061196785943
78500500.05392097466-0.0539209746602864
79750500.053917410109249.946082589891
80680500.07044058613179.92955941387
81280500.082335182561-220.082335182561
82360500.067786208134-140.067786208134
83590500.05852675240589.9414732475951
84580500.06447250990179.9355274900992
85490500.069756804727-10.0697568047273
86610500.069091123703109.930908876297
87170500.076358322048-330.076358322048
88320500.054537976985-180.054537976985
89440500.042635118602-60.0426351186017
90510500.0386658824429.96133411755756
91770500.039324395972269.960675604028
92660500.057170675921159.942829324079
93300500.067744010357-200.067744010357
94350500.054518139736-150.054518139736
95580500.04459849150579.9554015084951
96620500.049884100142119.950115899858
97490500.057813637818-10.0578136378182
98640500.057148746321139.942851253679
99150500.06639994298-350.06639994298
100290500.043258117008-210.043258117008
101370500.029372795462-130.029372795462
102560500.0207769487459.9792230512601
103780500.02474199292279.97525800708
104690500.043250306481189.956749693519
105310500.055807769991-190.055807769991
106280500.043243758052-220.043243758052
107590500.02869736784189.9713026321587
108590500.03464509726789.9653549027328

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
2 & 510 & 500 & 10 \tabularnewline
3 & 590 & 500.000661069613 & 89.9993389303865 \tabularnewline
4 & 490 & 500.006610652434 & -10.0066106524339 \tabularnewline
5 & 540 & 500.00594914581 & 39.9940508541898 \tabularnewline
6 & 530 & 500.008593030984 & 29.9914069690157 \tabularnewline
7 & 550 & 500.010575671766 & 49.9894243282343 \tabularnewline
8 & 510 & 500.013880320708 & 9.98611967929224 \tabularnewline
9 & 390 & 500.014540472735 & -110.014540472735 \tabularnewline
10 & 480 & 500.00726774576 & -20.0072677457603 \tabularnewline
11 & 530 & 500.005945126085 & 29.9940548739154 \tabularnewline
12 & 690 & 500.007927941911 & 189.992072058089 \tabularnewline
13 & 570 & 500.020487740476 & 69.9795122595243 \tabularnewline
14 & 460 & 500.025113873388 & -40.0251138733881 \tabularnewline
15 & 540 & 500.022467934732 & 39.9775320652678 \tabularnewline
16 & 510 & 500.025110727899 & 9.97488927210065 \tabularnewline
17 & 520 & 500.025770137519 & 19.9742298624811 \tabularnewline
18 & 520 & 500.02709057316 & 19.9729094268395 \tabularnewline
19 & 580 & 500.028410921512 & 79.971589078488 \tabularnewline
20 & 480 & 500.03369760026 & -20.0336976002605 \tabularnewline
21 & 410 & 500.032373233387 & -90.0323732333875 \tabularnewline
22 & 530 & 500.02642146677 & 29.9735785332303 \tabularnewline
23 & 540 & 500.028402928967 & 39.9715970710326 \tabularnewline
24 & 670 & 500.03104532979 & 169.96895467021 \tabularnewline
25 & 570 & 500.042281460908 & 69.9577185390925 \tabularnewline
26 & 400 & 500.046906153103 & -100.046906153103 \tabularnewline
27 & 510 & 500.040292356145 & 9.95970764385521 \tabularnewline
28 & 570 & 500.040950762153 & 69.9590492378469 \tabularnewline
29 & 470 & 500.045575542317 & -30.0455755423173 \tabularnewline
30 & 640 & 500.043589320616 & 139.956410679384 \tabularnewline
31 & 650 & 500.052841413648 & 149.947158586352 \tabularnewline
32 & 500 & 500.062753964665 & -0.0627539646653759 \tabularnewline
33 & 340 & 500.062749816191 & -160.062749816191 \tabularnewline
34 & 450 & 500.052168554175 & -50.0521685541755 \tabularnewline
35 & 600 & 500.048859757403 & 99.9511402425968 \tabularnewline
36 & 680 & 500.055467223568 & 179.944532776432 \tabularnewline
37 & 630 & 500.067362809842 & 129.932637190158 \tabularnewline
38 & 480 & 500.075952261667 & -20.0759522616672 \tabularnewline
39 & 400 & 500.074625101467 & -100.074625101467 \tabularnewline
40 & 520 & 500.068009472093 & 19.931990527907 \tabularnewline
41 & 470 & 500.06932711542 & -30.0693271154205 \tabularnewline
42 & 610 & 500.067339323575 & 109.932660676425 \tabularnewline
43 & 670 & 500.074606637726 & 169.925393362274 \tabularnewline
44 & 500 & 500.085839889137 & -0.0858398891372758 \tabularnewline
45 & 290 & 500.085834214523 & -210.085834214523 \tabularnewline
46 & 470 & 500.0719460784 & -30.0719460784001 \tabularnewline
47 & 660 & 500.069958113423 & 159.930041886577 \tabularnewline
48 & 650 & 500.080530602521 & 149.919469397479 \tabularnewline
49 & 570 & 500.09044132309 & 69.9095586769097 \tabularnewline
50 & 500 & 500.095062831584 & -0.0950628315838458 \tabularnewline
51 & 400 & 500.095056547269 & -100.095056547269 \tabularnewline
52 & 500 & 500.088439567234 & -0.0884395672342748 \tabularnewline
53 & 340 & 500.088433720763 & -160.088433720763 \tabularnewline
54 & 530 & 500.077850760862 & 29.9221492391376 \tabularnewline
55 & 680 & 500.079828823226 & 179.920171176774 \tabularnewline
56 & 480 & 500.091722799028 & -20.0917227990281 \tabularnewline
57 & 340 & 500.090394596286 & -160.090394596286 \tabularnewline
58 & 460 & 500.079811506757 & -40.0798115067572 \tabularnewline
59 & 630 & 500.077161952207 & 129.922838047793 \tabularnewline
60 & 650 & 500.08575075624 & 149.91424924376 \tabularnewline
61 & 550 & 500.095661131721 & 49.9043388682787 \tabularnewline
62 & 470 & 500.098960155922 & -30.0989601559222 \tabularnewline
63 & 240 & 500.096970405126 & -260.096970405126 \tabularnewline
64 & 430 & 500.079776184756 & -70.0797761847561 \tabularnewline
65 & 390 & 500.0751434237 & -110.0751434237 \tabularnewline
66 & 570 & 500.067866690448 & 69.9321333095518 \tabularnewline
67 & 700 & 500.072489691282 & 199.927510308718 \tabularnewline
68 & 620 & 500.085706291479 & 119.914293708521 \tabularnewline
69 & 280 & 500.093633461059 & -220.093633461059 \tabularnewline
70 & 480 & 500.079083739738 & -20.0790837397379 \tabularnewline
71 & 560 & 500.077756372525 & 59.9222436274748 \tabularnewline
72 & 560 & 500.081717649969 & 59.9182823500312 \tabularnewline
73 & 560 & 500.085678665544 & 59.9143213344556 \tabularnewline
74 & 550 & 500.089639419269 & 49.9103605807308 \tabularnewline
75 & 140 & 500.092938841547 & -360.092938841547 \tabularnewline
76 & 380 & 500.069134191556 & -120.069134191556 \tabularnewline
77 & 390 & 500.061196785943 & -110.061196785943 \tabularnewline
78 & 500 & 500.05392097466 & -0.0539209746602864 \tabularnewline
79 & 750 & 500.053917410109 & 249.946082589891 \tabularnewline
80 & 680 & 500.07044058613 & 179.92955941387 \tabularnewline
81 & 280 & 500.082335182561 & -220.082335182561 \tabularnewline
82 & 360 & 500.067786208134 & -140.067786208134 \tabularnewline
83 & 590 & 500.058526752405 & 89.9414732475951 \tabularnewline
84 & 580 & 500.064472509901 & 79.9355274900992 \tabularnewline
85 & 490 & 500.069756804727 & -10.0697568047273 \tabularnewline
86 & 610 & 500.069091123703 & 109.930908876297 \tabularnewline
87 & 170 & 500.076358322048 & -330.076358322048 \tabularnewline
88 & 320 & 500.054537976985 & -180.054537976985 \tabularnewline
89 & 440 & 500.042635118602 & -60.0426351186017 \tabularnewline
90 & 510 & 500.038665882442 & 9.96133411755756 \tabularnewline
91 & 770 & 500.039324395972 & 269.960675604028 \tabularnewline
92 & 660 & 500.057170675921 & 159.942829324079 \tabularnewline
93 & 300 & 500.067744010357 & -200.067744010357 \tabularnewline
94 & 350 & 500.054518139736 & -150.054518139736 \tabularnewline
95 & 580 & 500.044598491505 & 79.9554015084951 \tabularnewline
96 & 620 & 500.049884100142 & 119.950115899858 \tabularnewline
97 & 490 & 500.057813637818 & -10.0578136378182 \tabularnewline
98 & 640 & 500.057148746321 & 139.942851253679 \tabularnewline
99 & 150 & 500.06639994298 & -350.06639994298 \tabularnewline
100 & 290 & 500.043258117008 & -210.043258117008 \tabularnewline
101 & 370 & 500.029372795462 & -130.029372795462 \tabularnewline
102 & 560 & 500.02077694874 & 59.9792230512601 \tabularnewline
103 & 780 & 500.02474199292 & 279.97525800708 \tabularnewline
104 & 690 & 500.043250306481 & 189.956749693519 \tabularnewline
105 & 310 & 500.055807769991 & -190.055807769991 \tabularnewline
106 & 280 & 500.043243758052 & -220.043243758052 \tabularnewline
107 & 590 & 500.028697367841 & 89.9713026321587 \tabularnewline
108 & 590 & 500.034645097267 & 89.9653549027328 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=123543&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]510[/C][C]500[/C][C]10[/C][/ROW]
[ROW][C]3[/C][C]590[/C][C]500.000661069613[/C][C]89.9993389303865[/C][/ROW]
[ROW][C]4[/C][C]490[/C][C]500.006610652434[/C][C]-10.0066106524339[/C][/ROW]
[ROW][C]5[/C][C]540[/C][C]500.00594914581[/C][C]39.9940508541898[/C][/ROW]
[ROW][C]6[/C][C]530[/C][C]500.008593030984[/C][C]29.9914069690157[/C][/ROW]
[ROW][C]7[/C][C]550[/C][C]500.010575671766[/C][C]49.9894243282343[/C][/ROW]
[ROW][C]8[/C][C]510[/C][C]500.013880320708[/C][C]9.98611967929224[/C][/ROW]
[ROW][C]9[/C][C]390[/C][C]500.014540472735[/C][C]-110.014540472735[/C][/ROW]
[ROW][C]10[/C][C]480[/C][C]500.00726774576[/C][C]-20.0072677457603[/C][/ROW]
[ROW][C]11[/C][C]530[/C][C]500.005945126085[/C][C]29.9940548739154[/C][/ROW]
[ROW][C]12[/C][C]690[/C][C]500.007927941911[/C][C]189.992072058089[/C][/ROW]
[ROW][C]13[/C][C]570[/C][C]500.020487740476[/C][C]69.9795122595243[/C][/ROW]
[ROW][C]14[/C][C]460[/C][C]500.025113873388[/C][C]-40.0251138733881[/C][/ROW]
[ROW][C]15[/C][C]540[/C][C]500.022467934732[/C][C]39.9775320652678[/C][/ROW]
[ROW][C]16[/C][C]510[/C][C]500.025110727899[/C][C]9.97488927210065[/C][/ROW]
[ROW][C]17[/C][C]520[/C][C]500.025770137519[/C][C]19.9742298624811[/C][/ROW]
[ROW][C]18[/C][C]520[/C][C]500.02709057316[/C][C]19.9729094268395[/C][/ROW]
[ROW][C]19[/C][C]580[/C][C]500.028410921512[/C][C]79.971589078488[/C][/ROW]
[ROW][C]20[/C][C]480[/C][C]500.03369760026[/C][C]-20.0336976002605[/C][/ROW]
[ROW][C]21[/C][C]410[/C][C]500.032373233387[/C][C]-90.0323732333875[/C][/ROW]
[ROW][C]22[/C][C]530[/C][C]500.02642146677[/C][C]29.9735785332303[/C][/ROW]
[ROW][C]23[/C][C]540[/C][C]500.028402928967[/C][C]39.9715970710326[/C][/ROW]
[ROW][C]24[/C][C]670[/C][C]500.03104532979[/C][C]169.96895467021[/C][/ROW]
[ROW][C]25[/C][C]570[/C][C]500.042281460908[/C][C]69.9577185390925[/C][/ROW]
[ROW][C]26[/C][C]400[/C][C]500.046906153103[/C][C]-100.046906153103[/C][/ROW]
[ROW][C]27[/C][C]510[/C][C]500.040292356145[/C][C]9.95970764385521[/C][/ROW]
[ROW][C]28[/C][C]570[/C][C]500.040950762153[/C][C]69.9590492378469[/C][/ROW]
[ROW][C]29[/C][C]470[/C][C]500.045575542317[/C][C]-30.0455755423173[/C][/ROW]
[ROW][C]30[/C][C]640[/C][C]500.043589320616[/C][C]139.956410679384[/C][/ROW]
[ROW][C]31[/C][C]650[/C][C]500.052841413648[/C][C]149.947158586352[/C][/ROW]
[ROW][C]32[/C][C]500[/C][C]500.062753964665[/C][C]-0.0627539646653759[/C][/ROW]
[ROW][C]33[/C][C]340[/C][C]500.062749816191[/C][C]-160.062749816191[/C][/ROW]
[ROW][C]34[/C][C]450[/C][C]500.052168554175[/C][C]-50.0521685541755[/C][/ROW]
[ROW][C]35[/C][C]600[/C][C]500.048859757403[/C][C]99.9511402425968[/C][/ROW]
[ROW][C]36[/C][C]680[/C][C]500.055467223568[/C][C]179.944532776432[/C][/ROW]
[ROW][C]37[/C][C]630[/C][C]500.067362809842[/C][C]129.932637190158[/C][/ROW]
[ROW][C]38[/C][C]480[/C][C]500.075952261667[/C][C]-20.0759522616672[/C][/ROW]
[ROW][C]39[/C][C]400[/C][C]500.074625101467[/C][C]-100.074625101467[/C][/ROW]
[ROW][C]40[/C][C]520[/C][C]500.068009472093[/C][C]19.931990527907[/C][/ROW]
[ROW][C]41[/C][C]470[/C][C]500.06932711542[/C][C]-30.0693271154205[/C][/ROW]
[ROW][C]42[/C][C]610[/C][C]500.067339323575[/C][C]109.932660676425[/C][/ROW]
[ROW][C]43[/C][C]670[/C][C]500.074606637726[/C][C]169.925393362274[/C][/ROW]
[ROW][C]44[/C][C]500[/C][C]500.085839889137[/C][C]-0.0858398891372758[/C][/ROW]
[ROW][C]45[/C][C]290[/C][C]500.085834214523[/C][C]-210.085834214523[/C][/ROW]
[ROW][C]46[/C][C]470[/C][C]500.0719460784[/C][C]-30.0719460784001[/C][/ROW]
[ROW][C]47[/C][C]660[/C][C]500.069958113423[/C][C]159.930041886577[/C][/ROW]
[ROW][C]48[/C][C]650[/C][C]500.080530602521[/C][C]149.919469397479[/C][/ROW]
[ROW][C]49[/C][C]570[/C][C]500.09044132309[/C][C]69.9095586769097[/C][/ROW]
[ROW][C]50[/C][C]500[/C][C]500.095062831584[/C][C]-0.0950628315838458[/C][/ROW]
[ROW][C]51[/C][C]400[/C][C]500.095056547269[/C][C]-100.095056547269[/C][/ROW]
[ROW][C]52[/C][C]500[/C][C]500.088439567234[/C][C]-0.0884395672342748[/C][/ROW]
[ROW][C]53[/C][C]340[/C][C]500.088433720763[/C][C]-160.088433720763[/C][/ROW]
[ROW][C]54[/C][C]530[/C][C]500.077850760862[/C][C]29.9221492391376[/C][/ROW]
[ROW][C]55[/C][C]680[/C][C]500.079828823226[/C][C]179.920171176774[/C][/ROW]
[ROW][C]56[/C][C]480[/C][C]500.091722799028[/C][C]-20.0917227990281[/C][/ROW]
[ROW][C]57[/C][C]340[/C][C]500.090394596286[/C][C]-160.090394596286[/C][/ROW]
[ROW][C]58[/C][C]460[/C][C]500.079811506757[/C][C]-40.0798115067572[/C][/ROW]
[ROW][C]59[/C][C]630[/C][C]500.077161952207[/C][C]129.922838047793[/C][/ROW]
[ROW][C]60[/C][C]650[/C][C]500.08575075624[/C][C]149.91424924376[/C][/ROW]
[ROW][C]61[/C][C]550[/C][C]500.095661131721[/C][C]49.9043388682787[/C][/ROW]
[ROW][C]62[/C][C]470[/C][C]500.098960155922[/C][C]-30.0989601559222[/C][/ROW]
[ROW][C]63[/C][C]240[/C][C]500.096970405126[/C][C]-260.096970405126[/C][/ROW]
[ROW][C]64[/C][C]430[/C][C]500.079776184756[/C][C]-70.0797761847561[/C][/ROW]
[ROW][C]65[/C][C]390[/C][C]500.0751434237[/C][C]-110.0751434237[/C][/ROW]
[ROW][C]66[/C][C]570[/C][C]500.067866690448[/C][C]69.9321333095518[/C][/ROW]
[ROW][C]67[/C][C]700[/C][C]500.072489691282[/C][C]199.927510308718[/C][/ROW]
[ROW][C]68[/C][C]620[/C][C]500.085706291479[/C][C]119.914293708521[/C][/ROW]
[ROW][C]69[/C][C]280[/C][C]500.093633461059[/C][C]-220.093633461059[/C][/ROW]
[ROW][C]70[/C][C]480[/C][C]500.079083739738[/C][C]-20.0790837397379[/C][/ROW]
[ROW][C]71[/C][C]560[/C][C]500.077756372525[/C][C]59.9222436274748[/C][/ROW]
[ROW][C]72[/C][C]560[/C][C]500.081717649969[/C][C]59.9182823500312[/C][/ROW]
[ROW][C]73[/C][C]560[/C][C]500.085678665544[/C][C]59.9143213344556[/C][/ROW]
[ROW][C]74[/C][C]550[/C][C]500.089639419269[/C][C]49.9103605807308[/C][/ROW]
[ROW][C]75[/C][C]140[/C][C]500.092938841547[/C][C]-360.092938841547[/C][/ROW]
[ROW][C]76[/C][C]380[/C][C]500.069134191556[/C][C]-120.069134191556[/C][/ROW]
[ROW][C]77[/C][C]390[/C][C]500.061196785943[/C][C]-110.061196785943[/C][/ROW]
[ROW][C]78[/C][C]500[/C][C]500.05392097466[/C][C]-0.0539209746602864[/C][/ROW]
[ROW][C]79[/C][C]750[/C][C]500.053917410109[/C][C]249.946082589891[/C][/ROW]
[ROW][C]80[/C][C]680[/C][C]500.07044058613[/C][C]179.92955941387[/C][/ROW]
[ROW][C]81[/C][C]280[/C][C]500.082335182561[/C][C]-220.082335182561[/C][/ROW]
[ROW][C]82[/C][C]360[/C][C]500.067786208134[/C][C]-140.067786208134[/C][/ROW]
[ROW][C]83[/C][C]590[/C][C]500.058526752405[/C][C]89.9414732475951[/C][/ROW]
[ROW][C]84[/C][C]580[/C][C]500.064472509901[/C][C]79.9355274900992[/C][/ROW]
[ROW][C]85[/C][C]490[/C][C]500.069756804727[/C][C]-10.0697568047273[/C][/ROW]
[ROW][C]86[/C][C]610[/C][C]500.069091123703[/C][C]109.930908876297[/C][/ROW]
[ROW][C]87[/C][C]170[/C][C]500.076358322048[/C][C]-330.076358322048[/C][/ROW]
[ROW][C]88[/C][C]320[/C][C]500.054537976985[/C][C]-180.054537976985[/C][/ROW]
[ROW][C]89[/C][C]440[/C][C]500.042635118602[/C][C]-60.0426351186017[/C][/ROW]
[ROW][C]90[/C][C]510[/C][C]500.038665882442[/C][C]9.96133411755756[/C][/ROW]
[ROW][C]91[/C][C]770[/C][C]500.039324395972[/C][C]269.960675604028[/C][/ROW]
[ROW][C]92[/C][C]660[/C][C]500.057170675921[/C][C]159.942829324079[/C][/ROW]
[ROW][C]93[/C][C]300[/C][C]500.067744010357[/C][C]-200.067744010357[/C][/ROW]
[ROW][C]94[/C][C]350[/C][C]500.054518139736[/C][C]-150.054518139736[/C][/ROW]
[ROW][C]95[/C][C]580[/C][C]500.044598491505[/C][C]79.9554015084951[/C][/ROW]
[ROW][C]96[/C][C]620[/C][C]500.049884100142[/C][C]119.950115899858[/C][/ROW]
[ROW][C]97[/C][C]490[/C][C]500.057813637818[/C][C]-10.0578136378182[/C][/ROW]
[ROW][C]98[/C][C]640[/C][C]500.057148746321[/C][C]139.942851253679[/C][/ROW]
[ROW][C]99[/C][C]150[/C][C]500.06639994298[/C][C]-350.06639994298[/C][/ROW]
[ROW][C]100[/C][C]290[/C][C]500.043258117008[/C][C]-210.043258117008[/C][/ROW]
[ROW][C]101[/C][C]370[/C][C]500.029372795462[/C][C]-130.029372795462[/C][/ROW]
[ROW][C]102[/C][C]560[/C][C]500.02077694874[/C][C]59.9792230512601[/C][/ROW]
[ROW][C]103[/C][C]780[/C][C]500.02474199292[/C][C]279.97525800708[/C][/ROW]
[ROW][C]104[/C][C]690[/C][C]500.043250306481[/C][C]189.956749693519[/C][/ROW]
[ROW][C]105[/C][C]310[/C][C]500.055807769991[/C][C]-190.055807769991[/C][/ROW]
[ROW][C]106[/C][C]280[/C][C]500.043243758052[/C][C]-220.043243758052[/C][/ROW]
[ROW][C]107[/C][C]590[/C][C]500.028697367841[/C][C]89.9713026321587[/C][/ROW]
[ROW][C]108[/C][C]590[/C][C]500.034645097267[/C][C]89.9653549027328[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=123543&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=123543&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
251050010
3590500.00066106961389.9993389303865
4490500.006610652434-10.0066106524339
5540500.0059491458139.9940508541898
6530500.00859303098429.9914069690157
7550500.01057567176649.9894243282343
8510500.0138803207089.98611967929224
9390500.014540472735-110.014540472735
10480500.00726774576-20.0072677457603
11530500.00594512608529.9940548739154
12690500.007927941911189.992072058089
13570500.02048774047669.9795122595243
14460500.025113873388-40.0251138733881
15540500.02246793473239.9775320652678
16510500.0251107278999.97488927210065
17520500.02577013751919.9742298624811
18520500.0270905731619.9729094268395
19580500.02841092151279.971589078488
20480500.03369760026-20.0336976002605
21410500.032373233387-90.0323732333875
22530500.0264214667729.9735785332303
23540500.02840292896739.9715970710326
24670500.03104532979169.96895467021
25570500.04228146090869.9577185390925
26400500.046906153103-100.046906153103
27510500.0402923561459.95970764385521
28570500.04095076215369.9590492378469
29470500.045575542317-30.0455755423173
30640500.043589320616139.956410679384
31650500.052841413648149.947158586352
32500500.062753964665-0.0627539646653759
33340500.062749816191-160.062749816191
34450500.052168554175-50.0521685541755
35600500.04885975740399.9511402425968
36680500.055467223568179.944532776432
37630500.067362809842129.932637190158
38480500.075952261667-20.0759522616672
39400500.074625101467-100.074625101467
40520500.06800947209319.931990527907
41470500.06932711542-30.0693271154205
42610500.067339323575109.932660676425
43670500.074606637726169.925393362274
44500500.085839889137-0.0858398891372758
45290500.085834214523-210.085834214523
46470500.0719460784-30.0719460784001
47660500.069958113423159.930041886577
48650500.080530602521149.919469397479
49570500.0904413230969.9095586769097
50500500.095062831584-0.0950628315838458
51400500.095056547269-100.095056547269
52500500.088439567234-0.0884395672342748
53340500.088433720763-160.088433720763
54530500.07785076086229.9221492391376
55680500.079828823226179.920171176774
56480500.091722799028-20.0917227990281
57340500.090394596286-160.090394596286
58460500.079811506757-40.0798115067572
59630500.077161952207129.922838047793
60650500.08575075624149.91424924376
61550500.09566113172149.9043388682787
62470500.098960155922-30.0989601559222
63240500.096970405126-260.096970405126
64430500.079776184756-70.0797761847561
65390500.0751434237-110.0751434237
66570500.06786669044869.9321333095518
67700500.072489691282199.927510308718
68620500.085706291479119.914293708521
69280500.093633461059-220.093633461059
70480500.079083739738-20.0790837397379
71560500.07775637252559.9222436274748
72560500.08171764996959.9182823500312
73560500.08567866554459.9143213344556
74550500.08963941926949.9103605807308
75140500.092938841547-360.092938841547
76380500.069134191556-120.069134191556
77390500.061196785943-110.061196785943
78500500.05392097466-0.0539209746602864
79750500.053917410109249.946082589891
80680500.07044058613179.92955941387
81280500.082335182561-220.082335182561
82360500.067786208134-140.067786208134
83590500.05852675240589.9414732475951
84580500.06447250990179.9355274900992
85490500.069756804727-10.0697568047273
86610500.069091123703109.930908876297
87170500.076358322048-330.076358322048
88320500.054537976985-180.054537976985
89440500.042635118602-60.0426351186017
90510500.0386658824429.96133411755756
91770500.039324395972269.960675604028
92660500.057170675921159.942829324079
93300500.067744010357-200.067744010357
94350500.054518139736-150.054518139736
95580500.04459849150579.9554015084951
96620500.049884100142119.950115899858
97490500.057813637818-10.0578136378182
98640500.057148746321139.942851253679
99150500.06639994298-350.06639994298
100290500.043258117008-210.043258117008
101370500.029372795462-130.029372795462
102560500.0207769487459.9792230512601
103780500.02474199292279.97525800708
104690500.043250306481189.956749693519
105310500.055807769991-190.055807769991
106280500.043243758052-220.043243758052
107590500.02869736784189.9713026321587
108590500.03464509726789.9653549027328







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
109500.040592433507240.721633337073759.359551529941
110500.040592433507240.721632770444759.35955209657
111500.040592433507240.721632203815759.359552663198
112500.040592433507240.721631637186759.359553229827
113500.040592433507240.721631070558759.359553796456
114500.040592433507240.721630503929759.359554363085
115500.040592433507240.7216299373759.359554929714
116500.040592433507240.721629370671759.359555496343
117500.040592433507240.721628804042759.359556062971
118500.040592433507240.721628237413759.3595566296
119500.040592433507240.721627670785759.359557196229
120500.040592433507240.721627104156759.359557762858

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
109 & 500.040592433507 & 240.721633337073 & 759.359551529941 \tabularnewline
110 & 500.040592433507 & 240.721632770444 & 759.35955209657 \tabularnewline
111 & 500.040592433507 & 240.721632203815 & 759.359552663198 \tabularnewline
112 & 500.040592433507 & 240.721631637186 & 759.359553229827 \tabularnewline
113 & 500.040592433507 & 240.721631070558 & 759.359553796456 \tabularnewline
114 & 500.040592433507 & 240.721630503929 & 759.359554363085 \tabularnewline
115 & 500.040592433507 & 240.7216299373 & 759.359554929714 \tabularnewline
116 & 500.040592433507 & 240.721629370671 & 759.359555496343 \tabularnewline
117 & 500.040592433507 & 240.721628804042 & 759.359556062971 \tabularnewline
118 & 500.040592433507 & 240.721628237413 & 759.3595566296 \tabularnewline
119 & 500.040592433507 & 240.721627670785 & 759.359557196229 \tabularnewline
120 & 500.040592433507 & 240.721627104156 & 759.359557762858 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=123543&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]500.040592433507[/C][C]240.721633337073[/C][C]759.359551529941[/C][/ROW]
[ROW][C]110[/C][C]500.040592433507[/C][C]240.721632770444[/C][C]759.35955209657[/C][/ROW]
[ROW][C]111[/C][C]500.040592433507[/C][C]240.721632203815[/C][C]759.359552663198[/C][/ROW]
[ROW][C]112[/C][C]500.040592433507[/C][C]240.721631637186[/C][C]759.359553229827[/C][/ROW]
[ROW][C]113[/C][C]500.040592433507[/C][C]240.721631070558[/C][C]759.359553796456[/C][/ROW]
[ROW][C]114[/C][C]500.040592433507[/C][C]240.721630503929[/C][C]759.359554363085[/C][/ROW]
[ROW][C]115[/C][C]500.040592433507[/C][C]240.7216299373[/C][C]759.359554929714[/C][/ROW]
[ROW][C]116[/C][C]500.040592433507[/C][C]240.721629370671[/C][C]759.359555496343[/C][/ROW]
[ROW][C]117[/C][C]500.040592433507[/C][C]240.721628804042[/C][C]759.359556062971[/C][/ROW]
[ROW][C]118[/C][C]500.040592433507[/C][C]240.721628237413[/C][C]759.3595566296[/C][/ROW]
[ROW][C]119[/C][C]500.040592433507[/C][C]240.721627670785[/C][C]759.359557196229[/C][/ROW]
[ROW][C]120[/C][C]500.040592433507[/C][C]240.721627104156[/C][C]759.359557762858[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=123543&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=123543&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
109500.040592433507240.721633337073759.359551529941
110500.040592433507240.721632770444759.35955209657
111500.040592433507240.721632203815759.359552663198
112500.040592433507240.721631637186759.359553229827
113500.040592433507240.721631070558759.359553796456
114500.040592433507240.721630503929759.359554363085
115500.040592433507240.7216299373759.359554929714
116500.040592433507240.721629370671759.359555496343
117500.040592433507240.721628804042759.359556062971
118500.040592433507240.721628237413759.3595566296
119500.040592433507240.721627670785759.359557196229
120500.040592433507240.721627104156759.359557762858



Parameters (Session):
par1 = 12 ; par2 = Single ; par3 = additive ;
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')