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Author's title

Exponential Smoothing - Verkoop vrouwenkleding VS 2000-2008 - Amelie Barrat...

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationFri, 05 Jun 2009 06:24:42 -0600
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2009/Jun/05/t1244204767cfgt3fwjfecjit9.htm/, Retrieved Fri, 10 May 2024 00:03:45 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=41816, Retrieved Fri, 10 May 2024 00:03:45 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact129
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [Exponential Smoot...] [2009-06-05 12:24:42] [770bd392bad9be4bfacb32bbbd82a4eb] [Current]
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Dataseries X:
461683
731993
522673
572709
382812
942567
802385
272643
992660
672651
122826
493878
801948
742156
612673
662804
572750
202510
652313
492663
292397
382618
872790
913865
221989
842162
142783
112683
862759
392482
602262
542540
982375
112533
622742
883970
562056
322091
832619
82723
872811
562534
112447
342593
422622
682787
602944
84298
942258
722391
662901
3007
452988
12759
942577
52626
882755
22968
433067
904437
812315
32428
53073
403145
243133
313018
32720
922852
192947
693108
33335
944749
962536
292541
953227
193417
73378
433219
962953
632986
333186
733212
463421
495024
752596
22640
123421
243440
623653
413304
852981
613232
493203
253344
803665
574904
132570
132785
393406
333452
583642
893230
272991
373159
133072
653091
373307




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'Sir Ronald Aylmer Fisher' @ 193.190.124.24

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input & view raw input (R code)  \tabularnewline
Raw Output & view raw output of R engine  \tabularnewline
Computing time & 2 seconds \tabularnewline
R Server & 'Sir Ronald Aylmer Fisher' @ 193.190.124.24 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=41816&T=0

[TABLE]
[ROW][C]Summary of computational transaction[/C][/ROW]
[ROW][C]Raw Input[/C][C]view raw input (R code) [/C][/ROW]
[ROW][C]Raw Output[/C][C]view raw output of R engine [/C][/ROW]
[ROW][C]Computing time[/C][C]2 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Sir Ronald Aylmer Fisher' @ 193.190.124.24[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=41816&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=41816&T=0

As an alternative you can also use a QR Code:  

The GUIDs for individual cells are displayed in the table below:

Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'Sir Ronald Aylmer Fisher' @ 193.190.124.24







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.00263339025737825
beta0
gamma0

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.00263339025737825 \tabularnewline
beta & 0 \tabularnewline
gamma & 0 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=41816&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]0.00263339025737825[/C][/ROW]
[ROW][C]beta[/C][C]0[/C][/ROW]
[ROW][C]gamma[/C][C]0[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=41816&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=41816&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
alpha0.00263339025737825
beta0
gamma0







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
2731993461683270310
3522673462394.83172047260278.1682795281
4572709462553.567661552110155.432338448
5382812462843.649903869-80031.6499038692
6942567462632.895336730479934.10466327
7802385463896.749132134338488.250867866
8272643464788.120794207-192145.120794207
9992660464282.127705104528377.872294896
10672651465673.55284622206977.44715378
11122826466218.605239052-343392.605239052
12493878465314.3184979628563.6815020404
13801948465389.537818542336558.462181458
14742156466275.827593889275880.172406111
15612673467002.327752107145670.672247893
16662804467385.93548119195418.064518810
17572750467900.54750841104849.452491590
18202510468176.657035093-265666.657035093
19652313467477.053048746184835.946951254
20492663467963.79823066124699.2017693392
21292397468028.840867965-175631.840867965
22382618467566.333689338-84948.3336893381
23872790467342.63157502405447.36842498
24913865468410.33272491445454.66727509
25221989469583.388705816-247594.388705816
26842162468931.376054817373230.623945183
27142783469914.237943669-327131.237943669
28112683469052.773728784-356369.773728784
29862759468114.313038623394644.686961377
30392482469153.566512393-76671.5665123927
31602262468951.660356121133310.339643879
32542540469302.71850574773237.281494253
33982375469495.580849311512879.419150689
34112533470846.192514912-358313.192514912
35622742469902.614044653152839.385955347
36883970470305.099794572413664.900205428
37562056471394.44091259290661.559087408
38322091471633.188179012-149542.188179012
39832619471239.385237594361379.614762406
4082723472191.038794324-389468.038794324
41872811471165.417455403401645.582544597
42562534472223.10701939590310.8929806048
43112447472460.930845105-360013.930845105
44342593471512.873667097-128919.873667097
45422622471173.3773278-48551.3773278001
46682787471045.522603763211741.477396237
47602944471603.120547421131340.879452579
4884298471948.992339767-387650.992339767
49942258470928.155993276471329.844006724
50722391472169.351412495250221.648587505
51662901472828.282664071190072.717335929
523007473328.818306096-470321.818306096
53452988472090.277411937-19102.2774119367
5412759472039.973660706-459280.973660706
55942577470830.507619269471746.492380731
5652626472072.800236257-419446.800236257
57882755470968.233119026411786.766880974
5822968472052.628379048-449084.628379048
59433067470870.013293936-37803.0132939362
60904437470770.463207028433666.536792972
61812315471912.47643997340402.52356003
6232428472808.8891291-440380.8891291
6353073471649.194386132-418576.194386132
64403145470546.919913865-67401.9199138649
65243133470369.424354635-227236.424354635
66313018469771.022168618-156753.022168618
6732720469358.230287225-436638.230287225
68922852468208.391425587454643.608574413
69192947469405.645474987-276458.645474987
70693108468677.621971425224430.378028575
7133335469268.634742385-435933.634742385
72944749468120.651355791476628.348644209
73962536469375.799805501493160.200194499
74292541470674.48307202-178133.483072020
75953227470205.388093185483021.611906815
76193417471477.372500084-278060.372500084
7773378470745.131024179-397367.131024179
78433219469698.708292737-36479.7082927374
79962953469602.642984327493350.357015673
80632986470901.827007966162084.172992034
81333186471328.657889999-138142.657889999
82733212470964.874360583262247.125639417
83463421471655.473386267-8234.47338626737
84495024471633.78880427723390.2111957227
85752596471695.384358558280900.615641442
8622640472435.10530308-449795.10530308
87123421471250.619254958-347829.619254958
88243440470334.648124385-226894.648124385
89623653469737.145968563153915.854031437
90413304470142.466479025-56838.4664790252
91852981469992.788615155382988.211384845
92613232471001.346039707142230.653960293
93493203471375.89485814621827.1051418538
94253344471433.374144174-218089.374144174
95803665470859.059711065332805.940288935
96574904471735.467631819103168.532368181
97132570472007.150639825-339437.150639825
98132785471113.280154338-338328.280154338
99393406470222.329757584-76816.3297575843
100333452470020.042383193-136568.042383193
101583642469660.405430912113981.594569088
102893230469960.563451571423269.436548429
103272991471075.197062023-198084.197062023
104373159470553.56406734-97394.5640673396
105133072470297.086171203-337225.086171203
106653091469409.040914736183681.959085264
107373307469892.747196248-96585.7471962476

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
2 & 731993 & 461683 & 270310 \tabularnewline
3 & 522673 & 462394.831720472 & 60278.1682795281 \tabularnewline
4 & 572709 & 462553.567661552 & 110155.432338448 \tabularnewline
5 & 382812 & 462843.649903869 & -80031.6499038692 \tabularnewline
6 & 942567 & 462632.895336730 & 479934.10466327 \tabularnewline
7 & 802385 & 463896.749132134 & 338488.250867866 \tabularnewline
8 & 272643 & 464788.120794207 & -192145.120794207 \tabularnewline
9 & 992660 & 464282.127705104 & 528377.872294896 \tabularnewline
10 & 672651 & 465673.55284622 & 206977.44715378 \tabularnewline
11 & 122826 & 466218.605239052 & -343392.605239052 \tabularnewline
12 & 493878 & 465314.31849796 & 28563.6815020404 \tabularnewline
13 & 801948 & 465389.537818542 & 336558.462181458 \tabularnewline
14 & 742156 & 466275.827593889 & 275880.172406111 \tabularnewline
15 & 612673 & 467002.327752107 & 145670.672247893 \tabularnewline
16 & 662804 & 467385.93548119 & 195418.064518810 \tabularnewline
17 & 572750 & 467900.54750841 & 104849.452491590 \tabularnewline
18 & 202510 & 468176.657035093 & -265666.657035093 \tabularnewline
19 & 652313 & 467477.053048746 & 184835.946951254 \tabularnewline
20 & 492663 & 467963.798230661 & 24699.2017693392 \tabularnewline
21 & 292397 & 468028.840867965 & -175631.840867965 \tabularnewline
22 & 382618 & 467566.333689338 & -84948.3336893381 \tabularnewline
23 & 872790 & 467342.63157502 & 405447.36842498 \tabularnewline
24 & 913865 & 468410.33272491 & 445454.66727509 \tabularnewline
25 & 221989 & 469583.388705816 & -247594.388705816 \tabularnewline
26 & 842162 & 468931.376054817 & 373230.623945183 \tabularnewline
27 & 142783 & 469914.237943669 & -327131.237943669 \tabularnewline
28 & 112683 & 469052.773728784 & -356369.773728784 \tabularnewline
29 & 862759 & 468114.313038623 & 394644.686961377 \tabularnewline
30 & 392482 & 469153.566512393 & -76671.5665123927 \tabularnewline
31 & 602262 & 468951.660356121 & 133310.339643879 \tabularnewline
32 & 542540 & 469302.718505747 & 73237.281494253 \tabularnewline
33 & 982375 & 469495.580849311 & 512879.419150689 \tabularnewline
34 & 112533 & 470846.192514912 & -358313.192514912 \tabularnewline
35 & 622742 & 469902.614044653 & 152839.385955347 \tabularnewline
36 & 883970 & 470305.099794572 & 413664.900205428 \tabularnewline
37 & 562056 & 471394.440912592 & 90661.559087408 \tabularnewline
38 & 322091 & 471633.188179012 & -149542.188179012 \tabularnewline
39 & 832619 & 471239.385237594 & 361379.614762406 \tabularnewline
40 & 82723 & 472191.038794324 & -389468.038794324 \tabularnewline
41 & 872811 & 471165.417455403 & 401645.582544597 \tabularnewline
42 & 562534 & 472223.107019395 & 90310.8929806048 \tabularnewline
43 & 112447 & 472460.930845105 & -360013.930845105 \tabularnewline
44 & 342593 & 471512.873667097 & -128919.873667097 \tabularnewline
45 & 422622 & 471173.3773278 & -48551.3773278001 \tabularnewline
46 & 682787 & 471045.522603763 & 211741.477396237 \tabularnewline
47 & 602944 & 471603.120547421 & 131340.879452579 \tabularnewline
48 & 84298 & 471948.992339767 & -387650.992339767 \tabularnewline
49 & 942258 & 470928.155993276 & 471329.844006724 \tabularnewline
50 & 722391 & 472169.351412495 & 250221.648587505 \tabularnewline
51 & 662901 & 472828.282664071 & 190072.717335929 \tabularnewline
52 & 3007 & 473328.818306096 & -470321.818306096 \tabularnewline
53 & 452988 & 472090.277411937 & -19102.2774119367 \tabularnewline
54 & 12759 & 472039.973660706 & -459280.973660706 \tabularnewline
55 & 942577 & 470830.507619269 & 471746.492380731 \tabularnewline
56 & 52626 & 472072.800236257 & -419446.800236257 \tabularnewline
57 & 882755 & 470968.233119026 & 411786.766880974 \tabularnewline
58 & 22968 & 472052.628379048 & -449084.628379048 \tabularnewline
59 & 433067 & 470870.013293936 & -37803.0132939362 \tabularnewline
60 & 904437 & 470770.463207028 & 433666.536792972 \tabularnewline
61 & 812315 & 471912.47643997 & 340402.52356003 \tabularnewline
62 & 32428 & 472808.8891291 & -440380.8891291 \tabularnewline
63 & 53073 & 471649.194386132 & -418576.194386132 \tabularnewline
64 & 403145 & 470546.919913865 & -67401.9199138649 \tabularnewline
65 & 243133 & 470369.424354635 & -227236.424354635 \tabularnewline
66 & 313018 & 469771.022168618 & -156753.022168618 \tabularnewline
67 & 32720 & 469358.230287225 & -436638.230287225 \tabularnewline
68 & 922852 & 468208.391425587 & 454643.608574413 \tabularnewline
69 & 192947 & 469405.645474987 & -276458.645474987 \tabularnewline
70 & 693108 & 468677.621971425 & 224430.378028575 \tabularnewline
71 & 33335 & 469268.634742385 & -435933.634742385 \tabularnewline
72 & 944749 & 468120.651355791 & 476628.348644209 \tabularnewline
73 & 962536 & 469375.799805501 & 493160.200194499 \tabularnewline
74 & 292541 & 470674.48307202 & -178133.483072020 \tabularnewline
75 & 953227 & 470205.388093185 & 483021.611906815 \tabularnewline
76 & 193417 & 471477.372500084 & -278060.372500084 \tabularnewline
77 & 73378 & 470745.131024179 & -397367.131024179 \tabularnewline
78 & 433219 & 469698.708292737 & -36479.7082927374 \tabularnewline
79 & 962953 & 469602.642984327 & 493350.357015673 \tabularnewline
80 & 632986 & 470901.827007966 & 162084.172992034 \tabularnewline
81 & 333186 & 471328.657889999 & -138142.657889999 \tabularnewline
82 & 733212 & 470964.874360583 & 262247.125639417 \tabularnewline
83 & 463421 & 471655.473386267 & -8234.47338626737 \tabularnewline
84 & 495024 & 471633.788804277 & 23390.2111957227 \tabularnewline
85 & 752596 & 471695.384358558 & 280900.615641442 \tabularnewline
86 & 22640 & 472435.10530308 & -449795.10530308 \tabularnewline
87 & 123421 & 471250.619254958 & -347829.619254958 \tabularnewline
88 & 243440 & 470334.648124385 & -226894.648124385 \tabularnewline
89 & 623653 & 469737.145968563 & 153915.854031437 \tabularnewline
90 & 413304 & 470142.466479025 & -56838.4664790252 \tabularnewline
91 & 852981 & 469992.788615155 & 382988.211384845 \tabularnewline
92 & 613232 & 471001.346039707 & 142230.653960293 \tabularnewline
93 & 493203 & 471375.894858146 & 21827.1051418538 \tabularnewline
94 & 253344 & 471433.374144174 & -218089.374144174 \tabularnewline
95 & 803665 & 470859.059711065 & 332805.940288935 \tabularnewline
96 & 574904 & 471735.467631819 & 103168.532368181 \tabularnewline
97 & 132570 & 472007.150639825 & -339437.150639825 \tabularnewline
98 & 132785 & 471113.280154338 & -338328.280154338 \tabularnewline
99 & 393406 & 470222.329757584 & -76816.3297575843 \tabularnewline
100 & 333452 & 470020.042383193 & -136568.042383193 \tabularnewline
101 & 583642 & 469660.405430912 & 113981.594569088 \tabularnewline
102 & 893230 & 469960.563451571 & 423269.436548429 \tabularnewline
103 & 272991 & 471075.197062023 & -198084.197062023 \tabularnewline
104 & 373159 & 470553.56406734 & -97394.5640673396 \tabularnewline
105 & 133072 & 470297.086171203 & -337225.086171203 \tabularnewline
106 & 653091 & 469409.040914736 & 183681.959085264 \tabularnewline
107 & 373307 & 469892.747196248 & -96585.7471962476 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=41816&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]731993[/C][C]461683[/C][C]270310[/C][/ROW]
[ROW][C]3[/C][C]522673[/C][C]462394.831720472[/C][C]60278.1682795281[/C][/ROW]
[ROW][C]4[/C][C]572709[/C][C]462553.567661552[/C][C]110155.432338448[/C][/ROW]
[ROW][C]5[/C][C]382812[/C][C]462843.649903869[/C][C]-80031.6499038692[/C][/ROW]
[ROW][C]6[/C][C]942567[/C][C]462632.895336730[/C][C]479934.10466327[/C][/ROW]
[ROW][C]7[/C][C]802385[/C][C]463896.749132134[/C][C]338488.250867866[/C][/ROW]
[ROW][C]8[/C][C]272643[/C][C]464788.120794207[/C][C]-192145.120794207[/C][/ROW]
[ROW][C]9[/C][C]992660[/C][C]464282.127705104[/C][C]528377.872294896[/C][/ROW]
[ROW][C]10[/C][C]672651[/C][C]465673.55284622[/C][C]206977.44715378[/C][/ROW]
[ROW][C]11[/C][C]122826[/C][C]466218.605239052[/C][C]-343392.605239052[/C][/ROW]
[ROW][C]12[/C][C]493878[/C][C]465314.31849796[/C][C]28563.6815020404[/C][/ROW]
[ROW][C]13[/C][C]801948[/C][C]465389.537818542[/C][C]336558.462181458[/C][/ROW]
[ROW][C]14[/C][C]742156[/C][C]466275.827593889[/C][C]275880.172406111[/C][/ROW]
[ROW][C]15[/C][C]612673[/C][C]467002.327752107[/C][C]145670.672247893[/C][/ROW]
[ROW][C]16[/C][C]662804[/C][C]467385.93548119[/C][C]195418.064518810[/C][/ROW]
[ROW][C]17[/C][C]572750[/C][C]467900.54750841[/C][C]104849.452491590[/C][/ROW]
[ROW][C]18[/C][C]202510[/C][C]468176.657035093[/C][C]-265666.657035093[/C][/ROW]
[ROW][C]19[/C][C]652313[/C][C]467477.053048746[/C][C]184835.946951254[/C][/ROW]
[ROW][C]20[/C][C]492663[/C][C]467963.798230661[/C][C]24699.2017693392[/C][/ROW]
[ROW][C]21[/C][C]292397[/C][C]468028.840867965[/C][C]-175631.840867965[/C][/ROW]
[ROW][C]22[/C][C]382618[/C][C]467566.333689338[/C][C]-84948.3336893381[/C][/ROW]
[ROW][C]23[/C][C]872790[/C][C]467342.63157502[/C][C]405447.36842498[/C][/ROW]
[ROW][C]24[/C][C]913865[/C][C]468410.33272491[/C][C]445454.66727509[/C][/ROW]
[ROW][C]25[/C][C]221989[/C][C]469583.388705816[/C][C]-247594.388705816[/C][/ROW]
[ROW][C]26[/C][C]842162[/C][C]468931.376054817[/C][C]373230.623945183[/C][/ROW]
[ROW][C]27[/C][C]142783[/C][C]469914.237943669[/C][C]-327131.237943669[/C][/ROW]
[ROW][C]28[/C][C]112683[/C][C]469052.773728784[/C][C]-356369.773728784[/C][/ROW]
[ROW][C]29[/C][C]862759[/C][C]468114.313038623[/C][C]394644.686961377[/C][/ROW]
[ROW][C]30[/C][C]392482[/C][C]469153.566512393[/C][C]-76671.5665123927[/C][/ROW]
[ROW][C]31[/C][C]602262[/C][C]468951.660356121[/C][C]133310.339643879[/C][/ROW]
[ROW][C]32[/C][C]542540[/C][C]469302.718505747[/C][C]73237.281494253[/C][/ROW]
[ROW][C]33[/C][C]982375[/C][C]469495.580849311[/C][C]512879.419150689[/C][/ROW]
[ROW][C]34[/C][C]112533[/C][C]470846.192514912[/C][C]-358313.192514912[/C][/ROW]
[ROW][C]35[/C][C]622742[/C][C]469902.614044653[/C][C]152839.385955347[/C][/ROW]
[ROW][C]36[/C][C]883970[/C][C]470305.099794572[/C][C]413664.900205428[/C][/ROW]
[ROW][C]37[/C][C]562056[/C][C]471394.440912592[/C][C]90661.559087408[/C][/ROW]
[ROW][C]38[/C][C]322091[/C][C]471633.188179012[/C][C]-149542.188179012[/C][/ROW]
[ROW][C]39[/C][C]832619[/C][C]471239.385237594[/C][C]361379.614762406[/C][/ROW]
[ROW][C]40[/C][C]82723[/C][C]472191.038794324[/C][C]-389468.038794324[/C][/ROW]
[ROW][C]41[/C][C]872811[/C][C]471165.417455403[/C][C]401645.582544597[/C][/ROW]
[ROW][C]42[/C][C]562534[/C][C]472223.107019395[/C][C]90310.8929806048[/C][/ROW]
[ROW][C]43[/C][C]112447[/C][C]472460.930845105[/C][C]-360013.930845105[/C][/ROW]
[ROW][C]44[/C][C]342593[/C][C]471512.873667097[/C][C]-128919.873667097[/C][/ROW]
[ROW][C]45[/C][C]422622[/C][C]471173.3773278[/C][C]-48551.3773278001[/C][/ROW]
[ROW][C]46[/C][C]682787[/C][C]471045.522603763[/C][C]211741.477396237[/C][/ROW]
[ROW][C]47[/C][C]602944[/C][C]471603.120547421[/C][C]131340.879452579[/C][/ROW]
[ROW][C]48[/C][C]84298[/C][C]471948.992339767[/C][C]-387650.992339767[/C][/ROW]
[ROW][C]49[/C][C]942258[/C][C]470928.155993276[/C][C]471329.844006724[/C][/ROW]
[ROW][C]50[/C][C]722391[/C][C]472169.351412495[/C][C]250221.648587505[/C][/ROW]
[ROW][C]51[/C][C]662901[/C][C]472828.282664071[/C][C]190072.717335929[/C][/ROW]
[ROW][C]52[/C][C]3007[/C][C]473328.818306096[/C][C]-470321.818306096[/C][/ROW]
[ROW][C]53[/C][C]452988[/C][C]472090.277411937[/C][C]-19102.2774119367[/C][/ROW]
[ROW][C]54[/C][C]12759[/C][C]472039.973660706[/C][C]-459280.973660706[/C][/ROW]
[ROW][C]55[/C][C]942577[/C][C]470830.507619269[/C][C]471746.492380731[/C][/ROW]
[ROW][C]56[/C][C]52626[/C][C]472072.800236257[/C][C]-419446.800236257[/C][/ROW]
[ROW][C]57[/C][C]882755[/C][C]470968.233119026[/C][C]411786.766880974[/C][/ROW]
[ROW][C]58[/C][C]22968[/C][C]472052.628379048[/C][C]-449084.628379048[/C][/ROW]
[ROW][C]59[/C][C]433067[/C][C]470870.013293936[/C][C]-37803.0132939362[/C][/ROW]
[ROW][C]60[/C][C]904437[/C][C]470770.463207028[/C][C]433666.536792972[/C][/ROW]
[ROW][C]61[/C][C]812315[/C][C]471912.47643997[/C][C]340402.52356003[/C][/ROW]
[ROW][C]62[/C][C]32428[/C][C]472808.8891291[/C][C]-440380.8891291[/C][/ROW]
[ROW][C]63[/C][C]53073[/C][C]471649.194386132[/C][C]-418576.194386132[/C][/ROW]
[ROW][C]64[/C][C]403145[/C][C]470546.919913865[/C][C]-67401.9199138649[/C][/ROW]
[ROW][C]65[/C][C]243133[/C][C]470369.424354635[/C][C]-227236.424354635[/C][/ROW]
[ROW][C]66[/C][C]313018[/C][C]469771.022168618[/C][C]-156753.022168618[/C][/ROW]
[ROW][C]67[/C][C]32720[/C][C]469358.230287225[/C][C]-436638.230287225[/C][/ROW]
[ROW][C]68[/C][C]922852[/C][C]468208.391425587[/C][C]454643.608574413[/C][/ROW]
[ROW][C]69[/C][C]192947[/C][C]469405.645474987[/C][C]-276458.645474987[/C][/ROW]
[ROW][C]70[/C][C]693108[/C][C]468677.621971425[/C][C]224430.378028575[/C][/ROW]
[ROW][C]71[/C][C]33335[/C][C]469268.634742385[/C][C]-435933.634742385[/C][/ROW]
[ROW][C]72[/C][C]944749[/C][C]468120.651355791[/C][C]476628.348644209[/C][/ROW]
[ROW][C]73[/C][C]962536[/C][C]469375.799805501[/C][C]493160.200194499[/C][/ROW]
[ROW][C]74[/C][C]292541[/C][C]470674.48307202[/C][C]-178133.483072020[/C][/ROW]
[ROW][C]75[/C][C]953227[/C][C]470205.388093185[/C][C]483021.611906815[/C][/ROW]
[ROW][C]76[/C][C]193417[/C][C]471477.372500084[/C][C]-278060.372500084[/C][/ROW]
[ROW][C]77[/C][C]73378[/C][C]470745.131024179[/C][C]-397367.131024179[/C][/ROW]
[ROW][C]78[/C][C]433219[/C][C]469698.708292737[/C][C]-36479.7082927374[/C][/ROW]
[ROW][C]79[/C][C]962953[/C][C]469602.642984327[/C][C]493350.357015673[/C][/ROW]
[ROW][C]80[/C][C]632986[/C][C]470901.827007966[/C][C]162084.172992034[/C][/ROW]
[ROW][C]81[/C][C]333186[/C][C]471328.657889999[/C][C]-138142.657889999[/C][/ROW]
[ROW][C]82[/C][C]733212[/C][C]470964.874360583[/C][C]262247.125639417[/C][/ROW]
[ROW][C]83[/C][C]463421[/C][C]471655.473386267[/C][C]-8234.47338626737[/C][/ROW]
[ROW][C]84[/C][C]495024[/C][C]471633.788804277[/C][C]23390.2111957227[/C][/ROW]
[ROW][C]85[/C][C]752596[/C][C]471695.384358558[/C][C]280900.615641442[/C][/ROW]
[ROW][C]86[/C][C]22640[/C][C]472435.10530308[/C][C]-449795.10530308[/C][/ROW]
[ROW][C]87[/C][C]123421[/C][C]471250.619254958[/C][C]-347829.619254958[/C][/ROW]
[ROW][C]88[/C][C]243440[/C][C]470334.648124385[/C][C]-226894.648124385[/C][/ROW]
[ROW][C]89[/C][C]623653[/C][C]469737.145968563[/C][C]153915.854031437[/C][/ROW]
[ROW][C]90[/C][C]413304[/C][C]470142.466479025[/C][C]-56838.4664790252[/C][/ROW]
[ROW][C]91[/C][C]852981[/C][C]469992.788615155[/C][C]382988.211384845[/C][/ROW]
[ROW][C]92[/C][C]613232[/C][C]471001.346039707[/C][C]142230.653960293[/C][/ROW]
[ROW][C]93[/C][C]493203[/C][C]471375.894858146[/C][C]21827.1051418538[/C][/ROW]
[ROW][C]94[/C][C]253344[/C][C]471433.374144174[/C][C]-218089.374144174[/C][/ROW]
[ROW][C]95[/C][C]803665[/C][C]470859.059711065[/C][C]332805.940288935[/C][/ROW]
[ROW][C]96[/C][C]574904[/C][C]471735.467631819[/C][C]103168.532368181[/C][/ROW]
[ROW][C]97[/C][C]132570[/C][C]472007.150639825[/C][C]-339437.150639825[/C][/ROW]
[ROW][C]98[/C][C]132785[/C][C]471113.280154338[/C][C]-338328.280154338[/C][/ROW]
[ROW][C]99[/C][C]393406[/C][C]470222.329757584[/C][C]-76816.3297575843[/C][/ROW]
[ROW][C]100[/C][C]333452[/C][C]470020.042383193[/C][C]-136568.042383193[/C][/ROW]
[ROW][C]101[/C][C]583642[/C][C]469660.405430912[/C][C]113981.594569088[/C][/ROW]
[ROW][C]102[/C][C]893230[/C][C]469960.563451571[/C][C]423269.436548429[/C][/ROW]
[ROW][C]103[/C][C]272991[/C][C]471075.197062023[/C][C]-198084.197062023[/C][/ROW]
[ROW][C]104[/C][C]373159[/C][C]470553.56406734[/C][C]-97394.5640673396[/C][/ROW]
[ROW][C]105[/C][C]133072[/C][C]470297.086171203[/C][C]-337225.086171203[/C][/ROW]
[ROW][C]106[/C][C]653091[/C][C]469409.040914736[/C][C]183681.959085264[/C][/ROW]
[ROW][C]107[/C][C]373307[/C][C]469892.747196248[/C][C]-96585.7471962476[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=41816&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=41816&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
2731993461683270310
3522673462394.83172047260278.1682795281
4572709462553.567661552110155.432338448
5382812462843.649903869-80031.6499038692
6942567462632.895336730479934.10466327
7802385463896.749132134338488.250867866
8272643464788.120794207-192145.120794207
9992660464282.127705104528377.872294896
10672651465673.55284622206977.44715378
11122826466218.605239052-343392.605239052
12493878465314.3184979628563.6815020404
13801948465389.537818542336558.462181458
14742156466275.827593889275880.172406111
15612673467002.327752107145670.672247893
16662804467385.93548119195418.064518810
17572750467900.54750841104849.452491590
18202510468176.657035093-265666.657035093
19652313467477.053048746184835.946951254
20492663467963.79823066124699.2017693392
21292397468028.840867965-175631.840867965
22382618467566.333689338-84948.3336893381
23872790467342.63157502405447.36842498
24913865468410.33272491445454.66727509
25221989469583.388705816-247594.388705816
26842162468931.376054817373230.623945183
27142783469914.237943669-327131.237943669
28112683469052.773728784-356369.773728784
29862759468114.313038623394644.686961377
30392482469153.566512393-76671.5665123927
31602262468951.660356121133310.339643879
32542540469302.71850574773237.281494253
33982375469495.580849311512879.419150689
34112533470846.192514912-358313.192514912
35622742469902.614044653152839.385955347
36883970470305.099794572413664.900205428
37562056471394.44091259290661.559087408
38322091471633.188179012-149542.188179012
39832619471239.385237594361379.614762406
4082723472191.038794324-389468.038794324
41872811471165.417455403401645.582544597
42562534472223.10701939590310.8929806048
43112447472460.930845105-360013.930845105
44342593471512.873667097-128919.873667097
45422622471173.3773278-48551.3773278001
46682787471045.522603763211741.477396237
47602944471603.120547421131340.879452579
4884298471948.992339767-387650.992339767
49942258470928.155993276471329.844006724
50722391472169.351412495250221.648587505
51662901472828.282664071190072.717335929
523007473328.818306096-470321.818306096
53452988472090.277411937-19102.2774119367
5412759472039.973660706-459280.973660706
55942577470830.507619269471746.492380731
5652626472072.800236257-419446.800236257
57882755470968.233119026411786.766880974
5822968472052.628379048-449084.628379048
59433067470870.013293936-37803.0132939362
60904437470770.463207028433666.536792972
61812315471912.47643997340402.52356003
6232428472808.8891291-440380.8891291
6353073471649.194386132-418576.194386132
64403145470546.919913865-67401.9199138649
65243133470369.424354635-227236.424354635
66313018469771.022168618-156753.022168618
6732720469358.230287225-436638.230287225
68922852468208.391425587454643.608574413
69192947469405.645474987-276458.645474987
70693108468677.621971425224430.378028575
7133335469268.634742385-435933.634742385
72944749468120.651355791476628.348644209
73962536469375.799805501493160.200194499
74292541470674.48307202-178133.483072020
75953227470205.388093185483021.611906815
76193417471477.372500084-278060.372500084
7773378470745.131024179-397367.131024179
78433219469698.708292737-36479.7082927374
79962953469602.642984327493350.357015673
80632986470901.827007966162084.172992034
81333186471328.657889999-138142.657889999
82733212470964.874360583262247.125639417
83463421471655.473386267-8234.47338626737
84495024471633.78880427723390.2111957227
85752596471695.384358558280900.615641442
8622640472435.10530308-449795.10530308
87123421471250.619254958-347829.619254958
88243440470334.648124385-226894.648124385
89623653469737.145968563153915.854031437
90413304470142.466479025-56838.4664790252
91852981469992.788615155382988.211384845
92613232471001.346039707142230.653960293
93493203471375.89485814621827.1051418538
94253344471433.374144174-218089.374144174
95803665470859.059711065332805.940288935
96574904471735.467631819103168.532368181
97132570472007.150639825-339437.150639825
98132785471113.280154338-338328.280154338
99393406470222.329757584-76816.3297575843
100333452470020.042383193-136568.042383193
101583642469660.405430912113981.594569088
102893230469960.563451571423269.436548429
103272991471075.197062023-198084.197062023
104373159470553.56406734-97394.5640673396
105133072470297.086171203-337225.086171203
106653091469409.040914736183681.959085264
107373307469892.747196248-96585.7471962476







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
108469638.399230579-117973.0281701121057249.82663127
109469638.399230579-117975.0656340631057251.86409522
110469638.399230579-117977.1030909491057253.90155211
111469638.399230579-117979.1405407711057255.93900193
112469638.399230579-117981.1779835281057257.97644469
113469638.399230579-117983.2154192211057260.01388038
114469638.399230579-117985.2528478491057262.05130901
115469638.399230579-117987.2902694141057264.08873057
116469638.399230579-117989.3276839141057266.12614507
117469638.399230579-117991.3650913501057268.16355251
118469638.399230579-117993.4024917221057270.20095288
119469638.399230579-117995.439885031057272.23834619

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
108 & 469638.399230579 & -117973.028170112 & 1057249.82663127 \tabularnewline
109 & 469638.399230579 & -117975.065634063 & 1057251.86409522 \tabularnewline
110 & 469638.399230579 & -117977.103090949 & 1057253.90155211 \tabularnewline
111 & 469638.399230579 & -117979.140540771 & 1057255.93900193 \tabularnewline
112 & 469638.399230579 & -117981.177983528 & 1057257.97644469 \tabularnewline
113 & 469638.399230579 & -117983.215419221 & 1057260.01388038 \tabularnewline
114 & 469638.399230579 & -117985.252847849 & 1057262.05130901 \tabularnewline
115 & 469638.399230579 & -117987.290269414 & 1057264.08873057 \tabularnewline
116 & 469638.399230579 & -117989.327683914 & 1057266.12614507 \tabularnewline
117 & 469638.399230579 & -117991.365091350 & 1057268.16355251 \tabularnewline
118 & 469638.399230579 & -117993.402491722 & 1057270.20095288 \tabularnewline
119 & 469638.399230579 & -117995.43988503 & 1057272.23834619 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=41816&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]108[/C][C]469638.399230579[/C][C]-117973.028170112[/C][C]1057249.82663127[/C][/ROW]
[ROW][C]109[/C][C]469638.399230579[/C][C]-117975.065634063[/C][C]1057251.86409522[/C][/ROW]
[ROW][C]110[/C][C]469638.399230579[/C][C]-117977.103090949[/C][C]1057253.90155211[/C][/ROW]
[ROW][C]111[/C][C]469638.399230579[/C][C]-117979.140540771[/C][C]1057255.93900193[/C][/ROW]
[ROW][C]112[/C][C]469638.399230579[/C][C]-117981.177983528[/C][C]1057257.97644469[/C][/ROW]
[ROW][C]113[/C][C]469638.399230579[/C][C]-117983.215419221[/C][C]1057260.01388038[/C][/ROW]
[ROW][C]114[/C][C]469638.399230579[/C][C]-117985.252847849[/C][C]1057262.05130901[/C][/ROW]
[ROW][C]115[/C][C]469638.399230579[/C][C]-117987.290269414[/C][C]1057264.08873057[/C][/ROW]
[ROW][C]116[/C][C]469638.399230579[/C][C]-117989.327683914[/C][C]1057266.12614507[/C][/ROW]
[ROW][C]117[/C][C]469638.399230579[/C][C]-117991.365091350[/C][C]1057268.16355251[/C][/ROW]
[ROW][C]118[/C][C]469638.399230579[/C][C]-117993.402491722[/C][C]1057270.20095288[/C][/ROW]
[ROW][C]119[/C][C]469638.399230579[/C][C]-117995.43988503[/C][C]1057272.23834619[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=41816&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=41816&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
108469638.399230579-117973.0281701121057249.82663127
109469638.399230579-117975.0656340631057251.86409522
110469638.399230579-117977.1030909491057253.90155211
111469638.399230579-117979.1405407711057255.93900193
112469638.399230579-117981.1779835281057257.97644469
113469638.399230579-117983.2154192211057260.01388038
114469638.399230579-117985.2528478491057262.05130901
115469638.399230579-117987.2902694141057264.08873057
116469638.399230579-117989.3276839141057266.12614507
117469638.399230579-117991.3650913501057268.16355251
118469638.399230579-117993.4024917221057270.20095288
119469638.399230579-117995.439885031057272.23834619



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=0, beta=0)
if (par2 == 'Double') fit <- HoltWinters(x, gamma=0)
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')