Free Statistics

of Irreproducible Research!

Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationThu, 12 Aug 2010 09:23:07 +0000
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2010/Aug/12/t1281604990xfuy8et1afuse1v.htm/, Retrieved Sat, 04 May 2024 08:43:39 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=78657, Retrieved Sat, 04 May 2024 08:43:39 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywordsHoes Isabelle
Estimated Impact151
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [TIJDREEKS A - STA...] [2010-08-12 09:23:07] [35611de12c9fa8a4a915f3548e0dcd01] [Current]
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Dataseries X:
698
697
696
694
714
713
698
688
689
689
690
692
688
679
677
673
694
690
673
659
657
654
644
643
638
626
621
615
640
633
620
610
601
595
585
584
580
574
560
550
580
569
551
536
535
526
517
512
510
501
496
491
524
514
495
479
479
467
451
459
461
460
452
449
483
470
442
419
419
406
393
396
390
389
373
371
407
391
357
327
321
317
300
304
296
296
283
279
319
295
255
227
228
233
210
219
212
209
201
198
245
216
173
144
143
152
127
141
129
127
113
117
174
143
103
81
92
104
81
89




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time4 seconds
R Server'RServer@AstonUniversity' @ vre.aston.ac.uk

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input & view raw input (R code)  \tabularnewline
Raw Output & view raw output of R engine  \tabularnewline
Computing time & 4 seconds \tabularnewline
R Server & 'RServer@AstonUniversity' @ vre.aston.ac.uk \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=78657&T=0

[TABLE]
[ROW][C]Summary of computational transaction[/C][/ROW]
[ROW][C]Raw Input[/C][C]view raw input (R code) [/C][/ROW]
[ROW][C]Raw Output[/C][C]view raw output of R engine [/C][/ROW]
[ROW][C]Computing time[/C][C]4 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'RServer@AstonUniversity' @ vre.aston.ac.uk[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=78657&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=78657&T=0

As an alternative you can also use a QR Code:  

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

Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time4 seconds
R Server'RServer@AstonUniversity' @ vre.aston.ac.uk







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.390729284726388
beta0.122141405310284
gamma1

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.390729284726388 \tabularnewline
beta & 0.122141405310284 \tabularnewline
gamma & 1 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=78657&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]0.390729284726388[/C][/ROW]
[ROW][C]beta[/C][C]0.122141405310284[/C][/ROW]
[ROW][C]gamma[/C][C]1[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=78657&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=78657&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
alpha0.390729284726388
beta0.122141405310284
gamma1







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
13688698.392361111112-10.3923611111115
14679684.902081797484-5.90208179748402
15677680.176280501588-3.17628050158783
16673674.613944074414-1.61394407441389
17694695.168367346843-1.1683673468433
18690691.424464403764-1.42446440376432
19673670.7625153826252.23748461737478
20659659.596512633478-0.596512633478483
21657658.669716063091-1.66971606309073
22654656.368901580986-2.36890158098629
23644654.723507518725-10.7235075187252
24643650.38528651341-7.38528651340994
25638634.8755211921743.12447880782577
26626627.938899260585-1.93889926058478
27621625.14795665825-4.14795665824988
28615618.837047553824-3.83704755382394
29640637.3674239770552.63257602294527
30633633.70713348529-0.707133485290683
31620614.3453240258325.65467597416762
32610601.7396683503088.26033164969238
33601602.994136681446-1.99413668144632
34595599.49959347137-4.49959347136951
35585591.188798507169-6.18879850716928
36584590.130056430245-6.13005643024474
37580581.047698397987-1.04769839798746
38574568.7304626561115.26953734388906
39560567.088716376729-7.08871637672928
40550559.3564116933-9.35641169329995
41580578.9467732780931.05322672190709
42569571.834034522757-2.83403452275684
43551554.615179000695-3.61517900069487
44536538.630604842518-2.63060484251844
45535527.5176922252147.48230777478591
46526524.7874020181211.21259798187907
47517516.5399843676570.460015632343129
48512517.29286799924-5.29286799923955
49510510.852059573827-0.852059573827432
50501501.687412756266-0.687412756266042
51496489.1315390881546.86846091184623
52491485.0801169572715.91988304272934
53524517.3197564126856.68024358731498
54514510.6439028184483.3560971815524
55495496.269843131521-1.2698431315207
56479482.815520472513-3.8155204725125
57479478.3585668345880.641433165412195
58467469.766359294742-2.76635929474162
59451459.946790759489-8.9467907594888
60459453.5112342304655.48876576953495
61461454.4954635833246.50453641667639
62460449.16333977575810.8366602242417
63452447.1215799305794.8784200694206
64449443.0274251689885.97257483101197
65483477.0662082577565.93379174224356
66470469.3530551704310.646944829568554
67442452.25237432666-10.2523743266601
68419434.458996661324-15.4589966613245
69419428.334101003334-9.33410100333401
70406413.457831128752-7.45783112875159
71393397.505653553361-4.50565355336096
72396401.278533359715-5.27853335971474
73390397.838674058958-7.8386740589578
74389388.0212865886620.978713411337651
75373376.5067066705-3.5067066704998
76371367.411849798453.58815020155026
77407397.990520150829.00947984918042
78391385.8999734992835.10002650071704
79357361.753091982011-4.75309198201086
80327341.053137330405-14.0531373304053
81321337.393300057954-16.3933000579545
82317318.74908429431-1.74908429430985
83300304.945735761255-4.94573576125543
84304306.17434607908-2.17434607907967
85296300.634286378242-4.63428637824171
86296295.8407713796590.159228620340798
87283279.6336987723973.366301227603
88279276.2355639682022.76443603179825
89319308.4446794315710.55532056843
90295293.2992335964881.7007664035122
91255260.381729032973-5.38172903297345
92227232.300684944992-5.30068494499199
93228229.583381261816-1.58338126181627
94233225.3034049182187.69659508178216
95210213.349200152569-3.34920015256853
96219217.0724100304581.92758996954242
97212212.014348766512-0.0143487665121427
98209212.54503141966-3.54503141966003
99201197.2662928435943.7337071564063
100198194.0842711053433.91572889465706
101245231.98418840669813.0158115933016
102216213.016933151932.98306684806994
103173176.958125888556-3.95812588855557
104144150.223465408778-6.22346540877811
105143150.10717204787-7.10717204786951
106152149.756011476522.24398852348037
107127129.114317441323-2.11431744132344
108141136.7668430228594.23315697714131
109129131.768316473222-2.76831647322248
110127129.282219346418-2.28221934641766
111113119.202305010908-6.20230501090795
112117112.0453887143874.95461128561318
113174155.74171739423118.2582826057694
114143132.80646009193910.1935399080613
11510395.7763131479727.22368685202804
1168173.00453546927927.99546453072082
1179279.558191390461212.4418086095388
11810495.12835180234568.87164819765435
1198177.32276367682033.67723632317968
1208994.283819984435-5.28381998443496

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 688 & 698.392361111112 & -10.3923611111115 \tabularnewline
14 & 679 & 684.902081797484 & -5.90208179748402 \tabularnewline
15 & 677 & 680.176280501588 & -3.17628050158783 \tabularnewline
16 & 673 & 674.613944074414 & -1.61394407441389 \tabularnewline
17 & 694 & 695.168367346843 & -1.1683673468433 \tabularnewline
18 & 690 & 691.424464403764 & -1.42446440376432 \tabularnewline
19 & 673 & 670.762515382625 & 2.23748461737478 \tabularnewline
20 & 659 & 659.596512633478 & -0.596512633478483 \tabularnewline
21 & 657 & 658.669716063091 & -1.66971606309073 \tabularnewline
22 & 654 & 656.368901580986 & -2.36890158098629 \tabularnewline
23 & 644 & 654.723507518725 & -10.7235075187252 \tabularnewline
24 & 643 & 650.38528651341 & -7.38528651340994 \tabularnewline
25 & 638 & 634.875521192174 & 3.12447880782577 \tabularnewline
26 & 626 & 627.938899260585 & -1.93889926058478 \tabularnewline
27 & 621 & 625.14795665825 & -4.14795665824988 \tabularnewline
28 & 615 & 618.837047553824 & -3.83704755382394 \tabularnewline
29 & 640 & 637.367423977055 & 2.63257602294527 \tabularnewline
30 & 633 & 633.70713348529 & -0.707133485290683 \tabularnewline
31 & 620 & 614.345324025832 & 5.65467597416762 \tabularnewline
32 & 610 & 601.739668350308 & 8.26033164969238 \tabularnewline
33 & 601 & 602.994136681446 & -1.99413668144632 \tabularnewline
34 & 595 & 599.49959347137 & -4.49959347136951 \tabularnewline
35 & 585 & 591.188798507169 & -6.18879850716928 \tabularnewline
36 & 584 & 590.130056430245 & -6.13005643024474 \tabularnewline
37 & 580 & 581.047698397987 & -1.04769839798746 \tabularnewline
38 & 574 & 568.730462656111 & 5.26953734388906 \tabularnewline
39 & 560 & 567.088716376729 & -7.08871637672928 \tabularnewline
40 & 550 & 559.3564116933 & -9.35641169329995 \tabularnewline
41 & 580 & 578.946773278093 & 1.05322672190709 \tabularnewline
42 & 569 & 571.834034522757 & -2.83403452275684 \tabularnewline
43 & 551 & 554.615179000695 & -3.61517900069487 \tabularnewline
44 & 536 & 538.630604842518 & -2.63060484251844 \tabularnewline
45 & 535 & 527.517692225214 & 7.48230777478591 \tabularnewline
46 & 526 & 524.787402018121 & 1.21259798187907 \tabularnewline
47 & 517 & 516.539984367657 & 0.460015632343129 \tabularnewline
48 & 512 & 517.29286799924 & -5.29286799923955 \tabularnewline
49 & 510 & 510.852059573827 & -0.852059573827432 \tabularnewline
50 & 501 & 501.687412756266 & -0.687412756266042 \tabularnewline
51 & 496 & 489.131539088154 & 6.86846091184623 \tabularnewline
52 & 491 & 485.080116957271 & 5.91988304272934 \tabularnewline
53 & 524 & 517.319756412685 & 6.68024358731498 \tabularnewline
54 & 514 & 510.643902818448 & 3.3560971815524 \tabularnewline
55 & 495 & 496.269843131521 & -1.2698431315207 \tabularnewline
56 & 479 & 482.815520472513 & -3.8155204725125 \tabularnewline
57 & 479 & 478.358566834588 & 0.641433165412195 \tabularnewline
58 & 467 & 469.766359294742 & -2.76635929474162 \tabularnewline
59 & 451 & 459.946790759489 & -8.9467907594888 \tabularnewline
60 & 459 & 453.511234230465 & 5.48876576953495 \tabularnewline
61 & 461 & 454.495463583324 & 6.50453641667639 \tabularnewline
62 & 460 & 449.163339775758 & 10.8366602242417 \tabularnewline
63 & 452 & 447.121579930579 & 4.8784200694206 \tabularnewline
64 & 449 & 443.027425168988 & 5.97257483101197 \tabularnewline
65 & 483 & 477.066208257756 & 5.93379174224356 \tabularnewline
66 & 470 & 469.353055170431 & 0.646944829568554 \tabularnewline
67 & 442 & 452.25237432666 & -10.2523743266601 \tabularnewline
68 & 419 & 434.458996661324 & -15.4589966613245 \tabularnewline
69 & 419 & 428.334101003334 & -9.33410100333401 \tabularnewline
70 & 406 & 413.457831128752 & -7.45783112875159 \tabularnewline
71 & 393 & 397.505653553361 & -4.50565355336096 \tabularnewline
72 & 396 & 401.278533359715 & -5.27853335971474 \tabularnewline
73 & 390 & 397.838674058958 & -7.8386740589578 \tabularnewline
74 & 389 & 388.021286588662 & 0.978713411337651 \tabularnewline
75 & 373 & 376.5067066705 & -3.5067066704998 \tabularnewline
76 & 371 & 367.41184979845 & 3.58815020155026 \tabularnewline
77 & 407 & 397.99052015082 & 9.00947984918042 \tabularnewline
78 & 391 & 385.899973499283 & 5.10002650071704 \tabularnewline
79 & 357 & 361.753091982011 & -4.75309198201086 \tabularnewline
80 & 327 & 341.053137330405 & -14.0531373304053 \tabularnewline
81 & 321 & 337.393300057954 & -16.3933000579545 \tabularnewline
82 & 317 & 318.74908429431 & -1.74908429430985 \tabularnewline
83 & 300 & 304.945735761255 & -4.94573576125543 \tabularnewline
84 & 304 & 306.17434607908 & -2.17434607907967 \tabularnewline
85 & 296 & 300.634286378242 & -4.63428637824171 \tabularnewline
86 & 296 & 295.840771379659 & 0.159228620340798 \tabularnewline
87 & 283 & 279.633698772397 & 3.366301227603 \tabularnewline
88 & 279 & 276.235563968202 & 2.76443603179825 \tabularnewline
89 & 319 & 308.44467943157 & 10.55532056843 \tabularnewline
90 & 295 & 293.299233596488 & 1.7007664035122 \tabularnewline
91 & 255 & 260.381729032973 & -5.38172903297345 \tabularnewline
92 & 227 & 232.300684944992 & -5.30068494499199 \tabularnewline
93 & 228 & 229.583381261816 & -1.58338126181627 \tabularnewline
94 & 233 & 225.303404918218 & 7.69659508178216 \tabularnewline
95 & 210 & 213.349200152569 & -3.34920015256853 \tabularnewline
96 & 219 & 217.072410030458 & 1.92758996954242 \tabularnewline
97 & 212 & 212.014348766512 & -0.0143487665121427 \tabularnewline
98 & 209 & 212.54503141966 & -3.54503141966003 \tabularnewline
99 & 201 & 197.266292843594 & 3.7337071564063 \tabularnewline
100 & 198 & 194.084271105343 & 3.91572889465706 \tabularnewline
101 & 245 & 231.984188406698 & 13.0158115933016 \tabularnewline
102 & 216 & 213.01693315193 & 2.98306684806994 \tabularnewline
103 & 173 & 176.958125888556 & -3.95812588855557 \tabularnewline
104 & 144 & 150.223465408778 & -6.22346540877811 \tabularnewline
105 & 143 & 150.10717204787 & -7.10717204786951 \tabularnewline
106 & 152 & 149.75601147652 & 2.24398852348037 \tabularnewline
107 & 127 & 129.114317441323 & -2.11431744132344 \tabularnewline
108 & 141 & 136.766843022859 & 4.23315697714131 \tabularnewline
109 & 129 & 131.768316473222 & -2.76831647322248 \tabularnewline
110 & 127 & 129.282219346418 & -2.28221934641766 \tabularnewline
111 & 113 & 119.202305010908 & -6.20230501090795 \tabularnewline
112 & 117 & 112.045388714387 & 4.95461128561318 \tabularnewline
113 & 174 & 155.741717394231 & 18.2582826057694 \tabularnewline
114 & 143 & 132.806460091939 & 10.1935399080613 \tabularnewline
115 & 103 & 95.776313147972 & 7.22368685202804 \tabularnewline
116 & 81 & 73.0045354692792 & 7.99546453072082 \tabularnewline
117 & 92 & 79.5581913904612 & 12.4418086095388 \tabularnewline
118 & 104 & 95.1283518023456 & 8.87164819765435 \tabularnewline
119 & 81 & 77.3227636768203 & 3.67723632317968 \tabularnewline
120 & 89 & 94.283819984435 & -5.28381998443496 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=78657&T=2

[TABLE]
[ROW][C]Interpolation Forecasts of Exponential Smoothing[/C][/ROW]
[ROW][C]t[/C][C]Observed[/C][C]Fitted[/C][C]Residuals[/C][/ROW]
[ROW][C]13[/C][C]688[/C][C]698.392361111112[/C][C]-10.3923611111115[/C][/ROW]
[ROW][C]14[/C][C]679[/C][C]684.902081797484[/C][C]-5.90208179748402[/C][/ROW]
[ROW][C]15[/C][C]677[/C][C]680.176280501588[/C][C]-3.17628050158783[/C][/ROW]
[ROW][C]16[/C][C]673[/C][C]674.613944074414[/C][C]-1.61394407441389[/C][/ROW]
[ROW][C]17[/C][C]694[/C][C]695.168367346843[/C][C]-1.1683673468433[/C][/ROW]
[ROW][C]18[/C][C]690[/C][C]691.424464403764[/C][C]-1.42446440376432[/C][/ROW]
[ROW][C]19[/C][C]673[/C][C]670.762515382625[/C][C]2.23748461737478[/C][/ROW]
[ROW][C]20[/C][C]659[/C][C]659.596512633478[/C][C]-0.596512633478483[/C][/ROW]
[ROW][C]21[/C][C]657[/C][C]658.669716063091[/C][C]-1.66971606309073[/C][/ROW]
[ROW][C]22[/C][C]654[/C][C]656.368901580986[/C][C]-2.36890158098629[/C][/ROW]
[ROW][C]23[/C][C]644[/C][C]654.723507518725[/C][C]-10.7235075187252[/C][/ROW]
[ROW][C]24[/C][C]643[/C][C]650.38528651341[/C][C]-7.38528651340994[/C][/ROW]
[ROW][C]25[/C][C]638[/C][C]634.875521192174[/C][C]3.12447880782577[/C][/ROW]
[ROW][C]26[/C][C]626[/C][C]627.938899260585[/C][C]-1.93889926058478[/C][/ROW]
[ROW][C]27[/C][C]621[/C][C]625.14795665825[/C][C]-4.14795665824988[/C][/ROW]
[ROW][C]28[/C][C]615[/C][C]618.837047553824[/C][C]-3.83704755382394[/C][/ROW]
[ROW][C]29[/C][C]640[/C][C]637.367423977055[/C][C]2.63257602294527[/C][/ROW]
[ROW][C]30[/C][C]633[/C][C]633.70713348529[/C][C]-0.707133485290683[/C][/ROW]
[ROW][C]31[/C][C]620[/C][C]614.345324025832[/C][C]5.65467597416762[/C][/ROW]
[ROW][C]32[/C][C]610[/C][C]601.739668350308[/C][C]8.26033164969238[/C][/ROW]
[ROW][C]33[/C][C]601[/C][C]602.994136681446[/C][C]-1.99413668144632[/C][/ROW]
[ROW][C]34[/C][C]595[/C][C]599.49959347137[/C][C]-4.49959347136951[/C][/ROW]
[ROW][C]35[/C][C]585[/C][C]591.188798507169[/C][C]-6.18879850716928[/C][/ROW]
[ROW][C]36[/C][C]584[/C][C]590.130056430245[/C][C]-6.13005643024474[/C][/ROW]
[ROW][C]37[/C][C]580[/C][C]581.047698397987[/C][C]-1.04769839798746[/C][/ROW]
[ROW][C]38[/C][C]574[/C][C]568.730462656111[/C][C]5.26953734388906[/C][/ROW]
[ROW][C]39[/C][C]560[/C][C]567.088716376729[/C][C]-7.08871637672928[/C][/ROW]
[ROW][C]40[/C][C]550[/C][C]559.3564116933[/C][C]-9.35641169329995[/C][/ROW]
[ROW][C]41[/C][C]580[/C][C]578.946773278093[/C][C]1.05322672190709[/C][/ROW]
[ROW][C]42[/C][C]569[/C][C]571.834034522757[/C][C]-2.83403452275684[/C][/ROW]
[ROW][C]43[/C][C]551[/C][C]554.615179000695[/C][C]-3.61517900069487[/C][/ROW]
[ROW][C]44[/C][C]536[/C][C]538.630604842518[/C][C]-2.63060484251844[/C][/ROW]
[ROW][C]45[/C][C]535[/C][C]527.517692225214[/C][C]7.48230777478591[/C][/ROW]
[ROW][C]46[/C][C]526[/C][C]524.787402018121[/C][C]1.21259798187907[/C][/ROW]
[ROW][C]47[/C][C]517[/C][C]516.539984367657[/C][C]0.460015632343129[/C][/ROW]
[ROW][C]48[/C][C]512[/C][C]517.29286799924[/C][C]-5.29286799923955[/C][/ROW]
[ROW][C]49[/C][C]510[/C][C]510.852059573827[/C][C]-0.852059573827432[/C][/ROW]
[ROW][C]50[/C][C]501[/C][C]501.687412756266[/C][C]-0.687412756266042[/C][/ROW]
[ROW][C]51[/C][C]496[/C][C]489.131539088154[/C][C]6.86846091184623[/C][/ROW]
[ROW][C]52[/C][C]491[/C][C]485.080116957271[/C][C]5.91988304272934[/C][/ROW]
[ROW][C]53[/C][C]524[/C][C]517.319756412685[/C][C]6.68024358731498[/C][/ROW]
[ROW][C]54[/C][C]514[/C][C]510.643902818448[/C][C]3.3560971815524[/C][/ROW]
[ROW][C]55[/C][C]495[/C][C]496.269843131521[/C][C]-1.2698431315207[/C][/ROW]
[ROW][C]56[/C][C]479[/C][C]482.815520472513[/C][C]-3.8155204725125[/C][/ROW]
[ROW][C]57[/C][C]479[/C][C]478.358566834588[/C][C]0.641433165412195[/C][/ROW]
[ROW][C]58[/C][C]467[/C][C]469.766359294742[/C][C]-2.76635929474162[/C][/ROW]
[ROW][C]59[/C][C]451[/C][C]459.946790759489[/C][C]-8.9467907594888[/C][/ROW]
[ROW][C]60[/C][C]459[/C][C]453.511234230465[/C][C]5.48876576953495[/C][/ROW]
[ROW][C]61[/C][C]461[/C][C]454.495463583324[/C][C]6.50453641667639[/C][/ROW]
[ROW][C]62[/C][C]460[/C][C]449.163339775758[/C][C]10.8366602242417[/C][/ROW]
[ROW][C]63[/C][C]452[/C][C]447.121579930579[/C][C]4.8784200694206[/C][/ROW]
[ROW][C]64[/C][C]449[/C][C]443.027425168988[/C][C]5.97257483101197[/C][/ROW]
[ROW][C]65[/C][C]483[/C][C]477.066208257756[/C][C]5.93379174224356[/C][/ROW]
[ROW][C]66[/C][C]470[/C][C]469.353055170431[/C][C]0.646944829568554[/C][/ROW]
[ROW][C]67[/C][C]442[/C][C]452.25237432666[/C][C]-10.2523743266601[/C][/ROW]
[ROW][C]68[/C][C]419[/C][C]434.458996661324[/C][C]-15.4589966613245[/C][/ROW]
[ROW][C]69[/C][C]419[/C][C]428.334101003334[/C][C]-9.33410100333401[/C][/ROW]
[ROW][C]70[/C][C]406[/C][C]413.457831128752[/C][C]-7.45783112875159[/C][/ROW]
[ROW][C]71[/C][C]393[/C][C]397.505653553361[/C][C]-4.50565355336096[/C][/ROW]
[ROW][C]72[/C][C]396[/C][C]401.278533359715[/C][C]-5.27853335971474[/C][/ROW]
[ROW][C]73[/C][C]390[/C][C]397.838674058958[/C][C]-7.8386740589578[/C][/ROW]
[ROW][C]74[/C][C]389[/C][C]388.021286588662[/C][C]0.978713411337651[/C][/ROW]
[ROW][C]75[/C][C]373[/C][C]376.5067066705[/C][C]-3.5067066704998[/C][/ROW]
[ROW][C]76[/C][C]371[/C][C]367.41184979845[/C][C]3.58815020155026[/C][/ROW]
[ROW][C]77[/C][C]407[/C][C]397.99052015082[/C][C]9.00947984918042[/C][/ROW]
[ROW][C]78[/C][C]391[/C][C]385.899973499283[/C][C]5.10002650071704[/C][/ROW]
[ROW][C]79[/C][C]357[/C][C]361.753091982011[/C][C]-4.75309198201086[/C][/ROW]
[ROW][C]80[/C][C]327[/C][C]341.053137330405[/C][C]-14.0531373304053[/C][/ROW]
[ROW][C]81[/C][C]321[/C][C]337.393300057954[/C][C]-16.3933000579545[/C][/ROW]
[ROW][C]82[/C][C]317[/C][C]318.74908429431[/C][C]-1.74908429430985[/C][/ROW]
[ROW][C]83[/C][C]300[/C][C]304.945735761255[/C][C]-4.94573576125543[/C][/ROW]
[ROW][C]84[/C][C]304[/C][C]306.17434607908[/C][C]-2.17434607907967[/C][/ROW]
[ROW][C]85[/C][C]296[/C][C]300.634286378242[/C][C]-4.63428637824171[/C][/ROW]
[ROW][C]86[/C][C]296[/C][C]295.840771379659[/C][C]0.159228620340798[/C][/ROW]
[ROW][C]87[/C][C]283[/C][C]279.633698772397[/C][C]3.366301227603[/C][/ROW]
[ROW][C]88[/C][C]279[/C][C]276.235563968202[/C][C]2.76443603179825[/C][/ROW]
[ROW][C]89[/C][C]319[/C][C]308.44467943157[/C][C]10.55532056843[/C][/ROW]
[ROW][C]90[/C][C]295[/C][C]293.299233596488[/C][C]1.7007664035122[/C][/ROW]
[ROW][C]91[/C][C]255[/C][C]260.381729032973[/C][C]-5.38172903297345[/C][/ROW]
[ROW][C]92[/C][C]227[/C][C]232.300684944992[/C][C]-5.30068494499199[/C][/ROW]
[ROW][C]93[/C][C]228[/C][C]229.583381261816[/C][C]-1.58338126181627[/C][/ROW]
[ROW][C]94[/C][C]233[/C][C]225.303404918218[/C][C]7.69659508178216[/C][/ROW]
[ROW][C]95[/C][C]210[/C][C]213.349200152569[/C][C]-3.34920015256853[/C][/ROW]
[ROW][C]96[/C][C]219[/C][C]217.072410030458[/C][C]1.92758996954242[/C][/ROW]
[ROW][C]97[/C][C]212[/C][C]212.014348766512[/C][C]-0.0143487665121427[/C][/ROW]
[ROW][C]98[/C][C]209[/C][C]212.54503141966[/C][C]-3.54503141966003[/C][/ROW]
[ROW][C]99[/C][C]201[/C][C]197.266292843594[/C][C]3.7337071564063[/C][/ROW]
[ROW][C]100[/C][C]198[/C][C]194.084271105343[/C][C]3.91572889465706[/C][/ROW]
[ROW][C]101[/C][C]245[/C][C]231.984188406698[/C][C]13.0158115933016[/C][/ROW]
[ROW][C]102[/C][C]216[/C][C]213.01693315193[/C][C]2.98306684806994[/C][/ROW]
[ROW][C]103[/C][C]173[/C][C]176.958125888556[/C][C]-3.95812588855557[/C][/ROW]
[ROW][C]104[/C][C]144[/C][C]150.223465408778[/C][C]-6.22346540877811[/C][/ROW]
[ROW][C]105[/C][C]143[/C][C]150.10717204787[/C][C]-7.10717204786951[/C][/ROW]
[ROW][C]106[/C][C]152[/C][C]149.75601147652[/C][C]2.24398852348037[/C][/ROW]
[ROW][C]107[/C][C]127[/C][C]129.114317441323[/C][C]-2.11431744132344[/C][/ROW]
[ROW][C]108[/C][C]141[/C][C]136.766843022859[/C][C]4.23315697714131[/C][/ROW]
[ROW][C]109[/C][C]129[/C][C]131.768316473222[/C][C]-2.76831647322248[/C][/ROW]
[ROW][C]110[/C][C]127[/C][C]129.282219346418[/C][C]-2.28221934641766[/C][/ROW]
[ROW][C]111[/C][C]113[/C][C]119.202305010908[/C][C]-6.20230501090795[/C][/ROW]
[ROW][C]112[/C][C]117[/C][C]112.045388714387[/C][C]4.95461128561318[/C][/ROW]
[ROW][C]113[/C][C]174[/C][C]155.741717394231[/C][C]18.2582826057694[/C][/ROW]
[ROW][C]114[/C][C]143[/C][C]132.806460091939[/C][C]10.1935399080613[/C][/ROW]
[ROW][C]115[/C][C]103[/C][C]95.776313147972[/C][C]7.22368685202804[/C][/ROW]
[ROW][C]116[/C][C]81[/C][C]73.0045354692792[/C][C]7.99546453072082[/C][/ROW]
[ROW][C]117[/C][C]92[/C][C]79.5581913904612[/C][C]12.4418086095388[/C][/ROW]
[ROW][C]118[/C][C]104[/C][C]95.1283518023456[/C][C]8.87164819765435[/C][/ROW]
[ROW][C]119[/C][C]81[/C][C]77.3227636768203[/C][C]3.67723632317968[/C][/ROW]
[ROW][C]120[/C][C]89[/C][C]94.283819984435[/C][C]-5.28381998443496[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=78657&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=78657&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
13688698.392361111112-10.3923611111115
14679684.902081797484-5.90208179748402
15677680.176280501588-3.17628050158783
16673674.613944074414-1.61394407441389
17694695.168367346843-1.1683673468433
18690691.424464403764-1.42446440376432
19673670.7625153826252.23748461737478
20659659.596512633478-0.596512633478483
21657658.669716063091-1.66971606309073
22654656.368901580986-2.36890158098629
23644654.723507518725-10.7235075187252
24643650.38528651341-7.38528651340994
25638634.8755211921743.12447880782577
26626627.938899260585-1.93889926058478
27621625.14795665825-4.14795665824988
28615618.837047553824-3.83704755382394
29640637.3674239770552.63257602294527
30633633.70713348529-0.707133485290683
31620614.3453240258325.65467597416762
32610601.7396683503088.26033164969238
33601602.994136681446-1.99413668144632
34595599.49959347137-4.49959347136951
35585591.188798507169-6.18879850716928
36584590.130056430245-6.13005643024474
37580581.047698397987-1.04769839798746
38574568.7304626561115.26953734388906
39560567.088716376729-7.08871637672928
40550559.3564116933-9.35641169329995
41580578.9467732780931.05322672190709
42569571.834034522757-2.83403452275684
43551554.615179000695-3.61517900069487
44536538.630604842518-2.63060484251844
45535527.5176922252147.48230777478591
46526524.7874020181211.21259798187907
47517516.5399843676570.460015632343129
48512517.29286799924-5.29286799923955
49510510.852059573827-0.852059573827432
50501501.687412756266-0.687412756266042
51496489.1315390881546.86846091184623
52491485.0801169572715.91988304272934
53524517.3197564126856.68024358731498
54514510.6439028184483.3560971815524
55495496.269843131521-1.2698431315207
56479482.815520472513-3.8155204725125
57479478.3585668345880.641433165412195
58467469.766359294742-2.76635929474162
59451459.946790759489-8.9467907594888
60459453.5112342304655.48876576953495
61461454.4954635833246.50453641667639
62460449.16333977575810.8366602242417
63452447.1215799305794.8784200694206
64449443.0274251689885.97257483101197
65483477.0662082577565.93379174224356
66470469.3530551704310.646944829568554
67442452.25237432666-10.2523743266601
68419434.458996661324-15.4589966613245
69419428.334101003334-9.33410100333401
70406413.457831128752-7.45783112875159
71393397.505653553361-4.50565355336096
72396401.278533359715-5.27853335971474
73390397.838674058958-7.8386740589578
74389388.0212865886620.978713411337651
75373376.5067066705-3.5067066704998
76371367.411849798453.58815020155026
77407397.990520150829.00947984918042
78391385.8999734992835.10002650071704
79357361.753091982011-4.75309198201086
80327341.053137330405-14.0531373304053
81321337.393300057954-16.3933000579545
82317318.74908429431-1.74908429430985
83300304.945735761255-4.94573576125543
84304306.17434607908-2.17434607907967
85296300.634286378242-4.63428637824171
86296295.8407713796590.159228620340798
87283279.6336987723973.366301227603
88279276.2355639682022.76443603179825
89319308.4446794315710.55532056843
90295293.2992335964881.7007664035122
91255260.381729032973-5.38172903297345
92227232.300684944992-5.30068494499199
93228229.583381261816-1.58338126181627
94233225.3034049182187.69659508178216
95210213.349200152569-3.34920015256853
96219217.0724100304581.92758996954242
97212212.014348766512-0.0143487665121427
98209212.54503141966-3.54503141966003
99201197.2662928435943.7337071564063
100198194.0842711053433.91572889465706
101245231.98418840669813.0158115933016
102216213.016933151932.98306684806994
103173176.958125888556-3.95812588855557
104144150.223465408778-6.22346540877811
105143150.10717204787-7.10717204786951
106152149.756011476522.24398852348037
107127129.114317441323-2.11431744132344
108141136.7668430228594.23315697714131
109129131.768316473222-2.76831647322248
110127129.282219346418-2.28221934641766
111113119.202305010908-6.20230501090795
112117112.0453887143874.95461128561318
113174155.74171739423118.2582826057694
114143132.80646009193910.1935399080613
11510395.7763131479727.22368685202804
1168173.00453546927927.99546453072082
1179279.558191390461212.4418086095388
11810495.12835180234568.87164819765435
1198177.32276367682033.67723632317968
1208994.283819984435-5.28381998443496







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
12184.025019544200571.767024419902896.283014668498
12285.77294567972772.388463990013399.1574273694406
12377.161481230157162.510175607182491.8127868531318
12482.486683049532866.440122007804298.5332440912614
125135.377295911256117.818170014486152.936421808027
126102.5476775510683.3685858841437121.726769217976
12761.391988969953740.494129181785282.2898487581222
12837.589999399540814.881932117964360.2980666811172
12944.669115647856520.065673963491669.2725573322214
13053.54942246006126.970783092854980.1280618272672
13129.03594558331930.40685266920842357.6650384974302
13238.84832257830518.0974449995050869.5992001571051

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
121 & 84.0250195442005 & 71.7670244199028 & 96.283014668498 \tabularnewline
122 & 85.772945679727 & 72.3884639900133 & 99.1574273694406 \tabularnewline
123 & 77.1614812301571 & 62.5101756071824 & 91.8127868531318 \tabularnewline
124 & 82.4866830495328 & 66.4401220078042 & 98.5332440912614 \tabularnewline
125 & 135.377295911256 & 117.818170014486 & 152.936421808027 \tabularnewline
126 & 102.54767755106 & 83.3685858841437 & 121.726769217976 \tabularnewline
127 & 61.3919889699537 & 40.4941291817852 & 82.2898487581222 \tabularnewline
128 & 37.5899993995408 & 14.8819321179643 & 60.2980666811172 \tabularnewline
129 & 44.6691156478565 & 20.0656739634916 & 69.2725573322214 \tabularnewline
130 & 53.549422460061 & 26.9707830928549 & 80.1280618272672 \tabularnewline
131 & 29.0359455833193 & 0.406852669208423 & 57.6650384974302 \tabularnewline
132 & 38.8483225783051 & 8.09744499950508 & 69.5992001571051 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=78657&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]121[/C][C]84.0250195442005[/C][C]71.7670244199028[/C][C]96.283014668498[/C][/ROW]
[ROW][C]122[/C][C]85.772945679727[/C][C]72.3884639900133[/C][C]99.1574273694406[/C][/ROW]
[ROW][C]123[/C][C]77.1614812301571[/C][C]62.5101756071824[/C][C]91.8127868531318[/C][/ROW]
[ROW][C]124[/C][C]82.4866830495328[/C][C]66.4401220078042[/C][C]98.5332440912614[/C][/ROW]
[ROW][C]125[/C][C]135.377295911256[/C][C]117.818170014486[/C][C]152.936421808027[/C][/ROW]
[ROW][C]126[/C][C]102.54767755106[/C][C]83.3685858841437[/C][C]121.726769217976[/C][/ROW]
[ROW][C]127[/C][C]61.3919889699537[/C][C]40.4941291817852[/C][C]82.2898487581222[/C][/ROW]
[ROW][C]128[/C][C]37.5899993995408[/C][C]14.8819321179643[/C][C]60.2980666811172[/C][/ROW]
[ROW][C]129[/C][C]44.6691156478565[/C][C]20.0656739634916[/C][C]69.2725573322214[/C][/ROW]
[ROW][C]130[/C][C]53.549422460061[/C][C]26.9707830928549[/C][C]80.1280618272672[/C][/ROW]
[ROW][C]131[/C][C]29.0359455833193[/C][C]0.406852669208423[/C][C]57.6650384974302[/C][/ROW]
[ROW][C]132[/C][C]38.8483225783051[/C][C]8.09744499950508[/C][C]69.5992001571051[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=78657&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=78657&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
12184.025019544200571.767024419902896.283014668498
12285.77294567972772.388463990013399.1574273694406
12377.161481230157162.510175607182491.8127868531318
12482.486683049532866.440122007804298.5332440912614
125135.377295911256117.818170014486152.936421808027
126102.5476775510683.3685858841437121.726769217976
12761.391988969953740.494129181785282.2898487581222
12837.589999399540814.881932117964360.2980666811172
12944.669115647856520.065673963491669.2725573322214
13053.54942246006126.970783092854980.1280618272672
13129.03594558331930.40685266920842357.6650384974302
13238.84832257830518.0974449995050869.5992001571051



Parameters (Session):
par1 = 12 ; par2 = Triple ; par3 = additive ;
Parameters (R input):
par1 = 12 ; par2 = Triple ; par3 = additive ;
R code (references can be found in the software module):
par1 <- as.numeric(par1)
if (par2 == 'Single') K <- 1
if (par2 == 'Double') K <- 2
if (par2 == 'Triple') K <- par1
nx <- length(x)
nxmK <- nx - K
x <- ts(x, frequency = par1)
if (par2 == 'Single') fit <- HoltWinters(x, gamma=F, beta=F)
if (par2 == 'Double') fit <- HoltWinters(x, gamma=F)
if (par2 == 'Triple') fit <- HoltWinters(x, seasonal=par3)
fit
myresid <- x - fit$fitted[,'xhat']
bitmap(file='test1.png')
op <- par(mfrow=c(2,1))
plot(fit,ylab='Observed (black) / Fitted (red)',main='Interpolation Fit of Exponential Smoothing')
plot(myresid,ylab='Residuals',main='Interpolation Prediction Errors')
par(op)
dev.off()
bitmap(file='test2.png')
p <- predict(fit, par1, prediction.interval=TRUE)
np <- length(p[,1])
plot(fit,p,ylab='Observed (black) / Fitted (red)',main='Extrapolation Fit of Exponential Smoothing')
dev.off()
bitmap(file='test3.png')
op <- par(mfrow = c(2,2))
acf(as.numeric(myresid),lag.max = nx/2,main='Residual ACF')
spectrum(myresid,main='Residals Periodogram')
cpgram(myresid,main='Residal Cumulative Periodogram')
qqnorm(myresid,main='Residual Normal QQ Plot')
qqline(myresid)
par(op)
dev.off()
load(file='createtable')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Estimated Parameters of Exponential Smoothing',2,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'Parameter',header=TRUE)
a<-table.element(a,'Value',header=TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'alpha',header=TRUE)
a<-table.element(a,fit$alpha)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'beta',header=TRUE)
a<-table.element(a,fit$beta)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'gamma',header=TRUE)
a<-table.element(a,fit$gamma)
a<-table.row.end(a)
a<-table.end(a)
table.save(a,file='mytable.tab')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Interpolation Forecasts of Exponential Smoothing',4,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'t',header=TRUE)
a<-table.element(a,'Observed',header=TRUE)
a<-table.element(a,'Fitted',header=TRUE)
a<-table.element(a,'Residuals',header=TRUE)
a<-table.row.end(a)
for (i in 1:nxmK) {
a<-table.row.start(a)
a<-table.element(a,i+K,header=TRUE)
a<-table.element(a,x[i+K])
a<-table.element(a,fit$fitted[i,'xhat'])
a<-table.element(a,myresid[i])
a<-table.row.end(a)
}
a<-table.end(a)
table.save(a,file='mytable1.tab')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Extrapolation Forecasts of Exponential Smoothing',4,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'t',header=TRUE)
a<-table.element(a,'Forecast',header=TRUE)
a<-table.element(a,'95% Lower Bound',header=TRUE)
a<-table.element(a,'95% Upper Bound',header=TRUE)
a<-table.row.end(a)
for (i in 1:np) {
a<-table.row.start(a)
a<-table.element(a,nx+i,header=TRUE)
a<-table.element(a,p[i,'fit'])
a<-table.element(a,p[i,'lwr'])
a<-table.element(a,p[i,'upr'])
a<-table.row.end(a)
}
a<-table.end(a)
table.save(a,file='mytable2.tab')