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Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationMon, 01 Aug 2011 05:35:03 -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/01/t13121915204mkscz4o0q24qt3.htm/, Retrieved Mon, 13 May 2024 21:10:34 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=123235, Retrieved Mon, 13 May 2024 21:10:34 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywordsvicky koopmans
Estimated Impact150
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [tijdreeks2-stap27] [2011-08-01 09:35:03] [30681199eb2b91d06bf445c1ee7d20a2] [Current]
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Dataseries X:
700
700
620
680
700
670
660
730
680
680
650
800
660
710
660
590
660
710
620
700
690
680
640
810
620
700
720
620
630
680
670
720
660
630
620
810
540
690
720
620
650
690
660
700
630
590
570
760
500
660
750
680
710
620
640
720
680
580
530
740
480
640
690
600
640
580
690
690
720
550
510
680
450
560
730
650
680
580
750
670
670
590
480
810
350
570
710
650
710
510
800
680
660
620
580
830
480
550
720
620
730
520
870
660
650
620
560
820




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time3 seconds
R Server'AstonUniversity' @ aston.wessa.net

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input & view raw input (R code)  \tabularnewline
Raw Output & view raw output of R engine  \tabularnewline
Computing time & 3 seconds \tabularnewline
R Server & 'AstonUniversity' @ aston.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=123235&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]3 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'AstonUniversity' @ aston.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=123235&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=123235&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 time3 seconds
R Server'AstonUniversity' @ aston.wessa.net







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.0189194452531731
beta0.117730865630558
gamma0.916097468622387

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.0189194452531731 \tabularnewline
beta & 0.117730865630558 \tabularnewline
gamma & 0.916097468622387 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=123235&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]0.0189194452531731[/C][/ROW]
[ROW][C]beta[/C][C]0.117730865630558[/C][/ROW]
[ROW][C]gamma[/C][C]0.916097468622387[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=123235&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=123235&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
alpha0.0189194452531731
beta0.117730865630558
gamma0.916097468622387







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
13660665.712087368267-5.7120873682668
14710717.897956695867-7.89795669586738
15660666.880326223937-6.88032622393678
16590594.632196703517-4.63219670351702
17660664.322443991852-4.32244399185242
18710713.292309418252-3.29230941825222
19620651.788020516128-31.7880205161282
20700720.189947241653-20.189947241653
21690667.15903843159522.8409615684049
22680668.34726141326611.6527385867345
23640642.957303750624-2.95730375062385
24810789.77915462166220.2208453783381
25620645.677395421156-25.6773954211557
26700694.1951793522085.8048206477921
27720645.37814668360374.621853316397
28620578.20979544384441.7902045561563
29630647.88586080217-17.8858608021693
30680696.716440053245-16.7164400532452
31670611.13641474441458.8635852555863
32720690.70233346655729.2976665334427
33660677.935897264537-17.9358972645373
34630668.79874047899-38.7987404789906
35620630.18486073803-10.1848607380299
36810795.28532618192914.7146738180713
37540612.949919798361-72.9499197983612
38690687.664727648352.33527235164968
39720700.37191743176319.6280825682373
40620604.37507648919615.6249235108037
41650619.52146856667830.4785314333221
42690669.41732130217320.5826786978274
43660652.7624167062947.2375832937056
44700703.765217612419-3.76521761241895
45630648.889249355582-18.8892493555825
46590621.381051132518-31.381051132518
47570608.768540535767-38.7685405357674
48760791.627328764036-31.627328764036
49500535.010784082175-35.0107840821747
50660674.854029575538-14.8540295755381
51750701.91362679389348.0863732061069
52680604.87048078160175.1295192183991
53710633.8895334664876.1104665335193
54620675.080000891621-55.080000891621
55640645.527485199658-5.52748519965769
56720685.42291251876634.5770874812337
57680619.04073792381360.959262076187
58580582.629070054424-2.62907005442355
59530564.398185089831-34.3981850898307
60740750.882876895005-10.8828768950048
61480495.842897781356-15.8428977813556
62640652.174183232906-12.1741832329061
63690734.998906552494-44.9989065524941
64600661.665926988434-61.6659269884335
65640688.078787635392-48.078787635392
66580610.348280079387-30.3482800793868
67690625.02603545452564.9739645454753
68690700.320441599296-10.3204415992957
69720657.38337335812862.6166266418725
70550565.852682138072-15.8526821380716
71510519.65857581516-9.65857581516036
72680722.164921486979-42.1649214869785
73450468.621275269283-18.6212752692827
74560623.47707816152-63.4770781615197
75730673.67388272469556.3261172753054
76650589.28870694325560.7112930567453
77680629.18441933794550.8155806620554
78580570.7129109082449.28708909175555
79750669.99176934213480.0082306578662
80670678.103853104641-8.10385310464062
81670700.583971105932-30.5839711059322
82590540.24480565523649.7551943447637
83480501.824449333845-21.8244493338454
84810671.926086090181138.073913909819
85350446.411615100297-96.4116151002968
86570557.94103462518612.0589653748135
87710715.81044097157-5.81044097156962
88650635.60410352905714.3958964709432
89710665.57119452653544.4288054734651
90510571.266511215171-61.2665112151709
91800730.18905367369569.8109463263048
92680660.16803503390919.8319649660912
93660663.067845919735-3.06784591973485
94620576.80219722938543.197802770615
95580475.509728511058104.490271488942
96830789.11550418029540.8844958197051
97480355.657738706614124.342261293386
98550569.915566345143-19.9155663451435
99720712.4416083495397.5583916504612
100620651.577341748562-31.5773417485619
101730708.91076492335321.089235076647
102520519.0244931492340.975506850766465
103870800.35659419922769.6434058007727
104660685.484916175435-25.4849161754348
105650667.808055477611-17.8080554776111
106620623.242426622769-3.24242662276947
107560576.01833858738-16.0183385873806
108820832.711271742123-12.7112717421231

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 660 & 665.712087368267 & -5.7120873682668 \tabularnewline
14 & 710 & 717.897956695867 & -7.89795669586738 \tabularnewline
15 & 660 & 666.880326223937 & -6.88032622393678 \tabularnewline
16 & 590 & 594.632196703517 & -4.63219670351702 \tabularnewline
17 & 660 & 664.322443991852 & -4.32244399185242 \tabularnewline
18 & 710 & 713.292309418252 & -3.29230941825222 \tabularnewline
19 & 620 & 651.788020516128 & -31.7880205161282 \tabularnewline
20 & 700 & 720.189947241653 & -20.189947241653 \tabularnewline
21 & 690 & 667.159038431595 & 22.8409615684049 \tabularnewline
22 & 680 & 668.347261413266 & 11.6527385867345 \tabularnewline
23 & 640 & 642.957303750624 & -2.95730375062385 \tabularnewline
24 & 810 & 789.779154621662 & 20.2208453783381 \tabularnewline
25 & 620 & 645.677395421156 & -25.6773954211557 \tabularnewline
26 & 700 & 694.195179352208 & 5.8048206477921 \tabularnewline
27 & 720 & 645.378146683603 & 74.621853316397 \tabularnewline
28 & 620 & 578.209795443844 & 41.7902045561563 \tabularnewline
29 & 630 & 647.88586080217 & -17.8858608021693 \tabularnewline
30 & 680 & 696.716440053245 & -16.7164400532452 \tabularnewline
31 & 670 & 611.136414744414 & 58.8635852555863 \tabularnewline
32 & 720 & 690.702333466557 & 29.2976665334427 \tabularnewline
33 & 660 & 677.935897264537 & -17.9358972645373 \tabularnewline
34 & 630 & 668.79874047899 & -38.7987404789906 \tabularnewline
35 & 620 & 630.18486073803 & -10.1848607380299 \tabularnewline
36 & 810 & 795.285326181929 & 14.7146738180713 \tabularnewline
37 & 540 & 612.949919798361 & -72.9499197983612 \tabularnewline
38 & 690 & 687.66472764835 & 2.33527235164968 \tabularnewline
39 & 720 & 700.371917431763 & 19.6280825682373 \tabularnewline
40 & 620 & 604.375076489196 & 15.6249235108037 \tabularnewline
41 & 650 & 619.521468566678 & 30.4785314333221 \tabularnewline
42 & 690 & 669.417321302173 & 20.5826786978274 \tabularnewline
43 & 660 & 652.762416706294 & 7.2375832937056 \tabularnewline
44 & 700 & 703.765217612419 & -3.76521761241895 \tabularnewline
45 & 630 & 648.889249355582 & -18.8892493555825 \tabularnewline
46 & 590 & 621.381051132518 & -31.381051132518 \tabularnewline
47 & 570 & 608.768540535767 & -38.7685405357674 \tabularnewline
48 & 760 & 791.627328764036 & -31.627328764036 \tabularnewline
49 & 500 & 535.010784082175 & -35.0107840821747 \tabularnewline
50 & 660 & 674.854029575538 & -14.8540295755381 \tabularnewline
51 & 750 & 701.913626793893 & 48.0863732061069 \tabularnewline
52 & 680 & 604.870480781601 & 75.1295192183991 \tabularnewline
53 & 710 & 633.88953346648 & 76.1104665335193 \tabularnewline
54 & 620 & 675.080000891621 & -55.080000891621 \tabularnewline
55 & 640 & 645.527485199658 & -5.52748519965769 \tabularnewline
56 & 720 & 685.422912518766 & 34.5770874812337 \tabularnewline
57 & 680 & 619.040737923813 & 60.959262076187 \tabularnewline
58 & 580 & 582.629070054424 & -2.62907005442355 \tabularnewline
59 & 530 & 564.398185089831 & -34.3981850898307 \tabularnewline
60 & 740 & 750.882876895005 & -10.8828768950048 \tabularnewline
61 & 480 & 495.842897781356 & -15.8428977813556 \tabularnewline
62 & 640 & 652.174183232906 & -12.1741832329061 \tabularnewline
63 & 690 & 734.998906552494 & -44.9989065524941 \tabularnewline
64 & 600 & 661.665926988434 & -61.6659269884335 \tabularnewline
65 & 640 & 688.078787635392 & -48.078787635392 \tabularnewline
66 & 580 & 610.348280079387 & -30.3482800793868 \tabularnewline
67 & 690 & 625.026035454525 & 64.9739645454753 \tabularnewline
68 & 690 & 700.320441599296 & -10.3204415992957 \tabularnewline
69 & 720 & 657.383373358128 & 62.6166266418725 \tabularnewline
70 & 550 & 565.852682138072 & -15.8526821380716 \tabularnewline
71 & 510 & 519.65857581516 & -9.65857581516036 \tabularnewline
72 & 680 & 722.164921486979 & -42.1649214869785 \tabularnewline
73 & 450 & 468.621275269283 & -18.6212752692827 \tabularnewline
74 & 560 & 623.47707816152 & -63.4770781615197 \tabularnewline
75 & 730 & 673.673882724695 & 56.3261172753054 \tabularnewline
76 & 650 & 589.288706943255 & 60.7112930567453 \tabularnewline
77 & 680 & 629.184419337945 & 50.8155806620554 \tabularnewline
78 & 580 & 570.712910908244 & 9.28708909175555 \tabularnewline
79 & 750 & 669.991769342134 & 80.0082306578662 \tabularnewline
80 & 670 & 678.103853104641 & -8.10385310464062 \tabularnewline
81 & 670 & 700.583971105932 & -30.5839711059322 \tabularnewline
82 & 590 & 540.244805655236 & 49.7551943447637 \tabularnewline
83 & 480 & 501.824449333845 & -21.8244493338454 \tabularnewline
84 & 810 & 671.926086090181 & 138.073913909819 \tabularnewline
85 & 350 & 446.411615100297 & -96.4116151002968 \tabularnewline
86 & 570 & 557.941034625186 & 12.0589653748135 \tabularnewline
87 & 710 & 715.81044097157 & -5.81044097156962 \tabularnewline
88 & 650 & 635.604103529057 & 14.3958964709432 \tabularnewline
89 & 710 & 665.571194526535 & 44.4288054734651 \tabularnewline
90 & 510 & 571.266511215171 & -61.2665112151709 \tabularnewline
91 & 800 & 730.189053673695 & 69.8109463263048 \tabularnewline
92 & 680 & 660.168035033909 & 19.8319649660912 \tabularnewline
93 & 660 & 663.067845919735 & -3.06784591973485 \tabularnewline
94 & 620 & 576.802197229385 & 43.197802770615 \tabularnewline
95 & 580 & 475.509728511058 & 104.490271488942 \tabularnewline
96 & 830 & 789.115504180295 & 40.8844958197051 \tabularnewline
97 & 480 & 355.657738706614 & 124.342261293386 \tabularnewline
98 & 550 & 569.915566345143 & -19.9155663451435 \tabularnewline
99 & 720 & 712.441608349539 & 7.5583916504612 \tabularnewline
100 & 620 & 651.577341748562 & -31.5773417485619 \tabularnewline
101 & 730 & 708.910764923353 & 21.089235076647 \tabularnewline
102 & 520 & 519.024493149234 & 0.975506850766465 \tabularnewline
103 & 870 & 800.356594199227 & 69.6434058007727 \tabularnewline
104 & 660 & 685.484916175435 & -25.4849161754348 \tabularnewline
105 & 650 & 667.808055477611 & -17.8080554776111 \tabularnewline
106 & 620 & 623.242426622769 & -3.24242662276947 \tabularnewline
107 & 560 & 576.01833858738 & -16.0183385873806 \tabularnewline
108 & 820 & 832.711271742123 & -12.7112717421231 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=123235&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]660[/C][C]665.712087368267[/C][C]-5.7120873682668[/C][/ROW]
[ROW][C]14[/C][C]710[/C][C]717.897956695867[/C][C]-7.89795669586738[/C][/ROW]
[ROW][C]15[/C][C]660[/C][C]666.880326223937[/C][C]-6.88032622393678[/C][/ROW]
[ROW][C]16[/C][C]590[/C][C]594.632196703517[/C][C]-4.63219670351702[/C][/ROW]
[ROW][C]17[/C][C]660[/C][C]664.322443991852[/C][C]-4.32244399185242[/C][/ROW]
[ROW][C]18[/C][C]710[/C][C]713.292309418252[/C][C]-3.29230941825222[/C][/ROW]
[ROW][C]19[/C][C]620[/C][C]651.788020516128[/C][C]-31.7880205161282[/C][/ROW]
[ROW][C]20[/C][C]700[/C][C]720.189947241653[/C][C]-20.189947241653[/C][/ROW]
[ROW][C]21[/C][C]690[/C][C]667.159038431595[/C][C]22.8409615684049[/C][/ROW]
[ROW][C]22[/C][C]680[/C][C]668.347261413266[/C][C]11.6527385867345[/C][/ROW]
[ROW][C]23[/C][C]640[/C][C]642.957303750624[/C][C]-2.95730375062385[/C][/ROW]
[ROW][C]24[/C][C]810[/C][C]789.779154621662[/C][C]20.2208453783381[/C][/ROW]
[ROW][C]25[/C][C]620[/C][C]645.677395421156[/C][C]-25.6773954211557[/C][/ROW]
[ROW][C]26[/C][C]700[/C][C]694.195179352208[/C][C]5.8048206477921[/C][/ROW]
[ROW][C]27[/C][C]720[/C][C]645.378146683603[/C][C]74.621853316397[/C][/ROW]
[ROW][C]28[/C][C]620[/C][C]578.209795443844[/C][C]41.7902045561563[/C][/ROW]
[ROW][C]29[/C][C]630[/C][C]647.88586080217[/C][C]-17.8858608021693[/C][/ROW]
[ROW][C]30[/C][C]680[/C][C]696.716440053245[/C][C]-16.7164400532452[/C][/ROW]
[ROW][C]31[/C][C]670[/C][C]611.136414744414[/C][C]58.8635852555863[/C][/ROW]
[ROW][C]32[/C][C]720[/C][C]690.702333466557[/C][C]29.2976665334427[/C][/ROW]
[ROW][C]33[/C][C]660[/C][C]677.935897264537[/C][C]-17.9358972645373[/C][/ROW]
[ROW][C]34[/C][C]630[/C][C]668.79874047899[/C][C]-38.7987404789906[/C][/ROW]
[ROW][C]35[/C][C]620[/C][C]630.18486073803[/C][C]-10.1848607380299[/C][/ROW]
[ROW][C]36[/C][C]810[/C][C]795.285326181929[/C][C]14.7146738180713[/C][/ROW]
[ROW][C]37[/C][C]540[/C][C]612.949919798361[/C][C]-72.9499197983612[/C][/ROW]
[ROW][C]38[/C][C]690[/C][C]687.66472764835[/C][C]2.33527235164968[/C][/ROW]
[ROW][C]39[/C][C]720[/C][C]700.371917431763[/C][C]19.6280825682373[/C][/ROW]
[ROW][C]40[/C][C]620[/C][C]604.375076489196[/C][C]15.6249235108037[/C][/ROW]
[ROW][C]41[/C][C]650[/C][C]619.521468566678[/C][C]30.4785314333221[/C][/ROW]
[ROW][C]42[/C][C]690[/C][C]669.417321302173[/C][C]20.5826786978274[/C][/ROW]
[ROW][C]43[/C][C]660[/C][C]652.762416706294[/C][C]7.2375832937056[/C][/ROW]
[ROW][C]44[/C][C]700[/C][C]703.765217612419[/C][C]-3.76521761241895[/C][/ROW]
[ROW][C]45[/C][C]630[/C][C]648.889249355582[/C][C]-18.8892493555825[/C][/ROW]
[ROW][C]46[/C][C]590[/C][C]621.381051132518[/C][C]-31.381051132518[/C][/ROW]
[ROW][C]47[/C][C]570[/C][C]608.768540535767[/C][C]-38.7685405357674[/C][/ROW]
[ROW][C]48[/C][C]760[/C][C]791.627328764036[/C][C]-31.627328764036[/C][/ROW]
[ROW][C]49[/C][C]500[/C][C]535.010784082175[/C][C]-35.0107840821747[/C][/ROW]
[ROW][C]50[/C][C]660[/C][C]674.854029575538[/C][C]-14.8540295755381[/C][/ROW]
[ROW][C]51[/C][C]750[/C][C]701.913626793893[/C][C]48.0863732061069[/C][/ROW]
[ROW][C]52[/C][C]680[/C][C]604.870480781601[/C][C]75.1295192183991[/C][/ROW]
[ROW][C]53[/C][C]710[/C][C]633.88953346648[/C][C]76.1104665335193[/C][/ROW]
[ROW][C]54[/C][C]620[/C][C]675.080000891621[/C][C]-55.080000891621[/C][/ROW]
[ROW][C]55[/C][C]640[/C][C]645.527485199658[/C][C]-5.52748519965769[/C][/ROW]
[ROW][C]56[/C][C]720[/C][C]685.422912518766[/C][C]34.5770874812337[/C][/ROW]
[ROW][C]57[/C][C]680[/C][C]619.040737923813[/C][C]60.959262076187[/C][/ROW]
[ROW][C]58[/C][C]580[/C][C]582.629070054424[/C][C]-2.62907005442355[/C][/ROW]
[ROW][C]59[/C][C]530[/C][C]564.398185089831[/C][C]-34.3981850898307[/C][/ROW]
[ROW][C]60[/C][C]740[/C][C]750.882876895005[/C][C]-10.8828768950048[/C][/ROW]
[ROW][C]61[/C][C]480[/C][C]495.842897781356[/C][C]-15.8428977813556[/C][/ROW]
[ROW][C]62[/C][C]640[/C][C]652.174183232906[/C][C]-12.1741832329061[/C][/ROW]
[ROW][C]63[/C][C]690[/C][C]734.998906552494[/C][C]-44.9989065524941[/C][/ROW]
[ROW][C]64[/C][C]600[/C][C]661.665926988434[/C][C]-61.6659269884335[/C][/ROW]
[ROW][C]65[/C][C]640[/C][C]688.078787635392[/C][C]-48.078787635392[/C][/ROW]
[ROW][C]66[/C][C]580[/C][C]610.348280079387[/C][C]-30.3482800793868[/C][/ROW]
[ROW][C]67[/C][C]690[/C][C]625.026035454525[/C][C]64.9739645454753[/C][/ROW]
[ROW][C]68[/C][C]690[/C][C]700.320441599296[/C][C]-10.3204415992957[/C][/ROW]
[ROW][C]69[/C][C]720[/C][C]657.383373358128[/C][C]62.6166266418725[/C][/ROW]
[ROW][C]70[/C][C]550[/C][C]565.852682138072[/C][C]-15.8526821380716[/C][/ROW]
[ROW][C]71[/C][C]510[/C][C]519.65857581516[/C][C]-9.65857581516036[/C][/ROW]
[ROW][C]72[/C][C]680[/C][C]722.164921486979[/C][C]-42.1649214869785[/C][/ROW]
[ROW][C]73[/C][C]450[/C][C]468.621275269283[/C][C]-18.6212752692827[/C][/ROW]
[ROW][C]74[/C][C]560[/C][C]623.47707816152[/C][C]-63.4770781615197[/C][/ROW]
[ROW][C]75[/C][C]730[/C][C]673.673882724695[/C][C]56.3261172753054[/C][/ROW]
[ROW][C]76[/C][C]650[/C][C]589.288706943255[/C][C]60.7112930567453[/C][/ROW]
[ROW][C]77[/C][C]680[/C][C]629.184419337945[/C][C]50.8155806620554[/C][/ROW]
[ROW][C]78[/C][C]580[/C][C]570.712910908244[/C][C]9.28708909175555[/C][/ROW]
[ROW][C]79[/C][C]750[/C][C]669.991769342134[/C][C]80.0082306578662[/C][/ROW]
[ROW][C]80[/C][C]670[/C][C]678.103853104641[/C][C]-8.10385310464062[/C][/ROW]
[ROW][C]81[/C][C]670[/C][C]700.583971105932[/C][C]-30.5839711059322[/C][/ROW]
[ROW][C]82[/C][C]590[/C][C]540.244805655236[/C][C]49.7551943447637[/C][/ROW]
[ROW][C]83[/C][C]480[/C][C]501.824449333845[/C][C]-21.8244493338454[/C][/ROW]
[ROW][C]84[/C][C]810[/C][C]671.926086090181[/C][C]138.073913909819[/C][/ROW]
[ROW][C]85[/C][C]350[/C][C]446.411615100297[/C][C]-96.4116151002968[/C][/ROW]
[ROW][C]86[/C][C]570[/C][C]557.941034625186[/C][C]12.0589653748135[/C][/ROW]
[ROW][C]87[/C][C]710[/C][C]715.81044097157[/C][C]-5.81044097156962[/C][/ROW]
[ROW][C]88[/C][C]650[/C][C]635.604103529057[/C][C]14.3958964709432[/C][/ROW]
[ROW][C]89[/C][C]710[/C][C]665.571194526535[/C][C]44.4288054734651[/C][/ROW]
[ROW][C]90[/C][C]510[/C][C]571.266511215171[/C][C]-61.2665112151709[/C][/ROW]
[ROW][C]91[/C][C]800[/C][C]730.189053673695[/C][C]69.8109463263048[/C][/ROW]
[ROW][C]92[/C][C]680[/C][C]660.168035033909[/C][C]19.8319649660912[/C][/ROW]
[ROW][C]93[/C][C]660[/C][C]663.067845919735[/C][C]-3.06784591973485[/C][/ROW]
[ROW][C]94[/C][C]620[/C][C]576.802197229385[/C][C]43.197802770615[/C][/ROW]
[ROW][C]95[/C][C]580[/C][C]475.509728511058[/C][C]104.490271488942[/C][/ROW]
[ROW][C]96[/C][C]830[/C][C]789.115504180295[/C][C]40.8844958197051[/C][/ROW]
[ROW][C]97[/C][C]480[/C][C]355.657738706614[/C][C]124.342261293386[/C][/ROW]
[ROW][C]98[/C][C]550[/C][C]569.915566345143[/C][C]-19.9155663451435[/C][/ROW]
[ROW][C]99[/C][C]720[/C][C]712.441608349539[/C][C]7.5583916504612[/C][/ROW]
[ROW][C]100[/C][C]620[/C][C]651.577341748562[/C][C]-31.5773417485619[/C][/ROW]
[ROW][C]101[/C][C]730[/C][C]708.910764923353[/C][C]21.089235076647[/C][/ROW]
[ROW][C]102[/C][C]520[/C][C]519.024493149234[/C][C]0.975506850766465[/C][/ROW]
[ROW][C]103[/C][C]870[/C][C]800.356594199227[/C][C]69.6434058007727[/C][/ROW]
[ROW][C]104[/C][C]660[/C][C]685.484916175435[/C][C]-25.4849161754348[/C][/ROW]
[ROW][C]105[/C][C]650[/C][C]667.808055477611[/C][C]-17.8080554776111[/C][/ROW]
[ROW][C]106[/C][C]620[/C][C]623.242426622769[/C][C]-3.24242662276947[/C][/ROW]
[ROW][C]107[/C][C]560[/C][C]576.01833858738[/C][C]-16.0183385873806[/C][/ROW]
[ROW][C]108[/C][C]820[/C][C]832.711271742123[/C][C]-12.7112717421231[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=123235&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=123235&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
13660665.712087368267-5.7120873682668
14710717.897956695867-7.89795669586738
15660666.880326223937-6.88032622393678
16590594.632196703517-4.63219670351702
17660664.322443991852-4.32244399185242
18710713.292309418252-3.29230941825222
19620651.788020516128-31.7880205161282
20700720.189947241653-20.189947241653
21690667.15903843159522.8409615684049
22680668.34726141326611.6527385867345
23640642.957303750624-2.95730375062385
24810789.77915462166220.2208453783381
25620645.677395421156-25.6773954211557
26700694.1951793522085.8048206477921
27720645.37814668360374.621853316397
28620578.20979544384441.7902045561563
29630647.88586080217-17.8858608021693
30680696.716440053245-16.7164400532452
31670611.13641474441458.8635852555863
32720690.70233346655729.2976665334427
33660677.935897264537-17.9358972645373
34630668.79874047899-38.7987404789906
35620630.18486073803-10.1848607380299
36810795.28532618192914.7146738180713
37540612.949919798361-72.9499197983612
38690687.664727648352.33527235164968
39720700.37191743176319.6280825682373
40620604.37507648919615.6249235108037
41650619.52146856667830.4785314333221
42690669.41732130217320.5826786978274
43660652.7624167062947.2375832937056
44700703.765217612419-3.76521761241895
45630648.889249355582-18.8892493555825
46590621.381051132518-31.381051132518
47570608.768540535767-38.7685405357674
48760791.627328764036-31.627328764036
49500535.010784082175-35.0107840821747
50660674.854029575538-14.8540295755381
51750701.91362679389348.0863732061069
52680604.87048078160175.1295192183991
53710633.8895334664876.1104665335193
54620675.080000891621-55.080000891621
55640645.527485199658-5.52748519965769
56720685.42291251876634.5770874812337
57680619.04073792381360.959262076187
58580582.629070054424-2.62907005442355
59530564.398185089831-34.3981850898307
60740750.882876895005-10.8828768950048
61480495.842897781356-15.8428977813556
62640652.174183232906-12.1741832329061
63690734.998906552494-44.9989065524941
64600661.665926988434-61.6659269884335
65640688.078787635392-48.078787635392
66580610.348280079387-30.3482800793868
67690625.02603545452564.9739645454753
68690700.320441599296-10.3204415992957
69720657.38337335812862.6166266418725
70550565.852682138072-15.8526821380716
71510519.65857581516-9.65857581516036
72680722.164921486979-42.1649214869785
73450468.621275269283-18.6212752692827
74560623.47707816152-63.4770781615197
75730673.67388272469556.3261172753054
76650589.28870694325560.7112930567453
77680629.18441933794550.8155806620554
78580570.7129109082449.28708909175555
79750669.99176934213480.0082306578662
80670678.103853104641-8.10385310464062
81670700.583971105932-30.5839711059322
82590540.24480565523649.7551943447637
83480501.824449333845-21.8244493338454
84810671.926086090181138.073913909819
85350446.411615100297-96.4116151002968
86570557.94103462518612.0589653748135
87710715.81044097157-5.81044097156962
88650635.60410352905714.3958964709432
89710665.57119452653544.4288054734651
90510571.266511215171-61.2665112151709
91800730.18905367369569.8109463263048
92680660.16803503390919.8319649660912
93660663.067845919735-3.06784591973485
94620576.80219722938543.197802770615
95580475.509728511058104.490271488942
96830789.11550418029540.8844958197051
97480355.657738706614124.342261293386
98550569.915566345143-19.9155663451435
99720712.4416083495397.5583916504612
100620651.577341748562-31.5773417485619
101730708.91076492335321.089235076647
102520519.0244931492340.975506850766465
103870800.35659419922769.6434058007727
104660685.484916175435-25.4849161754348
105650667.808055477611-17.8080554776111
106620623.242426622769-3.24242662276947
107560576.01833858738-16.0183385873806
108820832.711271742123-12.7112717421231







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
109470.268315239977393.61045289554546.926177584415
110552.514135205365475.828189118925629.200081291806
111720.323270981791643.572561328641797.073980634941
112623.931013765914547.173773116564700.688254415264
113729.421346930083652.573730328832806.268963531334
114520.700170840704443.917516561089597.482825120319
115864.093253038578786.977565593223941.208940483933
116662.265061014611585.2813411451739.248780884122
117651.850551187615574.808146721952728.892955653278
118620.627470900413543.550761472962697.704180327864
119561.886564792803484.819781275435638.953348310171
120822.086557781013-776.0486489373412420.22176449937

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
109 & 470.268315239977 & 393.61045289554 & 546.926177584415 \tabularnewline
110 & 552.514135205365 & 475.828189118925 & 629.200081291806 \tabularnewline
111 & 720.323270981791 & 643.572561328641 & 797.073980634941 \tabularnewline
112 & 623.931013765914 & 547.173773116564 & 700.688254415264 \tabularnewline
113 & 729.421346930083 & 652.573730328832 & 806.268963531334 \tabularnewline
114 & 520.700170840704 & 443.917516561089 & 597.482825120319 \tabularnewline
115 & 864.093253038578 & 786.977565593223 & 941.208940483933 \tabularnewline
116 & 662.265061014611 & 585.2813411451 & 739.248780884122 \tabularnewline
117 & 651.850551187615 & 574.808146721952 & 728.892955653278 \tabularnewline
118 & 620.627470900413 & 543.550761472962 & 697.704180327864 \tabularnewline
119 & 561.886564792803 & 484.819781275435 & 638.953348310171 \tabularnewline
120 & 822.086557781013 & -776.048648937341 & 2420.22176449937 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=123235&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]470.268315239977[/C][C]393.61045289554[/C][C]546.926177584415[/C][/ROW]
[ROW][C]110[/C][C]552.514135205365[/C][C]475.828189118925[/C][C]629.200081291806[/C][/ROW]
[ROW][C]111[/C][C]720.323270981791[/C][C]643.572561328641[/C][C]797.073980634941[/C][/ROW]
[ROW][C]112[/C][C]623.931013765914[/C][C]547.173773116564[/C][C]700.688254415264[/C][/ROW]
[ROW][C]113[/C][C]729.421346930083[/C][C]652.573730328832[/C][C]806.268963531334[/C][/ROW]
[ROW][C]114[/C][C]520.700170840704[/C][C]443.917516561089[/C][C]597.482825120319[/C][/ROW]
[ROW][C]115[/C][C]864.093253038578[/C][C]786.977565593223[/C][C]941.208940483933[/C][/ROW]
[ROW][C]116[/C][C]662.265061014611[/C][C]585.2813411451[/C][C]739.248780884122[/C][/ROW]
[ROW][C]117[/C][C]651.850551187615[/C][C]574.808146721952[/C][C]728.892955653278[/C][/ROW]
[ROW][C]118[/C][C]620.627470900413[/C][C]543.550761472962[/C][C]697.704180327864[/C][/ROW]
[ROW][C]119[/C][C]561.886564792803[/C][C]484.819781275435[/C][C]638.953348310171[/C][/ROW]
[ROW][C]120[/C][C]822.086557781013[/C][C]-776.048648937341[/C][C]2420.22176449937[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=123235&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=123235&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
109470.268315239977393.61045289554546.926177584415
110552.514135205365475.828189118925629.200081291806
111720.323270981791643.572561328641797.073980634941
112623.931013765914547.173773116564700.688254415264
113729.421346930083652.573730328832806.268963531334
114520.700170840704443.917516561089597.482825120319
115864.093253038578786.977565593223941.208940483933
116662.265061014611585.2813411451739.248780884122
117651.850551187615574.808146721952728.892955653278
118620.627470900413543.550761472962697.704180327864
119561.886564792803484.819781275435638.953348310171
120822.086557781013-776.0486489373412420.22176449937



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