Free Statistics

of Irreproducible Research!

Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationThu, 29 Jul 2010 12:07:54 +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/Jul/29/t1280405277bgorhoc3v4w8szg.htm/, Retrieved Sun, 28 Apr 2024 23:50:05 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=78168, Retrieved Sun, 28 Apr 2024 23:50:05 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywordsHabimana Christelle
Estimated Impact160
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [Standard Deviation-Mean Plot] [] [2010-05-26 18:42:57] [5a3034bcadf7735f2909fd8cdba599d5]
- RMPD    [Exponential Smoothing] [Tijdreeks 1 - Sta...] [2010-07-29 12:07:54] [ac302f869d0778eba7cafda3b14e71eb] [Current]
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Dataseries X:
900
899
898
896
916
915
900
890
891
891
892
894
896
889
878
883
901
897
881
866
867
866
862
871
865
856
847
859
870
872
856
839
829
825
822
827
822
812
810
816
820
823
810
793
777
772
765
765
753
742
736
740
742
742
728
707
699
696
689
692
673
653
642
648
654
653
630
609
598
601
592
591
568
538
523
530
529
534
513
491
480
478
462
461
437
411
400
405
395
407
385
366
349
343
332
327
306
276
269
268
260
274
247
226
212
199
188
179
155
124
117
116
105
112
86
64
53
42
32
24




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=78168&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=78168&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=78168&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
alpha0.768991824691135
beta0.729803955352783
gamma1

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.768991824691135 \tabularnewline
beta & 0.729803955352783 \tabularnewline
gamma & 1 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=78168&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]0.768991824691135[/C][/ROW]
[ROW][C]beta[/C][C]0.729803955352783[/C][/ROW]
[ROW][C]gamma[/C][C]1[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=78168&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=78168&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
alpha0.768991824691135
beta0.729803955352783
gamma1







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
13896903.770032051282-7.77003205128221
14889886.6124717802982.38752821970195
15878874.8142381818763.18576181812375
16883881.4593981857561.54060181424438
17901900.9540497864380.0459502135618095
18897897.241781061954-0.241781061954157
19881880.3392252638740.660774736125859
20866869.70989638307-3.70989638307083
21867865.3041807097161.69581929028436
22866865.1321324939820.867867506018456
23862865.602121557149-3.60212155714862
24871861.8215004705229.17849952947813
25865871.391894037613-6.3918940376135
26856860.792986846258-4.7929868462578
27847842.7799907236524.22000927634758
28859849.543462932099.45653706791052
29870878.925685014414-8.92568501441428
30872867.3583908033234.64160919667722
31856856.270800335272-0.270800335272043
32839845.243805159692-6.24380515969244
33829840.044603702055-11.0446037020552
34825822.6402210505352.35977894946518
35822816.8183646267245.18163537327587
36827821.2678605894915.73213941050903
37822821.1800519664590.819948033541323
38812817.13264328428-5.13264328428022
39810801.3862005066568.61379949334412
40816815.6496661807630.350333819237335
41820831.583850658154-11.5838506581536
42823817.415808659375.58419134062945
43810802.756442985457.24355701454988
44793797.183464927787-4.1834649277871
45777794.671265536733-17.6712655367334
46772773.760226477783-1.76022647778268
47765761.6024601170913.3975398829092
48765759.9863827437615.01361725623906
49753752.9872464972280.0127535027721706
50742741.2669726806050.733027319395319
51736730.8215736372085.17842636279181
52740736.2212106562253.77878934377543
53742749.645923301676-7.64592330167602
54742742.293058489909-0.293058489908503
55728720.0200573419177.97994265808313
56707709.309482295501-2.30948229550097
57699703.110135911258-4.11013591125823
58696701.901328632517-5.90132863251654
59689691.024787126059-2.02478712605864
60692685.8434421575686.15655784243177
61673679.440541357478-6.44054135747831
62653660.175014836356-7.17501483635579
63642637.4881104532744.51188954672614
64648634.4905801122413.5094198877603
65654650.658546707933.34145329207013
66653657.519398794553-4.51939879455335
67630635.601571358116-5.6015713581163
68609606.1419197729972.85808022700292
69598600.472463694726-2.47246369472634
70601598.000358867082.99964113292026
71592597.750571584554-5.75057158455377
72591592.389595163245-1.38959516324496
73568573.834239012965-5.83423901296533
74538551.766057103879-13.7660571038787
75523519.9122575828513.08774241714946
76530510.30061455872119.6993854412788
77529524.7561632428974.2438367571026
78534526.8778819125287.12211808747224
79513516.578531067405-3.57853106740504
80491494.680422662202-3.68042266220232
81480483.133610528595-3.1336105285954
82478481.428244198975-3.42824419897539
83462470.617734449276-8.61773444927587
84461458.8539040450132.14609595498695
85437438.769542800978-1.76954280097806
86411417.054752106214-6.05475210621438
87400398.4119231765061.58807682349357
88405394.03051729135310.9694827086469
89395395.849189114665-0.849189114664853
90407389.50775038427817.4922496157224
91385385.319295289814-0.31929528981442
92366368.341387966974-2.34138796697374
93349361.139497893285-12.1394978932851
94343350.575288727777-7.57528872777664
95332331.1842182307230.815781769276782
96327330.262729297620-3.26272929761961
97306303.1804883534352.81951164656454
98276284.646170170953-8.6461701709535
99269264.9632252220654.03677477793508
100268265.1933786213042.80662137869615
101260253.9849099814986.01509001850235
102274256.99163563359317.0083643664070
103247247.877468977656-0.87746897765615
104226229.250960956314-3.25096095631363
105212217.823459001706-5.823459001706
106199215.452532419926-16.4525324199259
107188188.473243654802-0.473243654801763
108179182.194820801609-3.19482080160881
109155153.1844449598421.81555504015776
110124127.280588985871-3.28058898587113
111117113.7159943304663.28400566953428
112116111.7230331877444.27696681225648
113105101.8515422688033.14845773119688
114112103.0497068972928.9502931027082
1158676.94119854769.05880145239999
1166464.3176950315437-0.317695031543721
1175355.1081601179772-2.10816011797725
1184255.7805178084333-13.7805178084333
1193238.6885555070466-6.68855550704657
1202427.6550092910357-3.65500929103571

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 896 & 903.770032051282 & -7.77003205128221 \tabularnewline
14 & 889 & 886.612471780298 & 2.38752821970195 \tabularnewline
15 & 878 & 874.814238181876 & 3.18576181812375 \tabularnewline
16 & 883 & 881.459398185756 & 1.54060181424438 \tabularnewline
17 & 901 & 900.954049786438 & 0.0459502135618095 \tabularnewline
18 & 897 & 897.241781061954 & -0.241781061954157 \tabularnewline
19 & 881 & 880.339225263874 & 0.660774736125859 \tabularnewline
20 & 866 & 869.70989638307 & -3.70989638307083 \tabularnewline
21 & 867 & 865.304180709716 & 1.69581929028436 \tabularnewline
22 & 866 & 865.132132493982 & 0.867867506018456 \tabularnewline
23 & 862 & 865.602121557149 & -3.60212155714862 \tabularnewline
24 & 871 & 861.821500470522 & 9.17849952947813 \tabularnewline
25 & 865 & 871.391894037613 & -6.3918940376135 \tabularnewline
26 & 856 & 860.792986846258 & -4.7929868462578 \tabularnewline
27 & 847 & 842.779990723652 & 4.22000927634758 \tabularnewline
28 & 859 & 849.54346293209 & 9.45653706791052 \tabularnewline
29 & 870 & 878.925685014414 & -8.92568501441428 \tabularnewline
30 & 872 & 867.358390803323 & 4.64160919667722 \tabularnewline
31 & 856 & 856.270800335272 & -0.270800335272043 \tabularnewline
32 & 839 & 845.243805159692 & -6.24380515969244 \tabularnewline
33 & 829 & 840.044603702055 & -11.0446037020552 \tabularnewline
34 & 825 & 822.640221050535 & 2.35977894946518 \tabularnewline
35 & 822 & 816.818364626724 & 5.18163537327587 \tabularnewline
36 & 827 & 821.267860589491 & 5.73213941050903 \tabularnewline
37 & 822 & 821.180051966459 & 0.819948033541323 \tabularnewline
38 & 812 & 817.13264328428 & -5.13264328428022 \tabularnewline
39 & 810 & 801.386200506656 & 8.61379949334412 \tabularnewline
40 & 816 & 815.649666180763 & 0.350333819237335 \tabularnewline
41 & 820 & 831.583850658154 & -11.5838506581536 \tabularnewline
42 & 823 & 817.41580865937 & 5.58419134062945 \tabularnewline
43 & 810 & 802.75644298545 & 7.24355701454988 \tabularnewline
44 & 793 & 797.183464927787 & -4.1834649277871 \tabularnewline
45 & 777 & 794.671265536733 & -17.6712655367334 \tabularnewline
46 & 772 & 773.760226477783 & -1.76022647778268 \tabularnewline
47 & 765 & 761.602460117091 & 3.3975398829092 \tabularnewline
48 & 765 & 759.986382743761 & 5.01361725623906 \tabularnewline
49 & 753 & 752.987246497228 & 0.0127535027721706 \tabularnewline
50 & 742 & 741.266972680605 & 0.733027319395319 \tabularnewline
51 & 736 & 730.821573637208 & 5.17842636279181 \tabularnewline
52 & 740 & 736.221210656225 & 3.77878934377543 \tabularnewline
53 & 742 & 749.645923301676 & -7.64592330167602 \tabularnewline
54 & 742 & 742.293058489909 & -0.293058489908503 \tabularnewline
55 & 728 & 720.020057341917 & 7.97994265808313 \tabularnewline
56 & 707 & 709.309482295501 & -2.30948229550097 \tabularnewline
57 & 699 & 703.110135911258 & -4.11013591125823 \tabularnewline
58 & 696 & 701.901328632517 & -5.90132863251654 \tabularnewline
59 & 689 & 691.024787126059 & -2.02478712605864 \tabularnewline
60 & 692 & 685.843442157568 & 6.15655784243177 \tabularnewline
61 & 673 & 679.440541357478 & -6.44054135747831 \tabularnewline
62 & 653 & 660.175014836356 & -7.17501483635579 \tabularnewline
63 & 642 & 637.488110453274 & 4.51188954672614 \tabularnewline
64 & 648 & 634.49058011224 & 13.5094198877603 \tabularnewline
65 & 654 & 650.65854670793 & 3.34145329207013 \tabularnewline
66 & 653 & 657.519398794553 & -4.51939879455335 \tabularnewline
67 & 630 & 635.601571358116 & -5.6015713581163 \tabularnewline
68 & 609 & 606.141919772997 & 2.85808022700292 \tabularnewline
69 & 598 & 600.472463694726 & -2.47246369472634 \tabularnewline
70 & 601 & 598.00035886708 & 2.99964113292026 \tabularnewline
71 & 592 & 597.750571584554 & -5.75057158455377 \tabularnewline
72 & 591 & 592.389595163245 & -1.38959516324496 \tabularnewline
73 & 568 & 573.834239012965 & -5.83423901296533 \tabularnewline
74 & 538 & 551.766057103879 & -13.7660571038787 \tabularnewline
75 & 523 & 519.912257582851 & 3.08774241714946 \tabularnewline
76 & 530 & 510.300614558721 & 19.6993854412788 \tabularnewline
77 & 529 & 524.756163242897 & 4.2438367571026 \tabularnewline
78 & 534 & 526.877881912528 & 7.12211808747224 \tabularnewline
79 & 513 & 516.578531067405 & -3.57853106740504 \tabularnewline
80 & 491 & 494.680422662202 & -3.68042266220232 \tabularnewline
81 & 480 & 483.133610528595 & -3.1336105285954 \tabularnewline
82 & 478 & 481.428244198975 & -3.42824419897539 \tabularnewline
83 & 462 & 470.617734449276 & -8.61773444927587 \tabularnewline
84 & 461 & 458.853904045013 & 2.14609595498695 \tabularnewline
85 & 437 & 438.769542800978 & -1.76954280097806 \tabularnewline
86 & 411 & 417.054752106214 & -6.05475210621438 \tabularnewline
87 & 400 & 398.411923176506 & 1.58807682349357 \tabularnewline
88 & 405 & 394.030517291353 & 10.9694827086469 \tabularnewline
89 & 395 & 395.849189114665 & -0.849189114664853 \tabularnewline
90 & 407 & 389.507750384278 & 17.4922496157224 \tabularnewline
91 & 385 & 385.319295289814 & -0.31929528981442 \tabularnewline
92 & 366 & 368.341387966974 & -2.34138796697374 \tabularnewline
93 & 349 & 361.139497893285 & -12.1394978932851 \tabularnewline
94 & 343 & 350.575288727777 & -7.57528872777664 \tabularnewline
95 & 332 & 331.184218230723 & 0.815781769276782 \tabularnewline
96 & 327 & 330.262729297620 & -3.26272929761961 \tabularnewline
97 & 306 & 303.180488353435 & 2.81951164656454 \tabularnewline
98 & 276 & 284.646170170953 & -8.6461701709535 \tabularnewline
99 & 269 & 264.963225222065 & 4.03677477793508 \tabularnewline
100 & 268 & 265.193378621304 & 2.80662137869615 \tabularnewline
101 & 260 & 253.984909981498 & 6.01509001850235 \tabularnewline
102 & 274 & 256.991635633593 & 17.0083643664070 \tabularnewline
103 & 247 & 247.877468977656 & -0.87746897765615 \tabularnewline
104 & 226 & 229.250960956314 & -3.25096095631363 \tabularnewline
105 & 212 & 217.823459001706 & -5.823459001706 \tabularnewline
106 & 199 & 215.452532419926 & -16.4525324199259 \tabularnewline
107 & 188 & 188.473243654802 & -0.473243654801763 \tabularnewline
108 & 179 & 182.194820801609 & -3.19482080160881 \tabularnewline
109 & 155 & 153.184444959842 & 1.81555504015776 \tabularnewline
110 & 124 & 127.280588985871 & -3.28058898587113 \tabularnewline
111 & 117 & 113.715994330466 & 3.28400566953428 \tabularnewline
112 & 116 & 111.723033187744 & 4.27696681225648 \tabularnewline
113 & 105 & 101.851542268803 & 3.14845773119688 \tabularnewline
114 & 112 & 103.049706897292 & 8.9502931027082 \tabularnewline
115 & 86 & 76.9411985476 & 9.05880145239999 \tabularnewline
116 & 64 & 64.3176950315437 & -0.317695031543721 \tabularnewline
117 & 53 & 55.1081601179772 & -2.10816011797725 \tabularnewline
118 & 42 & 55.7805178084333 & -13.7805178084333 \tabularnewline
119 & 32 & 38.6885555070466 & -6.68855550704657 \tabularnewline
120 & 24 & 27.6550092910357 & -3.65500929103571 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=78168&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]896[/C][C]903.770032051282[/C][C]-7.77003205128221[/C][/ROW]
[ROW][C]14[/C][C]889[/C][C]886.612471780298[/C][C]2.38752821970195[/C][/ROW]
[ROW][C]15[/C][C]878[/C][C]874.814238181876[/C][C]3.18576181812375[/C][/ROW]
[ROW][C]16[/C][C]883[/C][C]881.459398185756[/C][C]1.54060181424438[/C][/ROW]
[ROW][C]17[/C][C]901[/C][C]900.954049786438[/C][C]0.0459502135618095[/C][/ROW]
[ROW][C]18[/C][C]897[/C][C]897.241781061954[/C][C]-0.241781061954157[/C][/ROW]
[ROW][C]19[/C][C]881[/C][C]880.339225263874[/C][C]0.660774736125859[/C][/ROW]
[ROW][C]20[/C][C]866[/C][C]869.70989638307[/C][C]-3.70989638307083[/C][/ROW]
[ROW][C]21[/C][C]867[/C][C]865.304180709716[/C][C]1.69581929028436[/C][/ROW]
[ROW][C]22[/C][C]866[/C][C]865.132132493982[/C][C]0.867867506018456[/C][/ROW]
[ROW][C]23[/C][C]862[/C][C]865.602121557149[/C][C]-3.60212155714862[/C][/ROW]
[ROW][C]24[/C][C]871[/C][C]861.821500470522[/C][C]9.17849952947813[/C][/ROW]
[ROW][C]25[/C][C]865[/C][C]871.391894037613[/C][C]-6.3918940376135[/C][/ROW]
[ROW][C]26[/C][C]856[/C][C]860.792986846258[/C][C]-4.7929868462578[/C][/ROW]
[ROW][C]27[/C][C]847[/C][C]842.779990723652[/C][C]4.22000927634758[/C][/ROW]
[ROW][C]28[/C][C]859[/C][C]849.54346293209[/C][C]9.45653706791052[/C][/ROW]
[ROW][C]29[/C][C]870[/C][C]878.925685014414[/C][C]-8.92568501441428[/C][/ROW]
[ROW][C]30[/C][C]872[/C][C]867.358390803323[/C][C]4.64160919667722[/C][/ROW]
[ROW][C]31[/C][C]856[/C][C]856.270800335272[/C][C]-0.270800335272043[/C][/ROW]
[ROW][C]32[/C][C]839[/C][C]845.243805159692[/C][C]-6.24380515969244[/C][/ROW]
[ROW][C]33[/C][C]829[/C][C]840.044603702055[/C][C]-11.0446037020552[/C][/ROW]
[ROW][C]34[/C][C]825[/C][C]822.640221050535[/C][C]2.35977894946518[/C][/ROW]
[ROW][C]35[/C][C]822[/C][C]816.818364626724[/C][C]5.18163537327587[/C][/ROW]
[ROW][C]36[/C][C]827[/C][C]821.267860589491[/C][C]5.73213941050903[/C][/ROW]
[ROW][C]37[/C][C]822[/C][C]821.180051966459[/C][C]0.819948033541323[/C][/ROW]
[ROW][C]38[/C][C]812[/C][C]817.13264328428[/C][C]-5.13264328428022[/C][/ROW]
[ROW][C]39[/C][C]810[/C][C]801.386200506656[/C][C]8.61379949334412[/C][/ROW]
[ROW][C]40[/C][C]816[/C][C]815.649666180763[/C][C]0.350333819237335[/C][/ROW]
[ROW][C]41[/C][C]820[/C][C]831.583850658154[/C][C]-11.5838506581536[/C][/ROW]
[ROW][C]42[/C][C]823[/C][C]817.41580865937[/C][C]5.58419134062945[/C][/ROW]
[ROW][C]43[/C][C]810[/C][C]802.75644298545[/C][C]7.24355701454988[/C][/ROW]
[ROW][C]44[/C][C]793[/C][C]797.183464927787[/C][C]-4.1834649277871[/C][/ROW]
[ROW][C]45[/C][C]777[/C][C]794.671265536733[/C][C]-17.6712655367334[/C][/ROW]
[ROW][C]46[/C][C]772[/C][C]773.760226477783[/C][C]-1.76022647778268[/C][/ROW]
[ROW][C]47[/C][C]765[/C][C]761.602460117091[/C][C]3.3975398829092[/C][/ROW]
[ROW][C]48[/C][C]765[/C][C]759.986382743761[/C][C]5.01361725623906[/C][/ROW]
[ROW][C]49[/C][C]753[/C][C]752.987246497228[/C][C]0.0127535027721706[/C][/ROW]
[ROW][C]50[/C][C]742[/C][C]741.266972680605[/C][C]0.733027319395319[/C][/ROW]
[ROW][C]51[/C][C]736[/C][C]730.821573637208[/C][C]5.17842636279181[/C][/ROW]
[ROW][C]52[/C][C]740[/C][C]736.221210656225[/C][C]3.77878934377543[/C][/ROW]
[ROW][C]53[/C][C]742[/C][C]749.645923301676[/C][C]-7.64592330167602[/C][/ROW]
[ROW][C]54[/C][C]742[/C][C]742.293058489909[/C][C]-0.293058489908503[/C][/ROW]
[ROW][C]55[/C][C]728[/C][C]720.020057341917[/C][C]7.97994265808313[/C][/ROW]
[ROW][C]56[/C][C]707[/C][C]709.309482295501[/C][C]-2.30948229550097[/C][/ROW]
[ROW][C]57[/C][C]699[/C][C]703.110135911258[/C][C]-4.11013591125823[/C][/ROW]
[ROW][C]58[/C][C]696[/C][C]701.901328632517[/C][C]-5.90132863251654[/C][/ROW]
[ROW][C]59[/C][C]689[/C][C]691.024787126059[/C][C]-2.02478712605864[/C][/ROW]
[ROW][C]60[/C][C]692[/C][C]685.843442157568[/C][C]6.15655784243177[/C][/ROW]
[ROW][C]61[/C][C]673[/C][C]679.440541357478[/C][C]-6.44054135747831[/C][/ROW]
[ROW][C]62[/C][C]653[/C][C]660.175014836356[/C][C]-7.17501483635579[/C][/ROW]
[ROW][C]63[/C][C]642[/C][C]637.488110453274[/C][C]4.51188954672614[/C][/ROW]
[ROW][C]64[/C][C]648[/C][C]634.49058011224[/C][C]13.5094198877603[/C][/ROW]
[ROW][C]65[/C][C]654[/C][C]650.65854670793[/C][C]3.34145329207013[/C][/ROW]
[ROW][C]66[/C][C]653[/C][C]657.519398794553[/C][C]-4.51939879455335[/C][/ROW]
[ROW][C]67[/C][C]630[/C][C]635.601571358116[/C][C]-5.6015713581163[/C][/ROW]
[ROW][C]68[/C][C]609[/C][C]606.141919772997[/C][C]2.85808022700292[/C][/ROW]
[ROW][C]69[/C][C]598[/C][C]600.472463694726[/C][C]-2.47246369472634[/C][/ROW]
[ROW][C]70[/C][C]601[/C][C]598.00035886708[/C][C]2.99964113292026[/C][/ROW]
[ROW][C]71[/C][C]592[/C][C]597.750571584554[/C][C]-5.75057158455377[/C][/ROW]
[ROW][C]72[/C][C]591[/C][C]592.389595163245[/C][C]-1.38959516324496[/C][/ROW]
[ROW][C]73[/C][C]568[/C][C]573.834239012965[/C][C]-5.83423901296533[/C][/ROW]
[ROW][C]74[/C][C]538[/C][C]551.766057103879[/C][C]-13.7660571038787[/C][/ROW]
[ROW][C]75[/C][C]523[/C][C]519.912257582851[/C][C]3.08774241714946[/C][/ROW]
[ROW][C]76[/C][C]530[/C][C]510.300614558721[/C][C]19.6993854412788[/C][/ROW]
[ROW][C]77[/C][C]529[/C][C]524.756163242897[/C][C]4.2438367571026[/C][/ROW]
[ROW][C]78[/C][C]534[/C][C]526.877881912528[/C][C]7.12211808747224[/C][/ROW]
[ROW][C]79[/C][C]513[/C][C]516.578531067405[/C][C]-3.57853106740504[/C][/ROW]
[ROW][C]80[/C][C]491[/C][C]494.680422662202[/C][C]-3.68042266220232[/C][/ROW]
[ROW][C]81[/C][C]480[/C][C]483.133610528595[/C][C]-3.1336105285954[/C][/ROW]
[ROW][C]82[/C][C]478[/C][C]481.428244198975[/C][C]-3.42824419897539[/C][/ROW]
[ROW][C]83[/C][C]462[/C][C]470.617734449276[/C][C]-8.61773444927587[/C][/ROW]
[ROW][C]84[/C][C]461[/C][C]458.853904045013[/C][C]2.14609595498695[/C][/ROW]
[ROW][C]85[/C][C]437[/C][C]438.769542800978[/C][C]-1.76954280097806[/C][/ROW]
[ROW][C]86[/C][C]411[/C][C]417.054752106214[/C][C]-6.05475210621438[/C][/ROW]
[ROW][C]87[/C][C]400[/C][C]398.411923176506[/C][C]1.58807682349357[/C][/ROW]
[ROW][C]88[/C][C]405[/C][C]394.030517291353[/C][C]10.9694827086469[/C][/ROW]
[ROW][C]89[/C][C]395[/C][C]395.849189114665[/C][C]-0.849189114664853[/C][/ROW]
[ROW][C]90[/C][C]407[/C][C]389.507750384278[/C][C]17.4922496157224[/C][/ROW]
[ROW][C]91[/C][C]385[/C][C]385.319295289814[/C][C]-0.31929528981442[/C][/ROW]
[ROW][C]92[/C][C]366[/C][C]368.341387966974[/C][C]-2.34138796697374[/C][/ROW]
[ROW][C]93[/C][C]349[/C][C]361.139497893285[/C][C]-12.1394978932851[/C][/ROW]
[ROW][C]94[/C][C]343[/C][C]350.575288727777[/C][C]-7.57528872777664[/C][/ROW]
[ROW][C]95[/C][C]332[/C][C]331.184218230723[/C][C]0.815781769276782[/C][/ROW]
[ROW][C]96[/C][C]327[/C][C]330.262729297620[/C][C]-3.26272929761961[/C][/ROW]
[ROW][C]97[/C][C]306[/C][C]303.180488353435[/C][C]2.81951164656454[/C][/ROW]
[ROW][C]98[/C][C]276[/C][C]284.646170170953[/C][C]-8.6461701709535[/C][/ROW]
[ROW][C]99[/C][C]269[/C][C]264.963225222065[/C][C]4.03677477793508[/C][/ROW]
[ROW][C]100[/C][C]268[/C][C]265.193378621304[/C][C]2.80662137869615[/C][/ROW]
[ROW][C]101[/C][C]260[/C][C]253.984909981498[/C][C]6.01509001850235[/C][/ROW]
[ROW][C]102[/C][C]274[/C][C]256.991635633593[/C][C]17.0083643664070[/C][/ROW]
[ROW][C]103[/C][C]247[/C][C]247.877468977656[/C][C]-0.87746897765615[/C][/ROW]
[ROW][C]104[/C][C]226[/C][C]229.250960956314[/C][C]-3.25096095631363[/C][/ROW]
[ROW][C]105[/C][C]212[/C][C]217.823459001706[/C][C]-5.823459001706[/C][/ROW]
[ROW][C]106[/C][C]199[/C][C]215.452532419926[/C][C]-16.4525324199259[/C][/ROW]
[ROW][C]107[/C][C]188[/C][C]188.473243654802[/C][C]-0.473243654801763[/C][/ROW]
[ROW][C]108[/C][C]179[/C][C]182.194820801609[/C][C]-3.19482080160881[/C][/ROW]
[ROW][C]109[/C][C]155[/C][C]153.184444959842[/C][C]1.81555504015776[/C][/ROW]
[ROW][C]110[/C][C]124[/C][C]127.280588985871[/C][C]-3.28058898587113[/C][/ROW]
[ROW][C]111[/C][C]117[/C][C]113.715994330466[/C][C]3.28400566953428[/C][/ROW]
[ROW][C]112[/C][C]116[/C][C]111.723033187744[/C][C]4.27696681225648[/C][/ROW]
[ROW][C]113[/C][C]105[/C][C]101.851542268803[/C][C]3.14845773119688[/C][/ROW]
[ROW][C]114[/C][C]112[/C][C]103.049706897292[/C][C]8.9502931027082[/C][/ROW]
[ROW][C]115[/C][C]86[/C][C]76.9411985476[/C][C]9.05880145239999[/C][/ROW]
[ROW][C]116[/C][C]64[/C][C]64.3176950315437[/C][C]-0.317695031543721[/C][/ROW]
[ROW][C]117[/C][C]53[/C][C]55.1081601179772[/C][C]-2.10816011797725[/C][/ROW]
[ROW][C]118[/C][C]42[/C][C]55.7805178084333[/C][C]-13.7805178084333[/C][/ROW]
[ROW][C]119[/C][C]32[/C][C]38.6885555070466[/C][C]-6.68855550704657[/C][/ROW]
[ROW][C]120[/C][C]24[/C][C]27.6550092910357[/C][C]-3.65500929103571[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=78168&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=78168&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
13896903.770032051282-7.77003205128221
14889886.6124717802982.38752821970195
15878874.8142381818763.18576181812375
16883881.4593981857561.54060181424438
17901900.9540497864380.0459502135618095
18897897.241781061954-0.241781061954157
19881880.3392252638740.660774736125859
20866869.70989638307-3.70989638307083
21867865.3041807097161.69581929028436
22866865.1321324939820.867867506018456
23862865.602121557149-3.60212155714862
24871861.8215004705229.17849952947813
25865871.391894037613-6.3918940376135
26856860.792986846258-4.7929868462578
27847842.7799907236524.22000927634758
28859849.543462932099.45653706791052
29870878.925685014414-8.92568501441428
30872867.3583908033234.64160919667722
31856856.270800335272-0.270800335272043
32839845.243805159692-6.24380515969244
33829840.044603702055-11.0446037020552
34825822.6402210505352.35977894946518
35822816.8183646267245.18163537327587
36827821.2678605894915.73213941050903
37822821.1800519664590.819948033541323
38812817.13264328428-5.13264328428022
39810801.3862005066568.61379949334412
40816815.6496661807630.350333819237335
41820831.583850658154-11.5838506581536
42823817.415808659375.58419134062945
43810802.756442985457.24355701454988
44793797.183464927787-4.1834649277871
45777794.671265536733-17.6712655367334
46772773.760226477783-1.76022647778268
47765761.6024601170913.3975398829092
48765759.9863827437615.01361725623906
49753752.9872464972280.0127535027721706
50742741.2669726806050.733027319395319
51736730.8215736372085.17842636279181
52740736.2212106562253.77878934377543
53742749.645923301676-7.64592330167602
54742742.293058489909-0.293058489908503
55728720.0200573419177.97994265808313
56707709.309482295501-2.30948229550097
57699703.110135911258-4.11013591125823
58696701.901328632517-5.90132863251654
59689691.024787126059-2.02478712605864
60692685.8434421575686.15655784243177
61673679.440541357478-6.44054135747831
62653660.175014836356-7.17501483635579
63642637.4881104532744.51188954672614
64648634.4905801122413.5094198877603
65654650.658546707933.34145329207013
66653657.519398794553-4.51939879455335
67630635.601571358116-5.6015713581163
68609606.1419197729972.85808022700292
69598600.472463694726-2.47246369472634
70601598.000358867082.99964113292026
71592597.750571584554-5.75057158455377
72591592.389595163245-1.38959516324496
73568573.834239012965-5.83423901296533
74538551.766057103879-13.7660571038787
75523519.9122575828513.08774241714946
76530510.30061455872119.6993854412788
77529524.7561632428974.2438367571026
78534526.8778819125287.12211808747224
79513516.578531067405-3.57853106740504
80491494.680422662202-3.68042266220232
81480483.133610528595-3.1336105285954
82478481.428244198975-3.42824419897539
83462470.617734449276-8.61773444927587
84461458.8539040450132.14609595498695
85437438.769542800978-1.76954280097806
86411417.054752106214-6.05475210621438
87400398.4119231765061.58807682349357
88405394.03051729135310.9694827086469
89395395.849189114665-0.849189114664853
90407389.50775038427817.4922496157224
91385385.319295289814-0.31929528981442
92366368.341387966974-2.34138796697374
93349361.139497893285-12.1394978932851
94343350.575288727777-7.57528872777664
95332331.1842182307230.815781769276782
96327330.262729297620-3.26272929761961
97306303.1804883534352.81951164656454
98276284.646170170953-8.6461701709535
99269264.9632252220654.03677477793508
100268265.1933786213042.80662137869615
101260253.9849099814986.01509001850235
102274256.99163563359317.0083643664070
103247247.877468977656-0.87746897765615
104226229.250960956314-3.25096095631363
105212217.823459001706-5.823459001706
106199215.452532419926-16.4525324199259
107188188.473243654802-0.473243654801763
108179182.194820801609-3.19482080160881
109155153.1844449598421.81555504015776
110124127.280588985871-3.28058898587113
111117113.7159943304663.28400566953428
112116111.7230331877444.27696681225648
113105101.8515422688033.14845773119688
114112103.0497068972928.9502931027082
1158676.94119854769.05880145239999
1166464.3176950315437-0.317695031543721
1175355.1081601179772-2.10816011797725
1184255.7805178084333-13.7805178084333
1193238.6885555070466-6.68855550704657
1202427.6550092910357-3.65500929103571







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
121-0.156966635392177-13.266085789997512.9521525192132
122-29.2582907949413-51.0740298877948-7.4425517020878
123-37.5666244872557-70.5925235666712-4.54072540784015
124-42.4815647584413-88.57333040847013.61020089158754
125-58.9289813252306-119.6364789394991.77851628903826
126-63.6049181363643-140.29787393916513.0880376664360
127-106.387320288330-200.31244851559-12.4621920610693
128-143.043192933233-255.355312657759-30.7310732087067
129-167.143917895076-298.925207483226-35.3626283069263
130-181.085567773435-333.358576216247-28.8125593306231
131-191.747069148066-365.484071319053-18.0100669770792
132-198.98763661954-395.117670008475-2.85760323060447

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
121 & -0.156966635392177 & -13.2660857899975 & 12.9521525192132 \tabularnewline
122 & -29.2582907949413 & -51.0740298877948 & -7.4425517020878 \tabularnewline
123 & -37.5666244872557 & -70.5925235666712 & -4.54072540784015 \tabularnewline
124 & -42.4815647584413 & -88.5733304084701 & 3.61020089158754 \tabularnewline
125 & -58.9289813252306 & -119.636478939499 & 1.77851628903826 \tabularnewline
126 & -63.6049181363643 & -140.297873939165 & 13.0880376664360 \tabularnewline
127 & -106.387320288330 & -200.31244851559 & -12.4621920610693 \tabularnewline
128 & -143.043192933233 & -255.355312657759 & -30.7310732087067 \tabularnewline
129 & -167.143917895076 & -298.925207483226 & -35.3626283069263 \tabularnewline
130 & -181.085567773435 & -333.358576216247 & -28.8125593306231 \tabularnewline
131 & -191.747069148066 & -365.484071319053 & -18.0100669770792 \tabularnewline
132 & -198.98763661954 & -395.117670008475 & -2.85760323060447 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=78168&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]-0.156966635392177[/C][C]-13.2660857899975[/C][C]12.9521525192132[/C][/ROW]
[ROW][C]122[/C][C]-29.2582907949413[/C][C]-51.0740298877948[/C][C]-7.4425517020878[/C][/ROW]
[ROW][C]123[/C][C]-37.5666244872557[/C][C]-70.5925235666712[/C][C]-4.54072540784015[/C][/ROW]
[ROW][C]124[/C][C]-42.4815647584413[/C][C]-88.5733304084701[/C][C]3.61020089158754[/C][/ROW]
[ROW][C]125[/C][C]-58.9289813252306[/C][C]-119.636478939499[/C][C]1.77851628903826[/C][/ROW]
[ROW][C]126[/C][C]-63.6049181363643[/C][C]-140.297873939165[/C][C]13.0880376664360[/C][/ROW]
[ROW][C]127[/C][C]-106.387320288330[/C][C]-200.31244851559[/C][C]-12.4621920610693[/C][/ROW]
[ROW][C]128[/C][C]-143.043192933233[/C][C]-255.355312657759[/C][C]-30.7310732087067[/C][/ROW]
[ROW][C]129[/C][C]-167.143917895076[/C][C]-298.925207483226[/C][C]-35.3626283069263[/C][/ROW]
[ROW][C]130[/C][C]-181.085567773435[/C][C]-333.358576216247[/C][C]-28.8125593306231[/C][/ROW]
[ROW][C]131[/C][C]-191.747069148066[/C][C]-365.484071319053[/C][C]-18.0100669770792[/C][/ROW]
[ROW][C]132[/C][C]-198.98763661954[/C][C]-395.117670008475[/C][C]-2.85760323060447[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=78168&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=78168&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
121-0.156966635392177-13.266085789997512.9521525192132
122-29.2582907949413-51.0740298877948-7.4425517020878
123-37.5666244872557-70.5925235666712-4.54072540784015
124-42.4815647584413-88.57333040847013.61020089158754
125-58.9289813252306-119.6364789394991.77851628903826
126-63.6049181363643-140.29787393916513.0880376664360
127-106.387320288330-200.31244851559-12.4621920610693
128-143.043192933233-255.355312657759-30.7310732087067
129-167.143917895076-298.925207483226-35.3626283069263
130-181.085567773435-333.358576216247-28.8125593306231
131-191.747069148066-365.484071319053-18.0100669770792
132-198.98763661954-395.117670008475-2.85760323060447



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')