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Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationTue, 09 Aug 2011 13:14:53 -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/09/t1312910179sslkwvlexuq2287.htm/, Retrieved Mon, 13 May 2024 22:55:01 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=123511, Retrieved Mon, 13 May 2024 22:55:01 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywordsVan den Buys Daphné
Estimated Impact128
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [tijdreeks B-stap 27] [2011-08-09 17:14:53] [d41d8cd98f00b204e9800998ecf8427e] [Current]
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Dataseries X:
760
730
730
680
730
710
800
830
820
770
800
840
800
710
800
780
760
730
770
880
850
810
770
810
890
790
840
830
740
760
630
890
900
820
810
820
890
810
810
840
830
790
610
870
870
820
800
840
860
860
730
850
860
900
610
960
820
860
810
820
820
880
840
910
860
880
620
970
810
880
870
800
740
1010
850
980
880
870
660
940
860
880
1000
840
800
1060
790
930
920
840
690
940
1010
890
1000
820
800
1000
780
1010
950
830
670
1000
960
920
1040
860




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time3 seconds
R Server'George Udny Yule' @ yule.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 & 'George Udny Yule' @ yule.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=123511&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]'George Udny Yule' @ yule.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=123511&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=123511&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'George Udny Yule' @ yule.wessa.net







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.00518576308690868
beta0.391444433823213
gamma1

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.00518576308690868 \tabularnewline
beta & 0.391444433823213 \tabularnewline
gamma & 1 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=123511&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]0.00518576308690868[/C][/ROW]
[ROW][C]beta[/C][C]0.391444433823213[/C][/ROW]
[ROW][C]gamma[/C][C]1[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=123511&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=123511&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
alpha0.00518576308690868
beta0.391444433823213
gamma1







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
13800780.6810897435919.3189102564104
14710692.32544260712317.674557392877
15800781.49714650364818.5028534963523
16780761.12737206138518.8726279386149
17760743.2978254481916.7021745518097
18730718.40759442500711.5924055749925
19770813.09773054951-43.0977305495103
20880844.50010419314235.4998958068578
21850835.13212909713614.8678709028638
22810780.6873420655229.3126579344806
23770808.043631824978-38.0436318249775
24810848.306734939131-38.3067349391307
25890830.20944032702359.7905596729772
26790740.63767357519649.3623264248039
27840831.071857338498.92814266150981
28830811.27500537124518.724994628755
29740791.539913327875-51.5399133278748
30760761.328414955958-1.32841495595756
31630801.634683142147-171.634683142147
32890910.389272643084-20.3892726430838
33900879.92172625184420.0782737481562
34820839.599704520739-19.599704520739
35810799.32192688778110.6780731122187
36820839.301429071773-19.3014290717731
37890918.655334925047-28.655334925047
38810817.835272294834-7.83527229483377
39810867.216752089873-57.2167520898727
40840856.157077034835-16.1570770348353
41830765.60389644692664.3961035530743
42790785.4434035719534.55659642804687
43610655.867711357623-45.8677113576227
44870915.501506929645-45.5015069296447
45870924.876370161737-54.8763701617368
46820844.256224882098-24.2562248820981
47800833.62840259189-33.6284025918897
48840843.01750560135-3.01750560135054
49860912.646911966771-52.6469119667711
50860831.86228266017428.1377173398262
51730831.82568689939-101.825686899391
52850860.811652590825-10.8116525908246
53860849.86271667205610.137283327944
54900809.22258843288190.7774115671187
55610629.437152225326-19.4371522253261
56960889.1319227506870.8680772493205
57820889.579833673373-69.579833673373
58860839.11077906414520.8892209358548
59810819.251119892333-9.2511198923329
60820859.125903568773-39.1259035687727
61820879.029832225747-59.0298322257474
62880878.3986569425671.6013430574335
63840748.70199279736591.2980072026346
64910869.390526226440.6094737735999
65860879.811946414572-19.8119464145717
66880919.441059749542-39.4410597495418
67620629.275592334042-9.2755923340419
68970978.818881697933-8.8188816979333
69810838.931109453398-28.9311094533981
70880878.55240327051.44759672949965
71870828.44806923403341.5519307659672
72800838.809757370954-38.809757370954
73740838.858567647658-98.8585676476575
741010898.200710242588111.799289757412
75850858.393823938525-8.39382393852497
76980928.024135101951.9758648981001
77880878.3039134100341.69608658996583
78870898.468404606717-28.4684046067166
79660638.34231274167721.6576872583234
80940988.536587163026-48.5365871630262
81860828.3905234720731.6094765279303
82880898.625435148419-18.6254351484187
831000888.35112188695111.64887811305
84840819.31140949010520.6885905098953
85800760.2321754581639.7678245418396
8610601030.4408630674329.5591369325662
87790871.052961434444-81.0529614344438
889301000.63089520965-70.6308952096506
89920900.27473023643519.7252697635647
90840890.58015495895-50.5801549589506
91690680.2161648838489.78383511615232
92940960.505115852658-20.5051158526577
931010880.278279150429129.721720849571
94890901.290151365662-11.2901513656616
9510001020.91008786625-20.910087866253
96820860.682749662127-40.6827496621273
97800820.129354709375-20.1293547093745
9810001079.61389706287-79.6138970628735
99780809.141960308363-29.1419603083629
1001010948.98308881284261.0169111871581
101950939.0904310974810.9095689025195
102830859.284620525435-29.2846205254353
103670709.000567674647-39.0005676746471
1041000958.72417222996241.2758277700378
1059601028.21044186013-68.2104418601264
106920907.4584057590612.5415942409396
10710401017.2233942658922.7766057341078
108860837.23267674079622.767323259204

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 800 & 780.68108974359 & 19.3189102564104 \tabularnewline
14 & 710 & 692.325442607123 & 17.674557392877 \tabularnewline
15 & 800 & 781.497146503648 & 18.5028534963523 \tabularnewline
16 & 780 & 761.127372061385 & 18.8726279386149 \tabularnewline
17 & 760 & 743.29782544819 & 16.7021745518097 \tabularnewline
18 & 730 & 718.407594425007 & 11.5924055749925 \tabularnewline
19 & 770 & 813.09773054951 & -43.0977305495103 \tabularnewline
20 & 880 & 844.500104193142 & 35.4998958068578 \tabularnewline
21 & 850 & 835.132129097136 & 14.8678709028638 \tabularnewline
22 & 810 & 780.68734206552 & 29.3126579344806 \tabularnewline
23 & 770 & 808.043631824978 & -38.0436318249775 \tabularnewline
24 & 810 & 848.306734939131 & -38.3067349391307 \tabularnewline
25 & 890 & 830.209440327023 & 59.7905596729772 \tabularnewline
26 & 790 & 740.637673575196 & 49.3623264248039 \tabularnewline
27 & 840 & 831.07185733849 & 8.92814266150981 \tabularnewline
28 & 830 & 811.275005371245 & 18.724994628755 \tabularnewline
29 & 740 & 791.539913327875 & -51.5399133278748 \tabularnewline
30 & 760 & 761.328414955958 & -1.32841495595756 \tabularnewline
31 & 630 & 801.634683142147 & -171.634683142147 \tabularnewline
32 & 890 & 910.389272643084 & -20.3892726430838 \tabularnewline
33 & 900 & 879.921726251844 & 20.0782737481562 \tabularnewline
34 & 820 & 839.599704520739 & -19.599704520739 \tabularnewline
35 & 810 & 799.321926887781 & 10.6780731122187 \tabularnewline
36 & 820 & 839.301429071773 & -19.3014290717731 \tabularnewline
37 & 890 & 918.655334925047 & -28.655334925047 \tabularnewline
38 & 810 & 817.835272294834 & -7.83527229483377 \tabularnewline
39 & 810 & 867.216752089873 & -57.2167520898727 \tabularnewline
40 & 840 & 856.157077034835 & -16.1570770348353 \tabularnewline
41 & 830 & 765.603896446926 & 64.3961035530743 \tabularnewline
42 & 790 & 785.443403571953 & 4.55659642804687 \tabularnewline
43 & 610 & 655.867711357623 & -45.8677113576227 \tabularnewline
44 & 870 & 915.501506929645 & -45.5015069296447 \tabularnewline
45 & 870 & 924.876370161737 & -54.8763701617368 \tabularnewline
46 & 820 & 844.256224882098 & -24.2562248820981 \tabularnewline
47 & 800 & 833.62840259189 & -33.6284025918897 \tabularnewline
48 & 840 & 843.01750560135 & -3.01750560135054 \tabularnewline
49 & 860 & 912.646911966771 & -52.6469119667711 \tabularnewline
50 & 860 & 831.862282660174 & 28.1377173398262 \tabularnewline
51 & 730 & 831.82568689939 & -101.825686899391 \tabularnewline
52 & 850 & 860.811652590825 & -10.8116525908246 \tabularnewline
53 & 860 & 849.862716672056 & 10.137283327944 \tabularnewline
54 & 900 & 809.222588432881 & 90.7774115671187 \tabularnewline
55 & 610 & 629.437152225326 & -19.4371522253261 \tabularnewline
56 & 960 & 889.13192275068 & 70.8680772493205 \tabularnewline
57 & 820 & 889.579833673373 & -69.579833673373 \tabularnewline
58 & 860 & 839.110779064145 & 20.8892209358548 \tabularnewline
59 & 810 & 819.251119892333 & -9.2511198923329 \tabularnewline
60 & 820 & 859.125903568773 & -39.1259035687727 \tabularnewline
61 & 820 & 879.029832225747 & -59.0298322257474 \tabularnewline
62 & 880 & 878.398656942567 & 1.6013430574335 \tabularnewline
63 & 840 & 748.701992797365 & 91.2980072026346 \tabularnewline
64 & 910 & 869.3905262264 & 40.6094737735999 \tabularnewline
65 & 860 & 879.811946414572 & -19.8119464145717 \tabularnewline
66 & 880 & 919.441059749542 & -39.4410597495418 \tabularnewline
67 & 620 & 629.275592334042 & -9.2755923340419 \tabularnewline
68 & 970 & 978.818881697933 & -8.8188816979333 \tabularnewline
69 & 810 & 838.931109453398 & -28.9311094533981 \tabularnewline
70 & 880 & 878.5524032705 & 1.44759672949965 \tabularnewline
71 & 870 & 828.448069234033 & 41.5519307659672 \tabularnewline
72 & 800 & 838.809757370954 & -38.809757370954 \tabularnewline
73 & 740 & 838.858567647658 & -98.8585676476575 \tabularnewline
74 & 1010 & 898.200710242588 & 111.799289757412 \tabularnewline
75 & 850 & 858.393823938525 & -8.39382393852497 \tabularnewline
76 & 980 & 928.0241351019 & 51.9758648981001 \tabularnewline
77 & 880 & 878.303913410034 & 1.69608658996583 \tabularnewline
78 & 870 & 898.468404606717 & -28.4684046067166 \tabularnewline
79 & 660 & 638.342312741677 & 21.6576872583234 \tabularnewline
80 & 940 & 988.536587163026 & -48.5365871630262 \tabularnewline
81 & 860 & 828.39052347207 & 31.6094765279303 \tabularnewline
82 & 880 & 898.625435148419 & -18.6254351484187 \tabularnewline
83 & 1000 & 888.35112188695 & 111.64887811305 \tabularnewline
84 & 840 & 819.311409490105 & 20.6885905098953 \tabularnewline
85 & 800 & 760.23217545816 & 39.7678245418396 \tabularnewline
86 & 1060 & 1030.44086306743 & 29.5591369325662 \tabularnewline
87 & 790 & 871.052961434444 & -81.0529614344438 \tabularnewline
88 & 930 & 1000.63089520965 & -70.6308952096506 \tabularnewline
89 & 920 & 900.274730236435 & 19.7252697635647 \tabularnewline
90 & 840 & 890.58015495895 & -50.5801549589506 \tabularnewline
91 & 690 & 680.216164883848 & 9.78383511615232 \tabularnewline
92 & 940 & 960.505115852658 & -20.5051158526577 \tabularnewline
93 & 1010 & 880.278279150429 & 129.721720849571 \tabularnewline
94 & 890 & 901.290151365662 & -11.2901513656616 \tabularnewline
95 & 1000 & 1020.91008786625 & -20.910087866253 \tabularnewline
96 & 820 & 860.682749662127 & -40.6827496621273 \tabularnewline
97 & 800 & 820.129354709375 & -20.1293547093745 \tabularnewline
98 & 1000 & 1079.61389706287 & -79.6138970628735 \tabularnewline
99 & 780 & 809.141960308363 & -29.1419603083629 \tabularnewline
100 & 1010 & 948.983088812842 & 61.0169111871581 \tabularnewline
101 & 950 & 939.09043109748 & 10.9095689025195 \tabularnewline
102 & 830 & 859.284620525435 & -29.2846205254353 \tabularnewline
103 & 670 & 709.000567674647 & -39.0005676746471 \tabularnewline
104 & 1000 & 958.724172229962 & 41.2758277700378 \tabularnewline
105 & 960 & 1028.21044186013 & -68.2104418601264 \tabularnewline
106 & 920 & 907.45840575906 & 12.5415942409396 \tabularnewline
107 & 1040 & 1017.22339426589 & 22.7766057341078 \tabularnewline
108 & 860 & 837.232676740796 & 22.767323259204 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=123511&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]800[/C][C]780.68108974359[/C][C]19.3189102564104[/C][/ROW]
[ROW][C]14[/C][C]710[/C][C]692.325442607123[/C][C]17.674557392877[/C][/ROW]
[ROW][C]15[/C][C]800[/C][C]781.497146503648[/C][C]18.5028534963523[/C][/ROW]
[ROW][C]16[/C][C]780[/C][C]761.127372061385[/C][C]18.8726279386149[/C][/ROW]
[ROW][C]17[/C][C]760[/C][C]743.29782544819[/C][C]16.7021745518097[/C][/ROW]
[ROW][C]18[/C][C]730[/C][C]718.407594425007[/C][C]11.5924055749925[/C][/ROW]
[ROW][C]19[/C][C]770[/C][C]813.09773054951[/C][C]-43.0977305495103[/C][/ROW]
[ROW][C]20[/C][C]880[/C][C]844.500104193142[/C][C]35.4998958068578[/C][/ROW]
[ROW][C]21[/C][C]850[/C][C]835.132129097136[/C][C]14.8678709028638[/C][/ROW]
[ROW][C]22[/C][C]810[/C][C]780.68734206552[/C][C]29.3126579344806[/C][/ROW]
[ROW][C]23[/C][C]770[/C][C]808.043631824978[/C][C]-38.0436318249775[/C][/ROW]
[ROW][C]24[/C][C]810[/C][C]848.306734939131[/C][C]-38.3067349391307[/C][/ROW]
[ROW][C]25[/C][C]890[/C][C]830.209440327023[/C][C]59.7905596729772[/C][/ROW]
[ROW][C]26[/C][C]790[/C][C]740.637673575196[/C][C]49.3623264248039[/C][/ROW]
[ROW][C]27[/C][C]840[/C][C]831.07185733849[/C][C]8.92814266150981[/C][/ROW]
[ROW][C]28[/C][C]830[/C][C]811.275005371245[/C][C]18.724994628755[/C][/ROW]
[ROW][C]29[/C][C]740[/C][C]791.539913327875[/C][C]-51.5399133278748[/C][/ROW]
[ROW][C]30[/C][C]760[/C][C]761.328414955958[/C][C]-1.32841495595756[/C][/ROW]
[ROW][C]31[/C][C]630[/C][C]801.634683142147[/C][C]-171.634683142147[/C][/ROW]
[ROW][C]32[/C][C]890[/C][C]910.389272643084[/C][C]-20.3892726430838[/C][/ROW]
[ROW][C]33[/C][C]900[/C][C]879.921726251844[/C][C]20.0782737481562[/C][/ROW]
[ROW][C]34[/C][C]820[/C][C]839.599704520739[/C][C]-19.599704520739[/C][/ROW]
[ROW][C]35[/C][C]810[/C][C]799.321926887781[/C][C]10.6780731122187[/C][/ROW]
[ROW][C]36[/C][C]820[/C][C]839.301429071773[/C][C]-19.3014290717731[/C][/ROW]
[ROW][C]37[/C][C]890[/C][C]918.655334925047[/C][C]-28.655334925047[/C][/ROW]
[ROW][C]38[/C][C]810[/C][C]817.835272294834[/C][C]-7.83527229483377[/C][/ROW]
[ROW][C]39[/C][C]810[/C][C]867.216752089873[/C][C]-57.2167520898727[/C][/ROW]
[ROW][C]40[/C][C]840[/C][C]856.157077034835[/C][C]-16.1570770348353[/C][/ROW]
[ROW][C]41[/C][C]830[/C][C]765.603896446926[/C][C]64.3961035530743[/C][/ROW]
[ROW][C]42[/C][C]790[/C][C]785.443403571953[/C][C]4.55659642804687[/C][/ROW]
[ROW][C]43[/C][C]610[/C][C]655.867711357623[/C][C]-45.8677113576227[/C][/ROW]
[ROW][C]44[/C][C]870[/C][C]915.501506929645[/C][C]-45.5015069296447[/C][/ROW]
[ROW][C]45[/C][C]870[/C][C]924.876370161737[/C][C]-54.8763701617368[/C][/ROW]
[ROW][C]46[/C][C]820[/C][C]844.256224882098[/C][C]-24.2562248820981[/C][/ROW]
[ROW][C]47[/C][C]800[/C][C]833.62840259189[/C][C]-33.6284025918897[/C][/ROW]
[ROW][C]48[/C][C]840[/C][C]843.01750560135[/C][C]-3.01750560135054[/C][/ROW]
[ROW][C]49[/C][C]860[/C][C]912.646911966771[/C][C]-52.6469119667711[/C][/ROW]
[ROW][C]50[/C][C]860[/C][C]831.862282660174[/C][C]28.1377173398262[/C][/ROW]
[ROW][C]51[/C][C]730[/C][C]831.82568689939[/C][C]-101.825686899391[/C][/ROW]
[ROW][C]52[/C][C]850[/C][C]860.811652590825[/C][C]-10.8116525908246[/C][/ROW]
[ROW][C]53[/C][C]860[/C][C]849.862716672056[/C][C]10.137283327944[/C][/ROW]
[ROW][C]54[/C][C]900[/C][C]809.222588432881[/C][C]90.7774115671187[/C][/ROW]
[ROW][C]55[/C][C]610[/C][C]629.437152225326[/C][C]-19.4371522253261[/C][/ROW]
[ROW][C]56[/C][C]960[/C][C]889.13192275068[/C][C]70.8680772493205[/C][/ROW]
[ROW][C]57[/C][C]820[/C][C]889.579833673373[/C][C]-69.579833673373[/C][/ROW]
[ROW][C]58[/C][C]860[/C][C]839.110779064145[/C][C]20.8892209358548[/C][/ROW]
[ROW][C]59[/C][C]810[/C][C]819.251119892333[/C][C]-9.2511198923329[/C][/ROW]
[ROW][C]60[/C][C]820[/C][C]859.125903568773[/C][C]-39.1259035687727[/C][/ROW]
[ROW][C]61[/C][C]820[/C][C]879.029832225747[/C][C]-59.0298322257474[/C][/ROW]
[ROW][C]62[/C][C]880[/C][C]878.398656942567[/C][C]1.6013430574335[/C][/ROW]
[ROW][C]63[/C][C]840[/C][C]748.701992797365[/C][C]91.2980072026346[/C][/ROW]
[ROW][C]64[/C][C]910[/C][C]869.3905262264[/C][C]40.6094737735999[/C][/ROW]
[ROW][C]65[/C][C]860[/C][C]879.811946414572[/C][C]-19.8119464145717[/C][/ROW]
[ROW][C]66[/C][C]880[/C][C]919.441059749542[/C][C]-39.4410597495418[/C][/ROW]
[ROW][C]67[/C][C]620[/C][C]629.275592334042[/C][C]-9.2755923340419[/C][/ROW]
[ROW][C]68[/C][C]970[/C][C]978.818881697933[/C][C]-8.8188816979333[/C][/ROW]
[ROW][C]69[/C][C]810[/C][C]838.931109453398[/C][C]-28.9311094533981[/C][/ROW]
[ROW][C]70[/C][C]880[/C][C]878.5524032705[/C][C]1.44759672949965[/C][/ROW]
[ROW][C]71[/C][C]870[/C][C]828.448069234033[/C][C]41.5519307659672[/C][/ROW]
[ROW][C]72[/C][C]800[/C][C]838.809757370954[/C][C]-38.809757370954[/C][/ROW]
[ROW][C]73[/C][C]740[/C][C]838.858567647658[/C][C]-98.8585676476575[/C][/ROW]
[ROW][C]74[/C][C]1010[/C][C]898.200710242588[/C][C]111.799289757412[/C][/ROW]
[ROW][C]75[/C][C]850[/C][C]858.393823938525[/C][C]-8.39382393852497[/C][/ROW]
[ROW][C]76[/C][C]980[/C][C]928.0241351019[/C][C]51.9758648981001[/C][/ROW]
[ROW][C]77[/C][C]880[/C][C]878.303913410034[/C][C]1.69608658996583[/C][/ROW]
[ROW][C]78[/C][C]870[/C][C]898.468404606717[/C][C]-28.4684046067166[/C][/ROW]
[ROW][C]79[/C][C]660[/C][C]638.342312741677[/C][C]21.6576872583234[/C][/ROW]
[ROW][C]80[/C][C]940[/C][C]988.536587163026[/C][C]-48.5365871630262[/C][/ROW]
[ROW][C]81[/C][C]860[/C][C]828.39052347207[/C][C]31.6094765279303[/C][/ROW]
[ROW][C]82[/C][C]880[/C][C]898.625435148419[/C][C]-18.6254351484187[/C][/ROW]
[ROW][C]83[/C][C]1000[/C][C]888.35112188695[/C][C]111.64887811305[/C][/ROW]
[ROW][C]84[/C][C]840[/C][C]819.311409490105[/C][C]20.6885905098953[/C][/ROW]
[ROW][C]85[/C][C]800[/C][C]760.23217545816[/C][C]39.7678245418396[/C][/ROW]
[ROW][C]86[/C][C]1060[/C][C]1030.44086306743[/C][C]29.5591369325662[/C][/ROW]
[ROW][C]87[/C][C]790[/C][C]871.052961434444[/C][C]-81.0529614344438[/C][/ROW]
[ROW][C]88[/C][C]930[/C][C]1000.63089520965[/C][C]-70.6308952096506[/C][/ROW]
[ROW][C]89[/C][C]920[/C][C]900.274730236435[/C][C]19.7252697635647[/C][/ROW]
[ROW][C]90[/C][C]840[/C][C]890.58015495895[/C][C]-50.5801549589506[/C][/ROW]
[ROW][C]91[/C][C]690[/C][C]680.216164883848[/C][C]9.78383511615232[/C][/ROW]
[ROW][C]92[/C][C]940[/C][C]960.505115852658[/C][C]-20.5051158526577[/C][/ROW]
[ROW][C]93[/C][C]1010[/C][C]880.278279150429[/C][C]129.721720849571[/C][/ROW]
[ROW][C]94[/C][C]890[/C][C]901.290151365662[/C][C]-11.2901513656616[/C][/ROW]
[ROW][C]95[/C][C]1000[/C][C]1020.91008786625[/C][C]-20.910087866253[/C][/ROW]
[ROW][C]96[/C][C]820[/C][C]860.682749662127[/C][C]-40.6827496621273[/C][/ROW]
[ROW][C]97[/C][C]800[/C][C]820.129354709375[/C][C]-20.1293547093745[/C][/ROW]
[ROW][C]98[/C][C]1000[/C][C]1079.61389706287[/C][C]-79.6138970628735[/C][/ROW]
[ROW][C]99[/C][C]780[/C][C]809.141960308363[/C][C]-29.1419603083629[/C][/ROW]
[ROW][C]100[/C][C]1010[/C][C]948.983088812842[/C][C]61.0169111871581[/C][/ROW]
[ROW][C]101[/C][C]950[/C][C]939.09043109748[/C][C]10.9095689025195[/C][/ROW]
[ROW][C]102[/C][C]830[/C][C]859.284620525435[/C][C]-29.2846205254353[/C][/ROW]
[ROW][C]103[/C][C]670[/C][C]709.000567674647[/C][C]-39.0005676746471[/C][/ROW]
[ROW][C]104[/C][C]1000[/C][C]958.724172229962[/C][C]41.2758277700378[/C][/ROW]
[ROW][C]105[/C][C]960[/C][C]1028.21044186013[/C][C]-68.2104418601264[/C][/ROW]
[ROW][C]106[/C][C]920[/C][C]907.45840575906[/C][C]12.5415942409396[/C][/ROW]
[ROW][C]107[/C][C]1040[/C][C]1017.22339426589[/C][C]22.7766057341078[/C][/ROW]
[ROW][C]108[/C][C]860[/C][C]837.232676740796[/C][C]22.767323259204[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=123511&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=123511&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
13800780.6810897435919.3189102564104
14710692.32544260712317.674557392877
15800781.49714650364818.5028534963523
16780761.12737206138518.8726279386149
17760743.2978254481916.7021745518097
18730718.40759442500711.5924055749925
19770813.09773054951-43.0977305495103
20880844.50010419314235.4998958068578
21850835.13212909713614.8678709028638
22810780.6873420655229.3126579344806
23770808.043631824978-38.0436318249775
24810848.306734939131-38.3067349391307
25890830.20944032702359.7905596729772
26790740.63767357519649.3623264248039
27840831.071857338498.92814266150981
28830811.27500537124518.724994628755
29740791.539913327875-51.5399133278748
30760761.328414955958-1.32841495595756
31630801.634683142147-171.634683142147
32890910.389272643084-20.3892726430838
33900879.92172625184420.0782737481562
34820839.599704520739-19.599704520739
35810799.32192688778110.6780731122187
36820839.301429071773-19.3014290717731
37890918.655334925047-28.655334925047
38810817.835272294834-7.83527229483377
39810867.216752089873-57.2167520898727
40840856.157077034835-16.1570770348353
41830765.60389644692664.3961035530743
42790785.4434035719534.55659642804687
43610655.867711357623-45.8677113576227
44870915.501506929645-45.5015069296447
45870924.876370161737-54.8763701617368
46820844.256224882098-24.2562248820981
47800833.62840259189-33.6284025918897
48840843.01750560135-3.01750560135054
49860912.646911966771-52.6469119667711
50860831.86228266017428.1377173398262
51730831.82568689939-101.825686899391
52850860.811652590825-10.8116525908246
53860849.86271667205610.137283327944
54900809.22258843288190.7774115671187
55610629.437152225326-19.4371522253261
56960889.1319227506870.8680772493205
57820889.579833673373-69.579833673373
58860839.11077906414520.8892209358548
59810819.251119892333-9.2511198923329
60820859.125903568773-39.1259035687727
61820879.029832225747-59.0298322257474
62880878.3986569425671.6013430574335
63840748.70199279736591.2980072026346
64910869.390526226440.6094737735999
65860879.811946414572-19.8119464145717
66880919.441059749542-39.4410597495418
67620629.275592334042-9.2755923340419
68970978.818881697933-8.8188816979333
69810838.931109453398-28.9311094533981
70880878.55240327051.44759672949965
71870828.44806923403341.5519307659672
72800838.809757370954-38.809757370954
73740838.858567647658-98.8585676476575
741010898.200710242588111.799289757412
75850858.393823938525-8.39382393852497
76980928.024135101951.9758648981001
77880878.3039134100341.69608658996583
78870898.468404606717-28.4684046067166
79660638.34231274167721.6576872583234
80940988.536587163026-48.5365871630262
81860828.3905234720731.6094765279303
82880898.625435148419-18.6254351484187
831000888.35112188695111.64887811305
84840819.31140949010520.6885905098953
85800760.2321754581639.7678245418396
8610601030.4408630674329.5591369325662
87790871.052961434444-81.0529614344438
889301000.63089520965-70.6308952096506
89920900.27473023643519.7252697635647
90840890.58015495895-50.5801549589506
91690680.2161648838489.78383511615232
92940960.505115852658-20.5051158526577
931010880.278279150429129.721720849571
94890901.290151365662-11.2901513656616
9510001020.91008786625-20.910087866253
96820860.682749662127-40.6827496621273
97800820.129354709375-20.1293547093745
9810001079.61389706287-79.6138970628735
99780809.141960308363-29.1419603083629
1001010948.98308881284261.0169111871581
101950939.0904310974810.9095689025195
102830859.284620525435-29.2846205254353
103670709.000567674647-39.0005676746471
1041000958.72417222996241.2758277700378
1059601028.21044186013-68.2104418601264
106920907.4584057590612.5415942409396
10710401017.2233942658922.7766057341078
108860837.23267674079622.767323259204







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
109817.264125762313722.958746965632911.569504558993
1101017.52684292722923.2190090943741111.83467676007
111797.689435868169703.377571527456892.001300208882
1121027.44364263676933.1257839697551121.76150130377
113967.33383365887873.0076287071971061.66003861054
114847.4103164753753.073025436168941.747607514432
115687.596629858628593.245125484849781.948134232407
1161017.44581761178923.0765857319981111.81504949156
117977.778987845285883.388128019931072.16984767064
118937.83186012523843.4150864534881032.24863379697
1191057.80619740045963.3588394933751152.25355530753
120877.734347712722783.251351847202972.217343578242

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
109 & 817.264125762313 & 722.958746965632 & 911.569504558993 \tabularnewline
110 & 1017.52684292722 & 923.219009094374 & 1111.83467676007 \tabularnewline
111 & 797.689435868169 & 703.377571527456 & 892.001300208882 \tabularnewline
112 & 1027.44364263676 & 933.125783969755 & 1121.76150130377 \tabularnewline
113 & 967.33383365887 & 873.007628707197 & 1061.66003861054 \tabularnewline
114 & 847.4103164753 & 753.073025436168 & 941.747607514432 \tabularnewline
115 & 687.596629858628 & 593.245125484849 & 781.948134232407 \tabularnewline
116 & 1017.44581761178 & 923.076585731998 & 1111.81504949156 \tabularnewline
117 & 977.778987845285 & 883.38812801993 & 1072.16984767064 \tabularnewline
118 & 937.83186012523 & 843.415086453488 & 1032.24863379697 \tabularnewline
119 & 1057.80619740045 & 963.358839493375 & 1152.25355530753 \tabularnewline
120 & 877.734347712722 & 783.251351847202 & 972.217343578242 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=123511&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]817.264125762313[/C][C]722.958746965632[/C][C]911.569504558993[/C][/ROW]
[ROW][C]110[/C][C]1017.52684292722[/C][C]923.219009094374[/C][C]1111.83467676007[/C][/ROW]
[ROW][C]111[/C][C]797.689435868169[/C][C]703.377571527456[/C][C]892.001300208882[/C][/ROW]
[ROW][C]112[/C][C]1027.44364263676[/C][C]933.125783969755[/C][C]1121.76150130377[/C][/ROW]
[ROW][C]113[/C][C]967.33383365887[/C][C]873.007628707197[/C][C]1061.66003861054[/C][/ROW]
[ROW][C]114[/C][C]847.4103164753[/C][C]753.073025436168[/C][C]941.747607514432[/C][/ROW]
[ROW][C]115[/C][C]687.596629858628[/C][C]593.245125484849[/C][C]781.948134232407[/C][/ROW]
[ROW][C]116[/C][C]1017.44581761178[/C][C]923.076585731998[/C][C]1111.81504949156[/C][/ROW]
[ROW][C]117[/C][C]977.778987845285[/C][C]883.38812801993[/C][C]1072.16984767064[/C][/ROW]
[ROW][C]118[/C][C]937.83186012523[/C][C]843.415086453488[/C][C]1032.24863379697[/C][/ROW]
[ROW][C]119[/C][C]1057.80619740045[/C][C]963.358839493375[/C][C]1152.25355530753[/C][/ROW]
[ROW][C]120[/C][C]877.734347712722[/C][C]783.251351847202[/C][C]972.217343578242[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=123511&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=123511&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
109817.264125762313722.958746965632911.569504558993
1101017.52684292722923.2190090943741111.83467676007
111797.689435868169703.377571527456892.001300208882
1121027.44364263676933.1257839697551121.76150130377
113967.33383365887873.0076287071971061.66003861054
114847.4103164753753.073025436168941.747607514432
115687.596629858628593.245125484849781.948134232407
1161017.44581761178923.0765857319981111.81504949156
117977.778987845285883.388128019931072.16984767064
118937.83186012523843.4150864534881032.24863379697
1191057.80619740045963.3588394933751152.25355530753
120877.734347712722783.251351847202972.217343578242



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')