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of Irreproducible Research!

Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationWed, 09 Jul 2014 18:19:28 +0100
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2014/Jul/09/t1404926386kp23cezxhhbduxq.htm/, Retrieved Wed, 15 May 2024 23:26:00 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=235298, Retrieved Wed, 15 May 2024 23:26:00 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact146
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [] [2014-07-09 17:19:28] [bdb7c0ed7ba273e65f9ee772c5dda4f0] [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 time1 seconds
R Server'Sir Ronald Aylmer Fisher' @ fisher.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 & 1 seconds \tabularnewline
R Server & 'Sir Ronald Aylmer Fisher' @ fisher.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=235298&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]1 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Sir Ronald Aylmer Fisher' @ fisher.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=235298&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=235298&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 time1 seconds
R Server'Sir Ronald Aylmer Fisher' @ fisher.wessa.net







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.00495167342617471
beta0.431853374449503
gamma1

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.00495167342617471 \tabularnewline
beta & 0.431853374449503 \tabularnewline
gamma & 1 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=235298&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]0.00495167342617471[/C][/ROW]
[ROW][C]beta[/C][C]0.431853374449503[/C][/ROW]
[ROW][C]gamma[/C][C]1[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=235298&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=235298&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
alpha0.00495167342617471
beta0.431853374449503
gamma1







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
13800780.11817448095519.8818255190446
14710693.84643866697216.1535613330277
15800781.02578678518418.9742132148164
16780761.19626460210818.8037353978915
17760743.76297256597816.237027434022
18730719.07119380577110.9288061942285
19770813.386920083153-43.3869200831531
20880845.40578195532734.5942180446734
21850835.82044234730214.1795576526979
22810780.30741309024229.6925869097581
23770807.932592651586-37.9325926515864
24810848.599737426163-38.5997374261632
25890831.50902272946758.4909772705333
26790738.24873823732951.7512617626711
27840832.2266153559647.77338464403613
28830811.53545330789418.4645466921063
29740790.897789855634-50.897789855634
30760759.4000954846950.599904515305184
31630801.223606037392-171.223606037392
32890914.216667469664-24.2166674696643
33900882.43371588540417.5662841145959
34820840.433393119751-20.4333931197515
35810798.53826399883711.4617360011632
36820839.875038386764-19.875038386764
37890922.008046344579-32.0080463445786
38810817.462910444511-7.46291044451095
39810868.422389082337-58.422389082337
40840856.876426297656-16.8764262976564
41830763.33163183492966.6683681650709
42790783.7341326343636.26586736563706
43610649.933190343638-39.9331903436379
44870917.657742143509-47.6577421435088
45870927.243582395796-57.243582395796
46820844.161394282992-24.1613942829915
47800833.186630946442-33.1866309464417
48840842.802320172698-2.80232017269793
49860914.279416535795-54.2794165357948
50860831.29272970898728.7072702910131
51730831.194541813437-101.194541813437
52850860.910357588622-10.9103575886218
53860849.63026497790910.369735022091
54900807.99446880286792.0055311971332
55610624.033318220279-14.0333182202789
56960889.64618055992470.3538194400764
57820890.017958716986-70.0179587169855
58860838.39598939051621.6040106094839
59810818.051424009992-8.05142400999239
60820858.811980385015-38.8119803850152
61820879.126823184938-59.1268231849383
62880878.4750507299581.52494927004227
63840745.9099174552294.0900825447801
64910869.31488216427140.6851178357288
65860879.998229986585-19.9982299865852
66880920.555886493835-40.5558864938347
67620623.825176512999-3.82517651299906
68970981.314201991685-11.3142019916854
69810838.298279966398-28.298279966398
70880878.8209949547631.17900504523698
71870827.62567954669242.3743204533076
72800838.203787353453-38.203787353453
73740838.253748563061-98.2537485630614
741010898.921138527329111.078861472671
75850858.140761426547-8.14076142654676
76980929.22335861763550.7766413823649
77880878.3581065739071.64189342609302
78870898.888124916421-28.8881249164215
79660633.1708939856526.8291060143497
80940990.886735764828-50.8867357648282
81860827.31284940084732.6871505991535
82880899.057697493325-19.0576974933246
831000888.557611360761111.442388639239
84840817.91747976593522.0825202340646
85800757.37955182804642.6204481719536
8610601034.1185820455225.8814179544754
87790870.886768591267-80.8867685912674
889301003.67560476462-73.675604764623
89920900.97169030918519.0283096908153
90840891.051944056049-51.051944056049
91690675.66396873269714.3360312673028
92940962.650323206681-22.650323206681
931010880.495431925314129.504568074686
94890901.977514781676-11.9775147816759
9510001024.57630895835-24.5763089583531
96820860.409270719615-40.4092707196149
97800818.873278525656-18.8732785256561
9810001084.37443934405-84.3744393440479
99780807.771794789403-27.7717947894027
1001010950.69042264854459.309577351456
101950940.5229353736229.47706462637814
102830858.879939124634-28.8799391246345
103670705.233835716969-35.2338357169695
1041000960.36939964782339.6306003521767
1059601031.21181401926-71.2118140192567
106920907.9057397541412.0942602458599
10710401019.7663755684820.2336244315246
108860836.12114201388123.8788579861191

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 800 & 780.118174480955 & 19.8818255190446 \tabularnewline
14 & 710 & 693.846438666972 & 16.1535613330277 \tabularnewline
15 & 800 & 781.025786785184 & 18.9742132148164 \tabularnewline
16 & 780 & 761.196264602108 & 18.8037353978915 \tabularnewline
17 & 760 & 743.762972565978 & 16.237027434022 \tabularnewline
18 & 730 & 719.071193805771 & 10.9288061942285 \tabularnewline
19 & 770 & 813.386920083153 & -43.3869200831531 \tabularnewline
20 & 880 & 845.405781955327 & 34.5942180446734 \tabularnewline
21 & 850 & 835.820442347302 & 14.1795576526979 \tabularnewline
22 & 810 & 780.307413090242 & 29.6925869097581 \tabularnewline
23 & 770 & 807.932592651586 & -37.9325926515864 \tabularnewline
24 & 810 & 848.599737426163 & -38.5997374261632 \tabularnewline
25 & 890 & 831.509022729467 & 58.4909772705333 \tabularnewline
26 & 790 & 738.248738237329 & 51.7512617626711 \tabularnewline
27 & 840 & 832.226615355964 & 7.77338464403613 \tabularnewline
28 & 830 & 811.535453307894 & 18.4645466921063 \tabularnewline
29 & 740 & 790.897789855634 & -50.897789855634 \tabularnewline
30 & 760 & 759.400095484695 & 0.599904515305184 \tabularnewline
31 & 630 & 801.223606037392 & -171.223606037392 \tabularnewline
32 & 890 & 914.216667469664 & -24.2166674696643 \tabularnewline
33 & 900 & 882.433715885404 & 17.5662841145959 \tabularnewline
34 & 820 & 840.433393119751 & -20.4333931197515 \tabularnewline
35 & 810 & 798.538263998837 & 11.4617360011632 \tabularnewline
36 & 820 & 839.875038386764 & -19.875038386764 \tabularnewline
37 & 890 & 922.008046344579 & -32.0080463445786 \tabularnewline
38 & 810 & 817.462910444511 & -7.46291044451095 \tabularnewline
39 & 810 & 868.422389082337 & -58.422389082337 \tabularnewline
40 & 840 & 856.876426297656 & -16.8764262976564 \tabularnewline
41 & 830 & 763.331631834929 & 66.6683681650709 \tabularnewline
42 & 790 & 783.734132634363 & 6.26586736563706 \tabularnewline
43 & 610 & 649.933190343638 & -39.9331903436379 \tabularnewline
44 & 870 & 917.657742143509 & -47.6577421435088 \tabularnewline
45 & 870 & 927.243582395796 & -57.243582395796 \tabularnewline
46 & 820 & 844.161394282992 & -24.1613942829915 \tabularnewline
47 & 800 & 833.186630946442 & -33.1866309464417 \tabularnewline
48 & 840 & 842.802320172698 & -2.80232017269793 \tabularnewline
49 & 860 & 914.279416535795 & -54.2794165357948 \tabularnewline
50 & 860 & 831.292729708987 & 28.7072702910131 \tabularnewline
51 & 730 & 831.194541813437 & -101.194541813437 \tabularnewline
52 & 850 & 860.910357588622 & -10.9103575886218 \tabularnewline
53 & 860 & 849.630264977909 & 10.369735022091 \tabularnewline
54 & 900 & 807.994468802867 & 92.0055311971332 \tabularnewline
55 & 610 & 624.033318220279 & -14.0333182202789 \tabularnewline
56 & 960 & 889.646180559924 & 70.3538194400764 \tabularnewline
57 & 820 & 890.017958716986 & -70.0179587169855 \tabularnewline
58 & 860 & 838.395989390516 & 21.6040106094839 \tabularnewline
59 & 810 & 818.051424009992 & -8.05142400999239 \tabularnewline
60 & 820 & 858.811980385015 & -38.8119803850152 \tabularnewline
61 & 820 & 879.126823184938 & -59.1268231849383 \tabularnewline
62 & 880 & 878.475050729958 & 1.52494927004227 \tabularnewline
63 & 840 & 745.90991745522 & 94.0900825447801 \tabularnewline
64 & 910 & 869.314882164271 & 40.6851178357288 \tabularnewline
65 & 860 & 879.998229986585 & -19.9982299865852 \tabularnewline
66 & 880 & 920.555886493835 & -40.5558864938347 \tabularnewline
67 & 620 & 623.825176512999 & -3.82517651299906 \tabularnewline
68 & 970 & 981.314201991685 & -11.3142019916854 \tabularnewline
69 & 810 & 838.298279966398 & -28.298279966398 \tabularnewline
70 & 880 & 878.820994954763 & 1.17900504523698 \tabularnewline
71 & 870 & 827.625679546692 & 42.3743204533076 \tabularnewline
72 & 800 & 838.203787353453 & -38.203787353453 \tabularnewline
73 & 740 & 838.253748563061 & -98.2537485630614 \tabularnewline
74 & 1010 & 898.921138527329 & 111.078861472671 \tabularnewline
75 & 850 & 858.140761426547 & -8.14076142654676 \tabularnewline
76 & 980 & 929.223358617635 & 50.7766413823649 \tabularnewline
77 & 880 & 878.358106573907 & 1.64189342609302 \tabularnewline
78 & 870 & 898.888124916421 & -28.8881249164215 \tabularnewline
79 & 660 & 633.17089398565 & 26.8291060143497 \tabularnewline
80 & 940 & 990.886735764828 & -50.8867357648282 \tabularnewline
81 & 860 & 827.312849400847 & 32.6871505991535 \tabularnewline
82 & 880 & 899.057697493325 & -19.0576974933246 \tabularnewline
83 & 1000 & 888.557611360761 & 111.442388639239 \tabularnewline
84 & 840 & 817.917479765935 & 22.0825202340646 \tabularnewline
85 & 800 & 757.379551828046 & 42.6204481719536 \tabularnewline
86 & 1060 & 1034.11858204552 & 25.8814179544754 \tabularnewline
87 & 790 & 870.886768591267 & -80.8867685912674 \tabularnewline
88 & 930 & 1003.67560476462 & -73.675604764623 \tabularnewline
89 & 920 & 900.971690309185 & 19.0283096908153 \tabularnewline
90 & 840 & 891.051944056049 & -51.051944056049 \tabularnewline
91 & 690 & 675.663968732697 & 14.3360312673028 \tabularnewline
92 & 940 & 962.650323206681 & -22.650323206681 \tabularnewline
93 & 1010 & 880.495431925314 & 129.504568074686 \tabularnewline
94 & 890 & 901.977514781676 & -11.9775147816759 \tabularnewline
95 & 1000 & 1024.57630895835 & -24.5763089583531 \tabularnewline
96 & 820 & 860.409270719615 & -40.4092707196149 \tabularnewline
97 & 800 & 818.873278525656 & -18.8732785256561 \tabularnewline
98 & 1000 & 1084.37443934405 & -84.3744393440479 \tabularnewline
99 & 780 & 807.771794789403 & -27.7717947894027 \tabularnewline
100 & 1010 & 950.690422648544 & 59.309577351456 \tabularnewline
101 & 950 & 940.522935373622 & 9.47706462637814 \tabularnewline
102 & 830 & 858.879939124634 & -28.8799391246345 \tabularnewline
103 & 670 & 705.233835716969 & -35.2338357169695 \tabularnewline
104 & 1000 & 960.369399647823 & 39.6306003521767 \tabularnewline
105 & 960 & 1031.21181401926 & -71.2118140192567 \tabularnewline
106 & 920 & 907.90573975414 & 12.0942602458599 \tabularnewline
107 & 1040 & 1019.76637556848 & 20.2336244315246 \tabularnewline
108 & 860 & 836.121142013881 & 23.8788579861191 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=235298&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]780.118174480955[/C][C]19.8818255190446[/C][/ROW]
[ROW][C]14[/C][C]710[/C][C]693.846438666972[/C][C]16.1535613330277[/C][/ROW]
[ROW][C]15[/C][C]800[/C][C]781.025786785184[/C][C]18.9742132148164[/C][/ROW]
[ROW][C]16[/C][C]780[/C][C]761.196264602108[/C][C]18.8037353978915[/C][/ROW]
[ROW][C]17[/C][C]760[/C][C]743.762972565978[/C][C]16.237027434022[/C][/ROW]
[ROW][C]18[/C][C]730[/C][C]719.071193805771[/C][C]10.9288061942285[/C][/ROW]
[ROW][C]19[/C][C]770[/C][C]813.386920083153[/C][C]-43.3869200831531[/C][/ROW]
[ROW][C]20[/C][C]880[/C][C]845.405781955327[/C][C]34.5942180446734[/C][/ROW]
[ROW][C]21[/C][C]850[/C][C]835.820442347302[/C][C]14.1795576526979[/C][/ROW]
[ROW][C]22[/C][C]810[/C][C]780.307413090242[/C][C]29.6925869097581[/C][/ROW]
[ROW][C]23[/C][C]770[/C][C]807.932592651586[/C][C]-37.9325926515864[/C][/ROW]
[ROW][C]24[/C][C]810[/C][C]848.599737426163[/C][C]-38.5997374261632[/C][/ROW]
[ROW][C]25[/C][C]890[/C][C]831.509022729467[/C][C]58.4909772705333[/C][/ROW]
[ROW][C]26[/C][C]790[/C][C]738.248738237329[/C][C]51.7512617626711[/C][/ROW]
[ROW][C]27[/C][C]840[/C][C]832.226615355964[/C][C]7.77338464403613[/C][/ROW]
[ROW][C]28[/C][C]830[/C][C]811.535453307894[/C][C]18.4645466921063[/C][/ROW]
[ROW][C]29[/C][C]740[/C][C]790.897789855634[/C][C]-50.897789855634[/C][/ROW]
[ROW][C]30[/C][C]760[/C][C]759.400095484695[/C][C]0.599904515305184[/C][/ROW]
[ROW][C]31[/C][C]630[/C][C]801.223606037392[/C][C]-171.223606037392[/C][/ROW]
[ROW][C]32[/C][C]890[/C][C]914.216667469664[/C][C]-24.2166674696643[/C][/ROW]
[ROW][C]33[/C][C]900[/C][C]882.433715885404[/C][C]17.5662841145959[/C][/ROW]
[ROW][C]34[/C][C]820[/C][C]840.433393119751[/C][C]-20.4333931197515[/C][/ROW]
[ROW][C]35[/C][C]810[/C][C]798.538263998837[/C][C]11.4617360011632[/C][/ROW]
[ROW][C]36[/C][C]820[/C][C]839.875038386764[/C][C]-19.875038386764[/C][/ROW]
[ROW][C]37[/C][C]890[/C][C]922.008046344579[/C][C]-32.0080463445786[/C][/ROW]
[ROW][C]38[/C][C]810[/C][C]817.462910444511[/C][C]-7.46291044451095[/C][/ROW]
[ROW][C]39[/C][C]810[/C][C]868.422389082337[/C][C]-58.422389082337[/C][/ROW]
[ROW][C]40[/C][C]840[/C][C]856.876426297656[/C][C]-16.8764262976564[/C][/ROW]
[ROW][C]41[/C][C]830[/C][C]763.331631834929[/C][C]66.6683681650709[/C][/ROW]
[ROW][C]42[/C][C]790[/C][C]783.734132634363[/C][C]6.26586736563706[/C][/ROW]
[ROW][C]43[/C][C]610[/C][C]649.933190343638[/C][C]-39.9331903436379[/C][/ROW]
[ROW][C]44[/C][C]870[/C][C]917.657742143509[/C][C]-47.6577421435088[/C][/ROW]
[ROW][C]45[/C][C]870[/C][C]927.243582395796[/C][C]-57.243582395796[/C][/ROW]
[ROW][C]46[/C][C]820[/C][C]844.161394282992[/C][C]-24.1613942829915[/C][/ROW]
[ROW][C]47[/C][C]800[/C][C]833.186630946442[/C][C]-33.1866309464417[/C][/ROW]
[ROW][C]48[/C][C]840[/C][C]842.802320172698[/C][C]-2.80232017269793[/C][/ROW]
[ROW][C]49[/C][C]860[/C][C]914.279416535795[/C][C]-54.2794165357948[/C][/ROW]
[ROW][C]50[/C][C]860[/C][C]831.292729708987[/C][C]28.7072702910131[/C][/ROW]
[ROW][C]51[/C][C]730[/C][C]831.194541813437[/C][C]-101.194541813437[/C][/ROW]
[ROW][C]52[/C][C]850[/C][C]860.910357588622[/C][C]-10.9103575886218[/C][/ROW]
[ROW][C]53[/C][C]860[/C][C]849.630264977909[/C][C]10.369735022091[/C][/ROW]
[ROW][C]54[/C][C]900[/C][C]807.994468802867[/C][C]92.0055311971332[/C][/ROW]
[ROW][C]55[/C][C]610[/C][C]624.033318220279[/C][C]-14.0333182202789[/C][/ROW]
[ROW][C]56[/C][C]960[/C][C]889.646180559924[/C][C]70.3538194400764[/C][/ROW]
[ROW][C]57[/C][C]820[/C][C]890.017958716986[/C][C]-70.0179587169855[/C][/ROW]
[ROW][C]58[/C][C]860[/C][C]838.395989390516[/C][C]21.6040106094839[/C][/ROW]
[ROW][C]59[/C][C]810[/C][C]818.051424009992[/C][C]-8.05142400999239[/C][/ROW]
[ROW][C]60[/C][C]820[/C][C]858.811980385015[/C][C]-38.8119803850152[/C][/ROW]
[ROW][C]61[/C][C]820[/C][C]879.126823184938[/C][C]-59.1268231849383[/C][/ROW]
[ROW][C]62[/C][C]880[/C][C]878.475050729958[/C][C]1.52494927004227[/C][/ROW]
[ROW][C]63[/C][C]840[/C][C]745.90991745522[/C][C]94.0900825447801[/C][/ROW]
[ROW][C]64[/C][C]910[/C][C]869.314882164271[/C][C]40.6851178357288[/C][/ROW]
[ROW][C]65[/C][C]860[/C][C]879.998229986585[/C][C]-19.9982299865852[/C][/ROW]
[ROW][C]66[/C][C]880[/C][C]920.555886493835[/C][C]-40.5558864938347[/C][/ROW]
[ROW][C]67[/C][C]620[/C][C]623.825176512999[/C][C]-3.82517651299906[/C][/ROW]
[ROW][C]68[/C][C]970[/C][C]981.314201991685[/C][C]-11.3142019916854[/C][/ROW]
[ROW][C]69[/C][C]810[/C][C]838.298279966398[/C][C]-28.298279966398[/C][/ROW]
[ROW][C]70[/C][C]880[/C][C]878.820994954763[/C][C]1.17900504523698[/C][/ROW]
[ROW][C]71[/C][C]870[/C][C]827.625679546692[/C][C]42.3743204533076[/C][/ROW]
[ROW][C]72[/C][C]800[/C][C]838.203787353453[/C][C]-38.203787353453[/C][/ROW]
[ROW][C]73[/C][C]740[/C][C]838.253748563061[/C][C]-98.2537485630614[/C][/ROW]
[ROW][C]74[/C][C]1010[/C][C]898.921138527329[/C][C]111.078861472671[/C][/ROW]
[ROW][C]75[/C][C]850[/C][C]858.140761426547[/C][C]-8.14076142654676[/C][/ROW]
[ROW][C]76[/C][C]980[/C][C]929.223358617635[/C][C]50.7766413823649[/C][/ROW]
[ROW][C]77[/C][C]880[/C][C]878.358106573907[/C][C]1.64189342609302[/C][/ROW]
[ROW][C]78[/C][C]870[/C][C]898.888124916421[/C][C]-28.8881249164215[/C][/ROW]
[ROW][C]79[/C][C]660[/C][C]633.17089398565[/C][C]26.8291060143497[/C][/ROW]
[ROW][C]80[/C][C]940[/C][C]990.886735764828[/C][C]-50.8867357648282[/C][/ROW]
[ROW][C]81[/C][C]860[/C][C]827.312849400847[/C][C]32.6871505991535[/C][/ROW]
[ROW][C]82[/C][C]880[/C][C]899.057697493325[/C][C]-19.0576974933246[/C][/ROW]
[ROW][C]83[/C][C]1000[/C][C]888.557611360761[/C][C]111.442388639239[/C][/ROW]
[ROW][C]84[/C][C]840[/C][C]817.917479765935[/C][C]22.0825202340646[/C][/ROW]
[ROW][C]85[/C][C]800[/C][C]757.379551828046[/C][C]42.6204481719536[/C][/ROW]
[ROW][C]86[/C][C]1060[/C][C]1034.11858204552[/C][C]25.8814179544754[/C][/ROW]
[ROW][C]87[/C][C]790[/C][C]870.886768591267[/C][C]-80.8867685912674[/C][/ROW]
[ROW][C]88[/C][C]930[/C][C]1003.67560476462[/C][C]-73.675604764623[/C][/ROW]
[ROW][C]89[/C][C]920[/C][C]900.971690309185[/C][C]19.0283096908153[/C][/ROW]
[ROW][C]90[/C][C]840[/C][C]891.051944056049[/C][C]-51.051944056049[/C][/ROW]
[ROW][C]91[/C][C]690[/C][C]675.663968732697[/C][C]14.3360312673028[/C][/ROW]
[ROW][C]92[/C][C]940[/C][C]962.650323206681[/C][C]-22.650323206681[/C][/ROW]
[ROW][C]93[/C][C]1010[/C][C]880.495431925314[/C][C]129.504568074686[/C][/ROW]
[ROW][C]94[/C][C]890[/C][C]901.977514781676[/C][C]-11.9775147816759[/C][/ROW]
[ROW][C]95[/C][C]1000[/C][C]1024.57630895835[/C][C]-24.5763089583531[/C][/ROW]
[ROW][C]96[/C][C]820[/C][C]860.409270719615[/C][C]-40.4092707196149[/C][/ROW]
[ROW][C]97[/C][C]800[/C][C]818.873278525656[/C][C]-18.8732785256561[/C][/ROW]
[ROW][C]98[/C][C]1000[/C][C]1084.37443934405[/C][C]-84.3744393440479[/C][/ROW]
[ROW][C]99[/C][C]780[/C][C]807.771794789403[/C][C]-27.7717947894027[/C][/ROW]
[ROW][C]100[/C][C]1010[/C][C]950.690422648544[/C][C]59.309577351456[/C][/ROW]
[ROW][C]101[/C][C]950[/C][C]940.522935373622[/C][C]9.47706462637814[/C][/ROW]
[ROW][C]102[/C][C]830[/C][C]858.879939124634[/C][C]-28.8799391246345[/C][/ROW]
[ROW][C]103[/C][C]670[/C][C]705.233835716969[/C][C]-35.2338357169695[/C][/ROW]
[ROW][C]104[/C][C]1000[/C][C]960.369399647823[/C][C]39.6306003521767[/C][/ROW]
[ROW][C]105[/C][C]960[/C][C]1031.21181401926[/C][C]-71.2118140192567[/C][/ROW]
[ROW][C]106[/C][C]920[/C][C]907.90573975414[/C][C]12.0942602458599[/C][/ROW]
[ROW][C]107[/C][C]1040[/C][C]1019.76637556848[/C][C]20.2336244315246[/C][/ROW]
[ROW][C]108[/C][C]860[/C][C]836.121142013881[/C][C]23.8788579861191[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=235298&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=235298&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
13800780.11817448095519.8818255190446
14710693.84643866697216.1535613330277
15800781.02578678518418.9742132148164
16780761.19626460210818.8037353978915
17760743.76297256597816.237027434022
18730719.07119380577110.9288061942285
19770813.386920083153-43.3869200831531
20880845.40578195532734.5942180446734
21850835.82044234730214.1795576526979
22810780.30741309024229.6925869097581
23770807.932592651586-37.9325926515864
24810848.599737426163-38.5997374261632
25890831.50902272946758.4909772705333
26790738.24873823732951.7512617626711
27840832.2266153559647.77338464403613
28830811.53545330789418.4645466921063
29740790.897789855634-50.897789855634
30760759.4000954846950.599904515305184
31630801.223606037392-171.223606037392
32890914.216667469664-24.2166674696643
33900882.43371588540417.5662841145959
34820840.433393119751-20.4333931197515
35810798.53826399883711.4617360011632
36820839.875038386764-19.875038386764
37890922.008046344579-32.0080463445786
38810817.462910444511-7.46291044451095
39810868.422389082337-58.422389082337
40840856.876426297656-16.8764262976564
41830763.33163183492966.6683681650709
42790783.7341326343636.26586736563706
43610649.933190343638-39.9331903436379
44870917.657742143509-47.6577421435088
45870927.243582395796-57.243582395796
46820844.161394282992-24.1613942829915
47800833.186630946442-33.1866309464417
48840842.802320172698-2.80232017269793
49860914.279416535795-54.2794165357948
50860831.29272970898728.7072702910131
51730831.194541813437-101.194541813437
52850860.910357588622-10.9103575886218
53860849.63026497790910.369735022091
54900807.99446880286792.0055311971332
55610624.033318220279-14.0333182202789
56960889.64618055992470.3538194400764
57820890.017958716986-70.0179587169855
58860838.39598939051621.6040106094839
59810818.051424009992-8.05142400999239
60820858.811980385015-38.8119803850152
61820879.126823184938-59.1268231849383
62880878.4750507299581.52494927004227
63840745.9099174552294.0900825447801
64910869.31488216427140.6851178357288
65860879.998229986585-19.9982299865852
66880920.555886493835-40.5558864938347
67620623.825176512999-3.82517651299906
68970981.314201991685-11.3142019916854
69810838.298279966398-28.298279966398
70880878.8209949547631.17900504523698
71870827.62567954669242.3743204533076
72800838.203787353453-38.203787353453
73740838.253748563061-98.2537485630614
741010898.921138527329111.078861472671
75850858.140761426547-8.14076142654676
76980929.22335861763550.7766413823649
77880878.3581065739071.64189342609302
78870898.888124916421-28.8881249164215
79660633.1708939856526.8291060143497
80940990.886735764828-50.8867357648282
81860827.31284940084732.6871505991535
82880899.057697493325-19.0576974933246
831000888.557611360761111.442388639239
84840817.91747976593522.0825202340646
85800757.37955182804642.6204481719536
8610601034.1185820455225.8814179544754
87790870.886768591267-80.8867685912674
889301003.67560476462-73.675604764623
89920900.97169030918519.0283096908153
90840891.051944056049-51.051944056049
91690675.66396873269714.3360312673028
92940962.650323206681-22.650323206681
931010880.495431925314129.504568074686
94890901.977514781676-11.9775147816759
9510001024.57630895835-24.5763089583531
96820860.409270719615-40.4092707196149
97800818.873278525656-18.8732785256561
9810001084.37443934405-84.3744393440479
99780807.771794789403-27.7717947894027
1001010950.69042264854459.309577351456
101950940.5229353736229.47706462637814
102830858.879939124634-28.8799391246345
103670705.233835716969-35.2338357169695
1041000960.36939964782339.6306003521767
1059601031.21181401926-71.2118140192567
106920907.9057397541412.0942602458599
10710401019.7663755684820.2336244315246
108860836.12114201388123.8788579861191







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
109815.71359786578720.873681878855910.553513852704
1101019.80738179668924.9637522336451114.65101135972
111795.53988830863700.694710436051890.385066181209
1121029.82088666324934.9632293911161124.67854393537
113968.482401516179873.616935679781063.34786735258
114846.17244425975751.302983204883941.041905314616
115683.179201052201588.311340048648778.047062055754
1161019.50401834734924.5757592271991114.43227746748
117979.01281306303884.0637601143911073.96186601167
118938.252795519557843.2822360654861033.22335497363
1191060.60534381012965.5527422024421155.6579454178
120876.940608786869821.394416879473932.486800694265

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
109 & 815.71359786578 & 720.873681878855 & 910.553513852704 \tabularnewline
110 & 1019.80738179668 & 924.963752233645 & 1114.65101135972 \tabularnewline
111 & 795.53988830863 & 700.694710436051 & 890.385066181209 \tabularnewline
112 & 1029.82088666324 & 934.963229391116 & 1124.67854393537 \tabularnewline
113 & 968.482401516179 & 873.61693567978 & 1063.34786735258 \tabularnewline
114 & 846.17244425975 & 751.302983204883 & 941.041905314616 \tabularnewline
115 & 683.179201052201 & 588.311340048648 & 778.047062055754 \tabularnewline
116 & 1019.50401834734 & 924.575759227199 & 1114.43227746748 \tabularnewline
117 & 979.01281306303 & 884.063760114391 & 1073.96186601167 \tabularnewline
118 & 938.252795519557 & 843.282236065486 & 1033.22335497363 \tabularnewline
119 & 1060.60534381012 & 965.552742202442 & 1155.6579454178 \tabularnewline
120 & 876.940608786869 & 821.394416879473 & 932.486800694265 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=235298&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]815.71359786578[/C][C]720.873681878855[/C][C]910.553513852704[/C][/ROW]
[ROW][C]110[/C][C]1019.80738179668[/C][C]924.963752233645[/C][C]1114.65101135972[/C][/ROW]
[ROW][C]111[/C][C]795.53988830863[/C][C]700.694710436051[/C][C]890.385066181209[/C][/ROW]
[ROW][C]112[/C][C]1029.82088666324[/C][C]934.963229391116[/C][C]1124.67854393537[/C][/ROW]
[ROW][C]113[/C][C]968.482401516179[/C][C]873.61693567978[/C][C]1063.34786735258[/C][/ROW]
[ROW][C]114[/C][C]846.17244425975[/C][C]751.302983204883[/C][C]941.041905314616[/C][/ROW]
[ROW][C]115[/C][C]683.179201052201[/C][C]588.311340048648[/C][C]778.047062055754[/C][/ROW]
[ROW][C]116[/C][C]1019.50401834734[/C][C]924.575759227199[/C][C]1114.43227746748[/C][/ROW]
[ROW][C]117[/C][C]979.01281306303[/C][C]884.063760114391[/C][C]1073.96186601167[/C][/ROW]
[ROW][C]118[/C][C]938.252795519557[/C][C]843.282236065486[/C][C]1033.22335497363[/C][/ROW]
[ROW][C]119[/C][C]1060.60534381012[/C][C]965.552742202442[/C][C]1155.6579454178[/C][/ROW]
[ROW][C]120[/C][C]876.940608786869[/C][C]821.394416879473[/C][C]932.486800694265[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=235298&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=235298&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
109815.71359786578720.873681878855910.553513852704
1101019.80738179668924.9637522336451114.65101135972
111795.53988830863700.694710436051890.385066181209
1121029.82088666324934.9632293911161124.67854393537
113968.482401516179873.616935679781063.34786735258
114846.17244425975751.302983204883941.041905314616
115683.179201052201588.311340048648778.047062055754
1161019.50401834734924.5757592271991114.43227746748
117979.01281306303884.0637601143911073.96186601167
118938.252795519557843.2822360654861033.22335497363
1191060.60534381012965.5527422024421155.6579454178
120876.940608786869821.394416879473932.486800694265



Parameters (Session):
par1 = grey ;
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')