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Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationThu, 04 Aug 2011 07:12:36 -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/04/t1312456382dqujg212kptjkw9.htm/, Retrieved Sun, 10 Nov 2024 19:47:15 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=123387, Retrieved Sun, 10 Nov 2024 19:47:15 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywordsDe Wolf Davy
Estimated Impact232
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [TIJDREEKS B - STA...] [2011-08-04 11:12:36] [75b7fe93b57f9e359de9d9cae642ffd9] [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'Herman Ole Andreas Wold' @ wold.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 & 'Herman Ole Andreas Wold' @ wold.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=123387&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]'Herman Ole Andreas Wold' @ wold.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=123387&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=123387&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'Herman Ole Andreas Wold' @ wold.wessa.net







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.00495167342553283
beta0.431853374512614
gamma1

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.00495167342553283 \tabularnewline
beta & 0.431853374512614 \tabularnewline
gamma & 1 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=123387&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]0.00495167342553283[/C][/ROW]
[ROW][C]beta[/C][C]0.431853374512614[/C][/ROW]
[ROW][C]gamma[/C][C]1[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=123387&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=123387&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
alpha0.00495167342553283
beta0.431853374512614
gamma1







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
13800780.11817448095619.8818255190445
14710693.84643866696216.1535613330382
15800781.02578678516218.9742132148382
16780761.19626460207818.8037353979223
17760743.76297256593916.2370274340609
18730719.07119380572810.9288061942723
19770813.3869200831-43.3869200831003
20880845.40578195530434.5942180446957
21850835.82044234726314.1795576527372
22810780.30741309020229.6925869097984
23770807.932592651531-37.9325926515312
24810848.599737426136-38.5997374261361
25890831.50902272948158.4909772705188
26790738.24873823732451.7512617626762
27840832.226615355947.77338464406023
28830811.53545330788418.4645466921164
29740790.897789855629-50.8977898556287
30760759.4000954847310.599904515269145
31630801.223606037403-171.223606037403
32890914.216667469824-24.2166674698235
33900882.43371588557617.5662841144242
34820840.433393119918-20.4333931199178
35810798.53826399897411.4617360010255
36820839.875038386869-19.8750383868692
37890922.008046344742-32.0080463447424
38810817.462910444701-7.46291044470127
39810868.422389082536-58.4223890825356
40840856.876426297886-16.8764262978856
41830763.33163183509566.6683681649051
42790783.7341326344776.26586736552258
43610649.93319034363-39.9331903436301
44870917.657742143511-47.6577421435111
45870927.243582395833-57.2435823958331
46820844.161394283036-24.161394283036
47800833.186630946499-33.1866309464991
48840842.802320172753-2.8023201727533
49860914.279416535825-54.2794165358255
50860831.29272970903128.7072702909687
51730831.194541813418-101.194541813418
52850860.910357588649-10.910357588649
53860849.63026497798110.369735022019
54900807.99446880292292.0055311970783
55610624.033318220244-14.0333182202444
56960889.6461805598570.3538194401503
57820890.017958716829-70.0179587168287
58860838.39598939039321.604010609607
59810818.051424009837-8.05142400983743
60820858.811980384857-38.8119803848574
61820879.126823184769-59.1268231847689
62880878.4750507298471.52494927015346
63840745.90991745506694.0900825449345
64910869.31488216402240.6851178359781
65860879.998229986325-19.9982299863246
66880920.555886493654-40.555886493654
67620623.825176512889-3.8251765128889
68970981.314201991572-11.3142019915718
69810838.298279966267-28.2982799662672
70880878.8209949546631.17900504533702
71870827.62567954659542.3743204534053
72800838.203787353307-38.2037873533066
73740838.253748562908-98.2537485629077
741010898.921138527236111.078861472764
75850858.140761426466-8.1407614264657
76980929.22335861758250.7766413824179
77880878.3581065738141.64189342618579
78870898.888124916302-28.8881249163021
79660633.17089398557926.8291060144214
80940990.886735764686-50.8867357646863
81860827.3128494007432.6871505992597
82880899.057697493192-19.0576974931923
831000888.557611360676111.442388639324
84840817.91747976577422.0825202342264
85800757.37955182783442.6204481721655
8610601034.118582045325.8814179547016
87790870.88676859107-80.8867685910701
889301003.6756047645-73.6756047645022
89920900.97169030912519.0283096908746
90840891.051944055965-51.0519440559655
91690675.66396873268114.3360312673192
92940962.650323206617-22.6503232066167
931010880.495431925295129.504568074705
94890901.977514781568-11.9775147815676
9510001024.57630895833-24.5763089583311
96820860.409270719627-40.4092707196273
97800818.873278525722-18.8732785257216
9810001084.37443934416-84.3744393441632
99780807.771794789473-27.7717947894735
1001010950.69042264859759.3095773514027
101950940.5229353736489.47706462635188
102830858.879939124619-28.8799391246195
103670705.233835716981-35.233835716981
1041000960.36939964785239.6306003521481
1059601031.21181401936-71.2118140193556
106920907.9057397542512.0942602457502
10710401019.7663755685620.2336244314361
108860836.12114201391123.878857986089

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 800 & 780.118174480956 & 19.8818255190445 \tabularnewline
14 & 710 & 693.846438666962 & 16.1535613330382 \tabularnewline
15 & 800 & 781.025786785162 & 18.9742132148382 \tabularnewline
16 & 780 & 761.196264602078 & 18.8037353979223 \tabularnewline
17 & 760 & 743.762972565939 & 16.2370274340609 \tabularnewline
18 & 730 & 719.071193805728 & 10.9288061942723 \tabularnewline
19 & 770 & 813.3869200831 & -43.3869200831003 \tabularnewline
20 & 880 & 845.405781955304 & 34.5942180446957 \tabularnewline
21 & 850 & 835.820442347263 & 14.1795576527372 \tabularnewline
22 & 810 & 780.307413090202 & 29.6925869097984 \tabularnewline
23 & 770 & 807.932592651531 & -37.9325926515312 \tabularnewline
24 & 810 & 848.599737426136 & -38.5997374261361 \tabularnewline
25 & 890 & 831.509022729481 & 58.4909772705188 \tabularnewline
26 & 790 & 738.248738237324 & 51.7512617626762 \tabularnewline
27 & 840 & 832.22661535594 & 7.77338464406023 \tabularnewline
28 & 830 & 811.535453307884 & 18.4645466921164 \tabularnewline
29 & 740 & 790.897789855629 & -50.8977898556287 \tabularnewline
30 & 760 & 759.400095484731 & 0.599904515269145 \tabularnewline
31 & 630 & 801.223606037403 & -171.223606037403 \tabularnewline
32 & 890 & 914.216667469824 & -24.2166674698235 \tabularnewline
33 & 900 & 882.433715885576 & 17.5662841144242 \tabularnewline
34 & 820 & 840.433393119918 & -20.4333931199178 \tabularnewline
35 & 810 & 798.538263998974 & 11.4617360010255 \tabularnewline
36 & 820 & 839.875038386869 & -19.8750383868692 \tabularnewline
37 & 890 & 922.008046344742 & -32.0080463447424 \tabularnewline
38 & 810 & 817.462910444701 & -7.46291044470127 \tabularnewline
39 & 810 & 868.422389082536 & -58.4223890825356 \tabularnewline
40 & 840 & 856.876426297886 & -16.8764262978856 \tabularnewline
41 & 830 & 763.331631835095 & 66.6683681649051 \tabularnewline
42 & 790 & 783.734132634477 & 6.26586736552258 \tabularnewline
43 & 610 & 649.93319034363 & -39.9331903436301 \tabularnewline
44 & 870 & 917.657742143511 & -47.6577421435111 \tabularnewline
45 & 870 & 927.243582395833 & -57.2435823958331 \tabularnewline
46 & 820 & 844.161394283036 & -24.161394283036 \tabularnewline
47 & 800 & 833.186630946499 & -33.1866309464991 \tabularnewline
48 & 840 & 842.802320172753 & -2.8023201727533 \tabularnewline
49 & 860 & 914.279416535825 & -54.2794165358255 \tabularnewline
50 & 860 & 831.292729709031 & 28.7072702909687 \tabularnewline
51 & 730 & 831.194541813418 & -101.194541813418 \tabularnewline
52 & 850 & 860.910357588649 & -10.910357588649 \tabularnewline
53 & 860 & 849.630264977981 & 10.369735022019 \tabularnewline
54 & 900 & 807.994468802922 & 92.0055311970783 \tabularnewline
55 & 610 & 624.033318220244 & -14.0333182202444 \tabularnewline
56 & 960 & 889.64618055985 & 70.3538194401503 \tabularnewline
57 & 820 & 890.017958716829 & -70.0179587168287 \tabularnewline
58 & 860 & 838.395989390393 & 21.604010609607 \tabularnewline
59 & 810 & 818.051424009837 & -8.05142400983743 \tabularnewline
60 & 820 & 858.811980384857 & -38.8119803848574 \tabularnewline
61 & 820 & 879.126823184769 & -59.1268231847689 \tabularnewline
62 & 880 & 878.475050729847 & 1.52494927015346 \tabularnewline
63 & 840 & 745.909917455066 & 94.0900825449345 \tabularnewline
64 & 910 & 869.314882164022 & 40.6851178359781 \tabularnewline
65 & 860 & 879.998229986325 & -19.9982299863246 \tabularnewline
66 & 880 & 920.555886493654 & -40.555886493654 \tabularnewline
67 & 620 & 623.825176512889 & -3.8251765128889 \tabularnewline
68 & 970 & 981.314201991572 & -11.3142019915718 \tabularnewline
69 & 810 & 838.298279966267 & -28.2982799662672 \tabularnewline
70 & 880 & 878.820994954663 & 1.17900504533702 \tabularnewline
71 & 870 & 827.625679546595 & 42.3743204534053 \tabularnewline
72 & 800 & 838.203787353307 & -38.2037873533066 \tabularnewline
73 & 740 & 838.253748562908 & -98.2537485629077 \tabularnewline
74 & 1010 & 898.921138527236 & 111.078861472764 \tabularnewline
75 & 850 & 858.140761426466 & -8.1407614264657 \tabularnewline
76 & 980 & 929.223358617582 & 50.7766413824179 \tabularnewline
77 & 880 & 878.358106573814 & 1.64189342618579 \tabularnewline
78 & 870 & 898.888124916302 & -28.8881249163021 \tabularnewline
79 & 660 & 633.170893985579 & 26.8291060144214 \tabularnewline
80 & 940 & 990.886735764686 & -50.8867357646863 \tabularnewline
81 & 860 & 827.31284940074 & 32.6871505992597 \tabularnewline
82 & 880 & 899.057697493192 & -19.0576974931923 \tabularnewline
83 & 1000 & 888.557611360676 & 111.442388639324 \tabularnewline
84 & 840 & 817.917479765774 & 22.0825202342264 \tabularnewline
85 & 800 & 757.379551827834 & 42.6204481721655 \tabularnewline
86 & 1060 & 1034.1185820453 & 25.8814179547016 \tabularnewline
87 & 790 & 870.88676859107 & -80.8867685910701 \tabularnewline
88 & 930 & 1003.6756047645 & -73.6756047645022 \tabularnewline
89 & 920 & 900.971690309125 & 19.0283096908746 \tabularnewline
90 & 840 & 891.051944055965 & -51.0519440559655 \tabularnewline
91 & 690 & 675.663968732681 & 14.3360312673192 \tabularnewline
92 & 940 & 962.650323206617 & -22.6503232066167 \tabularnewline
93 & 1010 & 880.495431925295 & 129.504568074705 \tabularnewline
94 & 890 & 901.977514781568 & -11.9775147815676 \tabularnewline
95 & 1000 & 1024.57630895833 & -24.5763089583311 \tabularnewline
96 & 820 & 860.409270719627 & -40.4092707196273 \tabularnewline
97 & 800 & 818.873278525722 & -18.8732785257216 \tabularnewline
98 & 1000 & 1084.37443934416 & -84.3744393441632 \tabularnewline
99 & 780 & 807.771794789473 & -27.7717947894735 \tabularnewline
100 & 1010 & 950.690422648597 & 59.3095773514027 \tabularnewline
101 & 950 & 940.522935373648 & 9.47706462635188 \tabularnewline
102 & 830 & 858.879939124619 & -28.8799391246195 \tabularnewline
103 & 670 & 705.233835716981 & -35.233835716981 \tabularnewline
104 & 1000 & 960.369399647852 & 39.6306003521481 \tabularnewline
105 & 960 & 1031.21181401936 & -71.2118140193556 \tabularnewline
106 & 920 & 907.90573975425 & 12.0942602457502 \tabularnewline
107 & 1040 & 1019.76637556856 & 20.2336244314361 \tabularnewline
108 & 860 & 836.121142013911 & 23.878857986089 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=123387&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]780.118174480956[/C][C]19.8818255190445[/C][/ROW]
[ROW][C]14[/C][C]710[/C][C]693.846438666962[/C][C]16.1535613330382[/C][/ROW]
[ROW][C]15[/C][C]800[/C][C]781.025786785162[/C][C]18.9742132148382[/C][/ROW]
[ROW][C]16[/C][C]780[/C][C]761.196264602078[/C][C]18.8037353979223[/C][/ROW]
[ROW][C]17[/C][C]760[/C][C]743.762972565939[/C][C]16.2370274340609[/C][/ROW]
[ROW][C]18[/C][C]730[/C][C]719.071193805728[/C][C]10.9288061942723[/C][/ROW]
[ROW][C]19[/C][C]770[/C][C]813.3869200831[/C][C]-43.3869200831003[/C][/ROW]
[ROW][C]20[/C][C]880[/C][C]845.405781955304[/C][C]34.5942180446957[/C][/ROW]
[ROW][C]21[/C][C]850[/C][C]835.820442347263[/C][C]14.1795576527372[/C][/ROW]
[ROW][C]22[/C][C]810[/C][C]780.307413090202[/C][C]29.6925869097984[/C][/ROW]
[ROW][C]23[/C][C]770[/C][C]807.932592651531[/C][C]-37.9325926515312[/C][/ROW]
[ROW][C]24[/C][C]810[/C][C]848.599737426136[/C][C]-38.5997374261361[/C][/ROW]
[ROW][C]25[/C][C]890[/C][C]831.509022729481[/C][C]58.4909772705188[/C][/ROW]
[ROW][C]26[/C][C]790[/C][C]738.248738237324[/C][C]51.7512617626762[/C][/ROW]
[ROW][C]27[/C][C]840[/C][C]832.22661535594[/C][C]7.77338464406023[/C][/ROW]
[ROW][C]28[/C][C]830[/C][C]811.535453307884[/C][C]18.4645466921164[/C][/ROW]
[ROW][C]29[/C][C]740[/C][C]790.897789855629[/C][C]-50.8977898556287[/C][/ROW]
[ROW][C]30[/C][C]760[/C][C]759.400095484731[/C][C]0.599904515269145[/C][/ROW]
[ROW][C]31[/C][C]630[/C][C]801.223606037403[/C][C]-171.223606037403[/C][/ROW]
[ROW][C]32[/C][C]890[/C][C]914.216667469824[/C][C]-24.2166674698235[/C][/ROW]
[ROW][C]33[/C][C]900[/C][C]882.433715885576[/C][C]17.5662841144242[/C][/ROW]
[ROW][C]34[/C][C]820[/C][C]840.433393119918[/C][C]-20.4333931199178[/C][/ROW]
[ROW][C]35[/C][C]810[/C][C]798.538263998974[/C][C]11.4617360010255[/C][/ROW]
[ROW][C]36[/C][C]820[/C][C]839.875038386869[/C][C]-19.8750383868692[/C][/ROW]
[ROW][C]37[/C][C]890[/C][C]922.008046344742[/C][C]-32.0080463447424[/C][/ROW]
[ROW][C]38[/C][C]810[/C][C]817.462910444701[/C][C]-7.46291044470127[/C][/ROW]
[ROW][C]39[/C][C]810[/C][C]868.422389082536[/C][C]-58.4223890825356[/C][/ROW]
[ROW][C]40[/C][C]840[/C][C]856.876426297886[/C][C]-16.8764262978856[/C][/ROW]
[ROW][C]41[/C][C]830[/C][C]763.331631835095[/C][C]66.6683681649051[/C][/ROW]
[ROW][C]42[/C][C]790[/C][C]783.734132634477[/C][C]6.26586736552258[/C][/ROW]
[ROW][C]43[/C][C]610[/C][C]649.93319034363[/C][C]-39.9331903436301[/C][/ROW]
[ROW][C]44[/C][C]870[/C][C]917.657742143511[/C][C]-47.6577421435111[/C][/ROW]
[ROW][C]45[/C][C]870[/C][C]927.243582395833[/C][C]-57.2435823958331[/C][/ROW]
[ROW][C]46[/C][C]820[/C][C]844.161394283036[/C][C]-24.161394283036[/C][/ROW]
[ROW][C]47[/C][C]800[/C][C]833.186630946499[/C][C]-33.1866309464991[/C][/ROW]
[ROW][C]48[/C][C]840[/C][C]842.802320172753[/C][C]-2.8023201727533[/C][/ROW]
[ROW][C]49[/C][C]860[/C][C]914.279416535825[/C][C]-54.2794165358255[/C][/ROW]
[ROW][C]50[/C][C]860[/C][C]831.292729709031[/C][C]28.7072702909687[/C][/ROW]
[ROW][C]51[/C][C]730[/C][C]831.194541813418[/C][C]-101.194541813418[/C][/ROW]
[ROW][C]52[/C][C]850[/C][C]860.910357588649[/C][C]-10.910357588649[/C][/ROW]
[ROW][C]53[/C][C]860[/C][C]849.630264977981[/C][C]10.369735022019[/C][/ROW]
[ROW][C]54[/C][C]900[/C][C]807.994468802922[/C][C]92.0055311970783[/C][/ROW]
[ROW][C]55[/C][C]610[/C][C]624.033318220244[/C][C]-14.0333182202444[/C][/ROW]
[ROW][C]56[/C][C]960[/C][C]889.64618055985[/C][C]70.3538194401503[/C][/ROW]
[ROW][C]57[/C][C]820[/C][C]890.017958716829[/C][C]-70.0179587168287[/C][/ROW]
[ROW][C]58[/C][C]860[/C][C]838.395989390393[/C][C]21.604010609607[/C][/ROW]
[ROW][C]59[/C][C]810[/C][C]818.051424009837[/C][C]-8.05142400983743[/C][/ROW]
[ROW][C]60[/C][C]820[/C][C]858.811980384857[/C][C]-38.8119803848574[/C][/ROW]
[ROW][C]61[/C][C]820[/C][C]879.126823184769[/C][C]-59.1268231847689[/C][/ROW]
[ROW][C]62[/C][C]880[/C][C]878.475050729847[/C][C]1.52494927015346[/C][/ROW]
[ROW][C]63[/C][C]840[/C][C]745.909917455066[/C][C]94.0900825449345[/C][/ROW]
[ROW][C]64[/C][C]910[/C][C]869.314882164022[/C][C]40.6851178359781[/C][/ROW]
[ROW][C]65[/C][C]860[/C][C]879.998229986325[/C][C]-19.9982299863246[/C][/ROW]
[ROW][C]66[/C][C]880[/C][C]920.555886493654[/C][C]-40.555886493654[/C][/ROW]
[ROW][C]67[/C][C]620[/C][C]623.825176512889[/C][C]-3.8251765128889[/C][/ROW]
[ROW][C]68[/C][C]970[/C][C]981.314201991572[/C][C]-11.3142019915718[/C][/ROW]
[ROW][C]69[/C][C]810[/C][C]838.298279966267[/C][C]-28.2982799662672[/C][/ROW]
[ROW][C]70[/C][C]880[/C][C]878.820994954663[/C][C]1.17900504533702[/C][/ROW]
[ROW][C]71[/C][C]870[/C][C]827.625679546595[/C][C]42.3743204534053[/C][/ROW]
[ROW][C]72[/C][C]800[/C][C]838.203787353307[/C][C]-38.2037873533066[/C][/ROW]
[ROW][C]73[/C][C]740[/C][C]838.253748562908[/C][C]-98.2537485629077[/C][/ROW]
[ROW][C]74[/C][C]1010[/C][C]898.921138527236[/C][C]111.078861472764[/C][/ROW]
[ROW][C]75[/C][C]850[/C][C]858.140761426466[/C][C]-8.1407614264657[/C][/ROW]
[ROW][C]76[/C][C]980[/C][C]929.223358617582[/C][C]50.7766413824179[/C][/ROW]
[ROW][C]77[/C][C]880[/C][C]878.358106573814[/C][C]1.64189342618579[/C][/ROW]
[ROW][C]78[/C][C]870[/C][C]898.888124916302[/C][C]-28.8881249163021[/C][/ROW]
[ROW][C]79[/C][C]660[/C][C]633.170893985579[/C][C]26.8291060144214[/C][/ROW]
[ROW][C]80[/C][C]940[/C][C]990.886735764686[/C][C]-50.8867357646863[/C][/ROW]
[ROW][C]81[/C][C]860[/C][C]827.31284940074[/C][C]32.6871505992597[/C][/ROW]
[ROW][C]82[/C][C]880[/C][C]899.057697493192[/C][C]-19.0576974931923[/C][/ROW]
[ROW][C]83[/C][C]1000[/C][C]888.557611360676[/C][C]111.442388639324[/C][/ROW]
[ROW][C]84[/C][C]840[/C][C]817.917479765774[/C][C]22.0825202342264[/C][/ROW]
[ROW][C]85[/C][C]800[/C][C]757.379551827834[/C][C]42.6204481721655[/C][/ROW]
[ROW][C]86[/C][C]1060[/C][C]1034.1185820453[/C][C]25.8814179547016[/C][/ROW]
[ROW][C]87[/C][C]790[/C][C]870.88676859107[/C][C]-80.8867685910701[/C][/ROW]
[ROW][C]88[/C][C]930[/C][C]1003.6756047645[/C][C]-73.6756047645022[/C][/ROW]
[ROW][C]89[/C][C]920[/C][C]900.971690309125[/C][C]19.0283096908746[/C][/ROW]
[ROW][C]90[/C][C]840[/C][C]891.051944055965[/C][C]-51.0519440559655[/C][/ROW]
[ROW][C]91[/C][C]690[/C][C]675.663968732681[/C][C]14.3360312673192[/C][/ROW]
[ROW][C]92[/C][C]940[/C][C]962.650323206617[/C][C]-22.6503232066167[/C][/ROW]
[ROW][C]93[/C][C]1010[/C][C]880.495431925295[/C][C]129.504568074705[/C][/ROW]
[ROW][C]94[/C][C]890[/C][C]901.977514781568[/C][C]-11.9775147815676[/C][/ROW]
[ROW][C]95[/C][C]1000[/C][C]1024.57630895833[/C][C]-24.5763089583311[/C][/ROW]
[ROW][C]96[/C][C]820[/C][C]860.409270719627[/C][C]-40.4092707196273[/C][/ROW]
[ROW][C]97[/C][C]800[/C][C]818.873278525722[/C][C]-18.8732785257216[/C][/ROW]
[ROW][C]98[/C][C]1000[/C][C]1084.37443934416[/C][C]-84.3744393441632[/C][/ROW]
[ROW][C]99[/C][C]780[/C][C]807.771794789473[/C][C]-27.7717947894735[/C][/ROW]
[ROW][C]100[/C][C]1010[/C][C]950.690422648597[/C][C]59.3095773514027[/C][/ROW]
[ROW][C]101[/C][C]950[/C][C]940.522935373648[/C][C]9.47706462635188[/C][/ROW]
[ROW][C]102[/C][C]830[/C][C]858.879939124619[/C][C]-28.8799391246195[/C][/ROW]
[ROW][C]103[/C][C]670[/C][C]705.233835716981[/C][C]-35.233835716981[/C][/ROW]
[ROW][C]104[/C][C]1000[/C][C]960.369399647852[/C][C]39.6306003521481[/C][/ROW]
[ROW][C]105[/C][C]960[/C][C]1031.21181401936[/C][C]-71.2118140193556[/C][/ROW]
[ROW][C]106[/C][C]920[/C][C]907.90573975425[/C][C]12.0942602457502[/C][/ROW]
[ROW][C]107[/C][C]1040[/C][C]1019.76637556856[/C][C]20.2336244314361[/C][/ROW]
[ROW][C]108[/C][C]860[/C][C]836.121142013911[/C][C]23.878857986089[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=123387&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=123387&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
13800780.11817448095619.8818255190445
14710693.84643866696216.1535613330382
15800781.02578678516218.9742132148382
16780761.19626460207818.8037353979223
17760743.76297256593916.2370274340609
18730719.07119380572810.9288061942723
19770813.3869200831-43.3869200831003
20880845.40578195530434.5942180446957
21850835.82044234726314.1795576527372
22810780.30741309020229.6925869097984
23770807.932592651531-37.9325926515312
24810848.599737426136-38.5997374261361
25890831.50902272948158.4909772705188
26790738.24873823732451.7512617626762
27840832.226615355947.77338464406023
28830811.53545330788418.4645466921164
29740790.897789855629-50.8977898556287
30760759.4000954847310.599904515269145
31630801.223606037403-171.223606037403
32890914.216667469824-24.2166674698235
33900882.43371588557617.5662841144242
34820840.433393119918-20.4333931199178
35810798.53826399897411.4617360010255
36820839.875038386869-19.8750383868692
37890922.008046344742-32.0080463447424
38810817.462910444701-7.46291044470127
39810868.422389082536-58.4223890825356
40840856.876426297886-16.8764262978856
41830763.33163183509566.6683681649051
42790783.7341326344776.26586736552258
43610649.93319034363-39.9331903436301
44870917.657742143511-47.6577421435111
45870927.243582395833-57.2435823958331
46820844.161394283036-24.161394283036
47800833.186630946499-33.1866309464991
48840842.802320172753-2.8023201727533
49860914.279416535825-54.2794165358255
50860831.29272970903128.7072702909687
51730831.194541813418-101.194541813418
52850860.910357588649-10.910357588649
53860849.63026497798110.369735022019
54900807.99446880292292.0055311970783
55610624.033318220244-14.0333182202444
56960889.6461805598570.3538194401503
57820890.017958716829-70.0179587168287
58860838.39598939039321.604010609607
59810818.051424009837-8.05142400983743
60820858.811980384857-38.8119803848574
61820879.126823184769-59.1268231847689
62880878.4750507298471.52494927015346
63840745.90991745506694.0900825449345
64910869.31488216402240.6851178359781
65860879.998229986325-19.9982299863246
66880920.555886493654-40.555886493654
67620623.825176512889-3.8251765128889
68970981.314201991572-11.3142019915718
69810838.298279966267-28.2982799662672
70880878.8209949546631.17900504533702
71870827.62567954659542.3743204534053
72800838.203787353307-38.2037873533066
73740838.253748562908-98.2537485629077
741010898.921138527236111.078861472764
75850858.140761426466-8.1407614264657
76980929.22335861758250.7766413824179
77880878.3581065738141.64189342618579
78870898.888124916302-28.8881249163021
79660633.17089398557926.8291060144214
80940990.886735764686-50.8867357646863
81860827.3128494007432.6871505992597
82880899.057697493192-19.0576974931923
831000888.557611360676111.442388639324
84840817.91747976577422.0825202342264
85800757.37955182783442.6204481721655
8610601034.118582045325.8814179547016
87790870.88676859107-80.8867685910701
889301003.6756047645-73.6756047645022
89920900.97169030912519.0283096908746
90840891.051944055965-51.0519440559655
91690675.66396873268114.3360312673192
92940962.650323206617-22.6503232066167
931010880.495431925295129.504568074705
94890901.977514781568-11.9775147815676
9510001024.57630895833-24.5763089583311
96820860.409270719627-40.4092707196273
97800818.873278525722-18.8732785257216
9810001084.37443934416-84.3744393441632
99780807.771794789473-27.7717947894735
1001010950.69042264859759.3095773514027
101950940.5229353736489.47706462635188
102830858.879939124619-28.8799391246195
103670705.233835716981-35.233835716981
1041000960.36939964785239.6306003521481
1059601031.21181401936-71.2118140193556
106920907.9057397542512.0942602457502
10710401019.7663755685620.2336244314361
108860836.12114201391123.878857986089







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
109815.713597865778720.873681878849910.553513852707
1101019.80738179662924.9637522335841114.65101135966
111795.539888308568700.694710435985890.38506618115
1121029.82088666321934.9632293910751124.67854393534
113968.482401516147873.6169356797461063.34786735255
114846.172444259701751.302983204833941.04190531457
115683.17920105214588.311340048584778.047062055695
1161019.50401834727924.5757592271361114.43227746741
117979.012813062925884.0637601142871073.96186601156
118938.252795519466843.2822360653971033.22335497354
1191060.60534381003965.552742202361155.6579454177
120876.940608786815821.394416879224932.486800694405

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
109 & 815.713597865778 & 720.873681878849 & 910.553513852707 \tabularnewline
110 & 1019.80738179662 & 924.963752233584 & 1114.65101135966 \tabularnewline
111 & 795.539888308568 & 700.694710435985 & 890.38506618115 \tabularnewline
112 & 1029.82088666321 & 934.963229391075 & 1124.67854393534 \tabularnewline
113 & 968.482401516147 & 873.616935679746 & 1063.34786735255 \tabularnewline
114 & 846.172444259701 & 751.302983204833 & 941.04190531457 \tabularnewline
115 & 683.17920105214 & 588.311340048584 & 778.047062055695 \tabularnewline
116 & 1019.50401834727 & 924.575759227136 & 1114.43227746741 \tabularnewline
117 & 979.012813062925 & 884.063760114287 & 1073.96186601156 \tabularnewline
118 & 938.252795519466 & 843.282236065397 & 1033.22335497354 \tabularnewline
119 & 1060.60534381003 & 965.55274220236 & 1155.6579454177 \tabularnewline
120 & 876.940608786815 & 821.394416879224 & 932.486800694405 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=123387&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]815.713597865778[/C][C]720.873681878849[/C][C]910.553513852707[/C][/ROW]
[ROW][C]110[/C][C]1019.80738179662[/C][C]924.963752233584[/C][C]1114.65101135966[/C][/ROW]
[ROW][C]111[/C][C]795.539888308568[/C][C]700.694710435985[/C][C]890.38506618115[/C][/ROW]
[ROW][C]112[/C][C]1029.82088666321[/C][C]934.963229391075[/C][C]1124.67854393534[/C][/ROW]
[ROW][C]113[/C][C]968.482401516147[/C][C]873.616935679746[/C][C]1063.34786735255[/C][/ROW]
[ROW][C]114[/C][C]846.172444259701[/C][C]751.302983204833[/C][C]941.04190531457[/C][/ROW]
[ROW][C]115[/C][C]683.17920105214[/C][C]588.311340048584[/C][C]778.047062055695[/C][/ROW]
[ROW][C]116[/C][C]1019.50401834727[/C][C]924.575759227136[/C][C]1114.43227746741[/C][/ROW]
[ROW][C]117[/C][C]979.012813062925[/C][C]884.063760114287[/C][C]1073.96186601156[/C][/ROW]
[ROW][C]118[/C][C]938.252795519466[/C][C]843.282236065397[/C][C]1033.22335497354[/C][/ROW]
[ROW][C]119[/C][C]1060.60534381003[/C][C]965.55274220236[/C][C]1155.6579454177[/C][/ROW]
[ROW][C]120[/C][C]876.940608786815[/C][C]821.394416879224[/C][C]932.486800694405[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=123387&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=123387&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
109815.713597865778720.873681878849910.553513852707
1101019.80738179662924.9637522335841114.65101135966
111795.539888308568700.694710435985890.38506618115
1121029.82088666321934.9632293910751124.67854393534
113968.482401516147873.6169356797461063.34786735255
114846.172444259701751.302983204833941.04190531457
115683.17920105214588.311340048584778.047062055695
1161019.50401834727924.5757592271361114.43227746741
117979.012813062925884.0637601142871073.96186601156
118938.252795519466843.2822360653971033.22335497354
1191060.60534381003965.552742202361155.6579454177
120876.940608786815821.394416879224932.486800694405



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