Free Statistics

of Irreproducible Research!

Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationThu, 23 Apr 2015 09:01:26 +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/2015/Apr/23/t1429776126mrk573sn2kqz1x6.htm/, Retrieved Thu, 09 May 2024 15:42:14 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=278811, Retrieved Thu, 09 May 2024 15:42:14 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact118
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [Opgave 10.2] [2015-04-23 08:01:26] [2dcc5595e1714d1f573b61116e4d8205] [Current]
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Dataseries X:
790
766
1040
949
758
1023
921
775
907
835
871
836
789
811
996
778
603
990
735
800
706
766
870
647
726
784
884
696
893
674
703
799
793
799
1022
758
1021
944
915
864
1022
891
1087
822
890
1092
967
833
1104
1063
1103
1039
1185
1047
1155
878
879
1133
920
943
938
900
781
1040
792
653
866
679
799
760
697
750




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=278811&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=278811&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=278811&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
alpha0.216529821272695
beta0.253710197629439
gammaFALSE

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.216529821272695 \tabularnewline
beta & 0.253710197629439 \tabularnewline
gamma & FALSE \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=278811&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]0.216529821272695[/C][/ROW]
[ROW][C]beta[/C][C]0.253710197629439[/C][/ROW]
[ROW][C]gamma[/C][C]FALSE[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=278811&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=278811&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
alpha0.216529821272695
beta0.253710197629439
gammaFALSE







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
31040742298
4949798.896762216096150.103237783904
5758832.015509957596-74.0155099575961
61023812.539762297137210.460237702863
7921866.22330395837154.7766960416292
8775889.205919087825-114.205919087825
9907869.32476252314637.6752374768542
10835884.40012584979-49.4001258497902
11871877.90723971126-6.9072397112601
12836880.235875710305-44.2358757103054
13789872.051614556775-83.0516145567747
14811850.900079548992-39.9000795489924
15996836.900194966462159.099805033538
16778874.7299986735-96.7299986735004
17603851.851078549376-248.851078549376
18990782.36256919729207.63743080271
19735823.124168490266-88.1241684902659
20800795.0033877609084.99661223909209
21706787.320526048954-81.3205260489542
22766756.4800197246199.51998027538127
23870745.832179957503124.167820042497
24647766.83027792146-119.83027792146
25726728.412536314865-2.41253631486541
26784715.28670264281268.7132973571885
27884721.336554616381162.663445383619
28696756.665465716455-60.6654657164549
29893740.304300278829152.695699721171
30674778.53065390687-104.53065390687
31703755.317353577938-52.3173535779379
32799740.5356929221858.46430707782
33793752.95335031766840.046649682332
34799763.58303133768635.4169686623138
351022775.155908702003246.844091297997
36758846.069646635548-88.0696466355481
371021839.626394167474181.373605832526
38944901.48954944195842.5104505580424
39915935.620037142789-20.6200371427893
40864954.948112898753-90.9481128987534
411022954.05175348042867.9482465195716
42891991.293987262604-100.293987262604
431087986.597027426187100.402972573813
448221030.87266443819-208.872664438189
45890996.706311164682-106.706311164682
461092978.800021002653113.199978997347
479671014.7287346406-47.7287346405985
488331013.18956532296-180.189565322955
491104973.069813810261130.930186189739
5010631007.509524118855.4904758812035
5111031028.6627024400574.3372975599495
5210391057.9805603676-18.9805603676
5311851066.04960647756118.950393522442
5410471110.51945523458-63.5194552345752
5511551111.9896466552643.0103533447409
568781138.88952767851-260.889527678512
578791085.65384066882-206.653840668824
5811331032.80909830616100.190901693836
599201051.90946288234-131.909462882339
609431013.50662199594-70.5066219959416
61938984.525987913292-46.5259879132922
62900958.18193277087-58.1819327708696
63781926.117745567667-145.117745567667
641040867.257199464199172.742800535801
65792886.712708642086-94.7127086420857
66653843.053003550652-190.053003550652
67866768.3085631367997.6914368632105
68679761.236134535135-82.2361345351352
69799710.68631126404788.3136887359526
70760701.91719598285158.0828040171489
71697689.7930193208397.20698067916135
72750667.04863114469482.9513688553055

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
3 & 1040 & 742 & 298 \tabularnewline
4 & 949 & 798.896762216096 & 150.103237783904 \tabularnewline
5 & 758 & 832.015509957596 & -74.0155099575961 \tabularnewline
6 & 1023 & 812.539762297137 & 210.460237702863 \tabularnewline
7 & 921 & 866.223303958371 & 54.7766960416292 \tabularnewline
8 & 775 & 889.205919087825 & -114.205919087825 \tabularnewline
9 & 907 & 869.324762523146 & 37.6752374768542 \tabularnewline
10 & 835 & 884.40012584979 & -49.4001258497902 \tabularnewline
11 & 871 & 877.90723971126 & -6.9072397112601 \tabularnewline
12 & 836 & 880.235875710305 & -44.2358757103054 \tabularnewline
13 & 789 & 872.051614556775 & -83.0516145567747 \tabularnewline
14 & 811 & 850.900079548992 & -39.9000795489924 \tabularnewline
15 & 996 & 836.900194966462 & 159.099805033538 \tabularnewline
16 & 778 & 874.7299986735 & -96.7299986735004 \tabularnewline
17 & 603 & 851.851078549376 & -248.851078549376 \tabularnewline
18 & 990 & 782.36256919729 & 207.63743080271 \tabularnewline
19 & 735 & 823.124168490266 & -88.1241684902659 \tabularnewline
20 & 800 & 795.003387760908 & 4.99661223909209 \tabularnewline
21 & 706 & 787.320526048954 & -81.3205260489542 \tabularnewline
22 & 766 & 756.480019724619 & 9.51998027538127 \tabularnewline
23 & 870 & 745.832179957503 & 124.167820042497 \tabularnewline
24 & 647 & 766.83027792146 & -119.83027792146 \tabularnewline
25 & 726 & 728.412536314865 & -2.41253631486541 \tabularnewline
26 & 784 & 715.286702642812 & 68.7132973571885 \tabularnewline
27 & 884 & 721.336554616381 & 162.663445383619 \tabularnewline
28 & 696 & 756.665465716455 & -60.6654657164549 \tabularnewline
29 & 893 & 740.304300278829 & 152.695699721171 \tabularnewline
30 & 674 & 778.53065390687 & -104.53065390687 \tabularnewline
31 & 703 & 755.317353577938 & -52.3173535779379 \tabularnewline
32 & 799 & 740.53569292218 & 58.46430707782 \tabularnewline
33 & 793 & 752.953350317668 & 40.046649682332 \tabularnewline
34 & 799 & 763.583031337686 & 35.4169686623138 \tabularnewline
35 & 1022 & 775.155908702003 & 246.844091297997 \tabularnewline
36 & 758 & 846.069646635548 & -88.0696466355481 \tabularnewline
37 & 1021 & 839.626394167474 & 181.373605832526 \tabularnewline
38 & 944 & 901.489549441958 & 42.5104505580424 \tabularnewline
39 & 915 & 935.620037142789 & -20.6200371427893 \tabularnewline
40 & 864 & 954.948112898753 & -90.9481128987534 \tabularnewline
41 & 1022 & 954.051753480428 & 67.9482465195716 \tabularnewline
42 & 891 & 991.293987262604 & -100.293987262604 \tabularnewline
43 & 1087 & 986.597027426187 & 100.402972573813 \tabularnewline
44 & 822 & 1030.87266443819 & -208.872664438189 \tabularnewline
45 & 890 & 996.706311164682 & -106.706311164682 \tabularnewline
46 & 1092 & 978.800021002653 & 113.199978997347 \tabularnewline
47 & 967 & 1014.7287346406 & -47.7287346405985 \tabularnewline
48 & 833 & 1013.18956532296 & -180.189565322955 \tabularnewline
49 & 1104 & 973.069813810261 & 130.930186189739 \tabularnewline
50 & 1063 & 1007.5095241188 & 55.4904758812035 \tabularnewline
51 & 1103 & 1028.66270244005 & 74.3372975599495 \tabularnewline
52 & 1039 & 1057.9805603676 & -18.9805603676 \tabularnewline
53 & 1185 & 1066.04960647756 & 118.950393522442 \tabularnewline
54 & 1047 & 1110.51945523458 & -63.5194552345752 \tabularnewline
55 & 1155 & 1111.98964665526 & 43.0103533447409 \tabularnewline
56 & 878 & 1138.88952767851 & -260.889527678512 \tabularnewline
57 & 879 & 1085.65384066882 & -206.653840668824 \tabularnewline
58 & 1133 & 1032.80909830616 & 100.190901693836 \tabularnewline
59 & 920 & 1051.90946288234 & -131.909462882339 \tabularnewline
60 & 943 & 1013.50662199594 & -70.5066219959416 \tabularnewline
61 & 938 & 984.525987913292 & -46.5259879132922 \tabularnewline
62 & 900 & 958.18193277087 & -58.1819327708696 \tabularnewline
63 & 781 & 926.117745567667 & -145.117745567667 \tabularnewline
64 & 1040 & 867.257199464199 & 172.742800535801 \tabularnewline
65 & 792 & 886.712708642086 & -94.7127086420857 \tabularnewline
66 & 653 & 843.053003550652 & -190.053003550652 \tabularnewline
67 & 866 & 768.30856313679 & 97.6914368632105 \tabularnewline
68 & 679 & 761.236134535135 & -82.2361345351352 \tabularnewline
69 & 799 & 710.686311264047 & 88.3136887359526 \tabularnewline
70 & 760 & 701.917195982851 & 58.0828040171489 \tabularnewline
71 & 697 & 689.793019320839 & 7.20698067916135 \tabularnewline
72 & 750 & 667.048631144694 & 82.9513688553055 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=278811&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]3[/C][C]1040[/C][C]742[/C][C]298[/C][/ROW]
[ROW][C]4[/C][C]949[/C][C]798.896762216096[/C][C]150.103237783904[/C][/ROW]
[ROW][C]5[/C][C]758[/C][C]832.015509957596[/C][C]-74.0155099575961[/C][/ROW]
[ROW][C]6[/C][C]1023[/C][C]812.539762297137[/C][C]210.460237702863[/C][/ROW]
[ROW][C]7[/C][C]921[/C][C]866.223303958371[/C][C]54.7766960416292[/C][/ROW]
[ROW][C]8[/C][C]775[/C][C]889.205919087825[/C][C]-114.205919087825[/C][/ROW]
[ROW][C]9[/C][C]907[/C][C]869.324762523146[/C][C]37.6752374768542[/C][/ROW]
[ROW][C]10[/C][C]835[/C][C]884.40012584979[/C][C]-49.4001258497902[/C][/ROW]
[ROW][C]11[/C][C]871[/C][C]877.90723971126[/C][C]-6.9072397112601[/C][/ROW]
[ROW][C]12[/C][C]836[/C][C]880.235875710305[/C][C]-44.2358757103054[/C][/ROW]
[ROW][C]13[/C][C]789[/C][C]872.051614556775[/C][C]-83.0516145567747[/C][/ROW]
[ROW][C]14[/C][C]811[/C][C]850.900079548992[/C][C]-39.9000795489924[/C][/ROW]
[ROW][C]15[/C][C]996[/C][C]836.900194966462[/C][C]159.099805033538[/C][/ROW]
[ROW][C]16[/C][C]778[/C][C]874.7299986735[/C][C]-96.7299986735004[/C][/ROW]
[ROW][C]17[/C][C]603[/C][C]851.851078549376[/C][C]-248.851078549376[/C][/ROW]
[ROW][C]18[/C][C]990[/C][C]782.36256919729[/C][C]207.63743080271[/C][/ROW]
[ROW][C]19[/C][C]735[/C][C]823.124168490266[/C][C]-88.1241684902659[/C][/ROW]
[ROW][C]20[/C][C]800[/C][C]795.003387760908[/C][C]4.99661223909209[/C][/ROW]
[ROW][C]21[/C][C]706[/C][C]787.320526048954[/C][C]-81.3205260489542[/C][/ROW]
[ROW][C]22[/C][C]766[/C][C]756.480019724619[/C][C]9.51998027538127[/C][/ROW]
[ROW][C]23[/C][C]870[/C][C]745.832179957503[/C][C]124.167820042497[/C][/ROW]
[ROW][C]24[/C][C]647[/C][C]766.83027792146[/C][C]-119.83027792146[/C][/ROW]
[ROW][C]25[/C][C]726[/C][C]728.412536314865[/C][C]-2.41253631486541[/C][/ROW]
[ROW][C]26[/C][C]784[/C][C]715.286702642812[/C][C]68.7132973571885[/C][/ROW]
[ROW][C]27[/C][C]884[/C][C]721.336554616381[/C][C]162.663445383619[/C][/ROW]
[ROW][C]28[/C][C]696[/C][C]756.665465716455[/C][C]-60.6654657164549[/C][/ROW]
[ROW][C]29[/C][C]893[/C][C]740.304300278829[/C][C]152.695699721171[/C][/ROW]
[ROW][C]30[/C][C]674[/C][C]778.53065390687[/C][C]-104.53065390687[/C][/ROW]
[ROW][C]31[/C][C]703[/C][C]755.317353577938[/C][C]-52.3173535779379[/C][/ROW]
[ROW][C]32[/C][C]799[/C][C]740.53569292218[/C][C]58.46430707782[/C][/ROW]
[ROW][C]33[/C][C]793[/C][C]752.953350317668[/C][C]40.046649682332[/C][/ROW]
[ROW][C]34[/C][C]799[/C][C]763.583031337686[/C][C]35.4169686623138[/C][/ROW]
[ROW][C]35[/C][C]1022[/C][C]775.155908702003[/C][C]246.844091297997[/C][/ROW]
[ROW][C]36[/C][C]758[/C][C]846.069646635548[/C][C]-88.0696466355481[/C][/ROW]
[ROW][C]37[/C][C]1021[/C][C]839.626394167474[/C][C]181.373605832526[/C][/ROW]
[ROW][C]38[/C][C]944[/C][C]901.489549441958[/C][C]42.5104505580424[/C][/ROW]
[ROW][C]39[/C][C]915[/C][C]935.620037142789[/C][C]-20.6200371427893[/C][/ROW]
[ROW][C]40[/C][C]864[/C][C]954.948112898753[/C][C]-90.9481128987534[/C][/ROW]
[ROW][C]41[/C][C]1022[/C][C]954.051753480428[/C][C]67.9482465195716[/C][/ROW]
[ROW][C]42[/C][C]891[/C][C]991.293987262604[/C][C]-100.293987262604[/C][/ROW]
[ROW][C]43[/C][C]1087[/C][C]986.597027426187[/C][C]100.402972573813[/C][/ROW]
[ROW][C]44[/C][C]822[/C][C]1030.87266443819[/C][C]-208.872664438189[/C][/ROW]
[ROW][C]45[/C][C]890[/C][C]996.706311164682[/C][C]-106.706311164682[/C][/ROW]
[ROW][C]46[/C][C]1092[/C][C]978.800021002653[/C][C]113.199978997347[/C][/ROW]
[ROW][C]47[/C][C]967[/C][C]1014.7287346406[/C][C]-47.7287346405985[/C][/ROW]
[ROW][C]48[/C][C]833[/C][C]1013.18956532296[/C][C]-180.189565322955[/C][/ROW]
[ROW][C]49[/C][C]1104[/C][C]973.069813810261[/C][C]130.930186189739[/C][/ROW]
[ROW][C]50[/C][C]1063[/C][C]1007.5095241188[/C][C]55.4904758812035[/C][/ROW]
[ROW][C]51[/C][C]1103[/C][C]1028.66270244005[/C][C]74.3372975599495[/C][/ROW]
[ROW][C]52[/C][C]1039[/C][C]1057.9805603676[/C][C]-18.9805603676[/C][/ROW]
[ROW][C]53[/C][C]1185[/C][C]1066.04960647756[/C][C]118.950393522442[/C][/ROW]
[ROW][C]54[/C][C]1047[/C][C]1110.51945523458[/C][C]-63.5194552345752[/C][/ROW]
[ROW][C]55[/C][C]1155[/C][C]1111.98964665526[/C][C]43.0103533447409[/C][/ROW]
[ROW][C]56[/C][C]878[/C][C]1138.88952767851[/C][C]-260.889527678512[/C][/ROW]
[ROW][C]57[/C][C]879[/C][C]1085.65384066882[/C][C]-206.653840668824[/C][/ROW]
[ROW][C]58[/C][C]1133[/C][C]1032.80909830616[/C][C]100.190901693836[/C][/ROW]
[ROW][C]59[/C][C]920[/C][C]1051.90946288234[/C][C]-131.909462882339[/C][/ROW]
[ROW][C]60[/C][C]943[/C][C]1013.50662199594[/C][C]-70.5066219959416[/C][/ROW]
[ROW][C]61[/C][C]938[/C][C]984.525987913292[/C][C]-46.5259879132922[/C][/ROW]
[ROW][C]62[/C][C]900[/C][C]958.18193277087[/C][C]-58.1819327708696[/C][/ROW]
[ROW][C]63[/C][C]781[/C][C]926.117745567667[/C][C]-145.117745567667[/C][/ROW]
[ROW][C]64[/C][C]1040[/C][C]867.257199464199[/C][C]172.742800535801[/C][/ROW]
[ROW][C]65[/C][C]792[/C][C]886.712708642086[/C][C]-94.7127086420857[/C][/ROW]
[ROW][C]66[/C][C]653[/C][C]843.053003550652[/C][C]-190.053003550652[/C][/ROW]
[ROW][C]67[/C][C]866[/C][C]768.30856313679[/C][C]97.6914368632105[/C][/ROW]
[ROW][C]68[/C][C]679[/C][C]761.236134535135[/C][C]-82.2361345351352[/C][/ROW]
[ROW][C]69[/C][C]799[/C][C]710.686311264047[/C][C]88.3136887359526[/C][/ROW]
[ROW][C]70[/C][C]760[/C][C]701.917195982851[/C][C]58.0828040171489[/C][/ROW]
[ROW][C]71[/C][C]697[/C][C]689.793019320839[/C][C]7.20698067916135[/C][/ROW]
[ROW][C]72[/C][C]750[/C][C]667.048631144694[/C][C]82.9513688553055[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=278811&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=278811&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
31040742298
4949798.896762216096150.103237783904
5758832.015509957596-74.0155099575961
61023812.539762297137210.460237702863
7921866.22330395837154.7766960416292
8775889.205919087825-114.205919087825
9907869.32476252314637.6752374768542
10835884.40012584979-49.4001258497902
11871877.90723971126-6.9072397112601
12836880.235875710305-44.2358757103054
13789872.051614556775-83.0516145567747
14811850.900079548992-39.9000795489924
15996836.900194966462159.099805033538
16778874.7299986735-96.7299986735004
17603851.851078549376-248.851078549376
18990782.36256919729207.63743080271
19735823.124168490266-88.1241684902659
20800795.0033877609084.99661223909209
21706787.320526048954-81.3205260489542
22766756.4800197246199.51998027538127
23870745.832179957503124.167820042497
24647766.83027792146-119.83027792146
25726728.412536314865-2.41253631486541
26784715.28670264281268.7132973571885
27884721.336554616381162.663445383619
28696756.665465716455-60.6654657164549
29893740.304300278829152.695699721171
30674778.53065390687-104.53065390687
31703755.317353577938-52.3173535779379
32799740.5356929221858.46430707782
33793752.95335031766840.046649682332
34799763.58303133768635.4169686623138
351022775.155908702003246.844091297997
36758846.069646635548-88.0696466355481
371021839.626394167474181.373605832526
38944901.48954944195842.5104505580424
39915935.620037142789-20.6200371427893
40864954.948112898753-90.9481128987534
411022954.05175348042867.9482465195716
42891991.293987262604-100.293987262604
431087986.597027426187100.402972573813
448221030.87266443819-208.872664438189
45890996.706311164682-106.706311164682
461092978.800021002653113.199978997347
479671014.7287346406-47.7287346405985
488331013.18956532296-180.189565322955
491104973.069813810261130.930186189739
5010631007.509524118855.4904758812035
5111031028.6627024400574.3372975599495
5210391057.9805603676-18.9805603676
5311851066.04960647756118.950393522442
5410471110.51945523458-63.5194552345752
5511551111.9896466552643.0103533447409
568781138.88952767851-260.889527678512
578791085.65384066882-206.653840668824
5811331032.80909830616100.190901693836
599201051.90946288234-131.909462882339
609431013.50662199594-70.5066219959416
61938984.525987913292-46.5259879132922
62900958.18193277087-58.1819327708696
63781926.117745567667-145.117745567667
641040867.257199464199172.742800535801
65792886.712708642086-94.7127086420857
66653843.053003550652-190.053003550652
67866768.3085631367997.6914368632105
68679761.236134535135-82.2361345351352
69799710.68631126404788.3136887359526
70760701.91719598285158.0828040171489
71697689.7930193208397.20698067916135
72750667.04863114469482.9513688553055







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
73665.262163581811427.171012634464903.353314529158
74645.514250946363398.806135444527892.222366448199
75625.766338310915367.107776758662884.424899863169
76606.018425675467331.887751277358880.149100073577
77586.270513040019293.12007613671879.420949943328
78566.522600404571250.904054762389882.141146046753
79546.774687769123205.419376409966888.129999128281
80527.026775133675156.885607154276897.167943113074
81507.278862498227105.532260607788909.025464388666
82487.53094986277951.5800912304319923.481808495126
83467.783037227331-4.76865319980055940.334727654463
84448.035124591883-63.3339573219355959.404206505702

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
73 & 665.262163581811 & 427.171012634464 & 903.353314529158 \tabularnewline
74 & 645.514250946363 & 398.806135444527 & 892.222366448199 \tabularnewline
75 & 625.766338310915 & 367.107776758662 & 884.424899863169 \tabularnewline
76 & 606.018425675467 & 331.887751277358 & 880.149100073577 \tabularnewline
77 & 586.270513040019 & 293.12007613671 & 879.420949943328 \tabularnewline
78 & 566.522600404571 & 250.904054762389 & 882.141146046753 \tabularnewline
79 & 546.774687769123 & 205.419376409966 & 888.129999128281 \tabularnewline
80 & 527.026775133675 & 156.885607154276 & 897.167943113074 \tabularnewline
81 & 507.278862498227 & 105.532260607788 & 909.025464388666 \tabularnewline
82 & 487.530949862779 & 51.5800912304319 & 923.481808495126 \tabularnewline
83 & 467.783037227331 & -4.76865319980055 & 940.334727654463 \tabularnewline
84 & 448.035124591883 & -63.3339573219355 & 959.404206505702 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=278811&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]73[/C][C]665.262163581811[/C][C]427.171012634464[/C][C]903.353314529158[/C][/ROW]
[ROW][C]74[/C][C]645.514250946363[/C][C]398.806135444527[/C][C]892.222366448199[/C][/ROW]
[ROW][C]75[/C][C]625.766338310915[/C][C]367.107776758662[/C][C]884.424899863169[/C][/ROW]
[ROW][C]76[/C][C]606.018425675467[/C][C]331.887751277358[/C][C]880.149100073577[/C][/ROW]
[ROW][C]77[/C][C]586.270513040019[/C][C]293.12007613671[/C][C]879.420949943328[/C][/ROW]
[ROW][C]78[/C][C]566.522600404571[/C][C]250.904054762389[/C][C]882.141146046753[/C][/ROW]
[ROW][C]79[/C][C]546.774687769123[/C][C]205.419376409966[/C][C]888.129999128281[/C][/ROW]
[ROW][C]80[/C][C]527.026775133675[/C][C]156.885607154276[/C][C]897.167943113074[/C][/ROW]
[ROW][C]81[/C][C]507.278862498227[/C][C]105.532260607788[/C][C]909.025464388666[/C][/ROW]
[ROW][C]82[/C][C]487.530949862779[/C][C]51.5800912304319[/C][C]923.481808495126[/C][/ROW]
[ROW][C]83[/C][C]467.783037227331[/C][C]-4.76865319980055[/C][C]940.334727654463[/C][/ROW]
[ROW][C]84[/C][C]448.035124591883[/C][C]-63.3339573219355[/C][C]959.404206505702[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=278811&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=278811&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
73665.262163581811427.171012634464903.353314529158
74645.514250946363398.806135444527892.222366448199
75625.766338310915367.107776758662884.424899863169
76606.018425675467331.887751277358880.149100073577
77586.270513040019293.12007613671879.420949943328
78566.522600404571250.904054762389882.141146046753
79546.774687769123205.419376409966888.129999128281
80527.026775133675156.885607154276897.167943113074
81507.278862498227105.532260607788909.025464388666
82487.53094986277951.5800912304319923.481808495126
83467.783037227331-4.76865319980055940.334727654463
84448.035124591883-63.3339573219355959.404206505702



Parameters (Session):
par1 = 12 ; par2 = Double ; par3 = multiplicative ;
Parameters (R input):
par1 = 12 ; par2 = Double ; par3 = multiplicative ;
R code (references can be found in the software module):
par3 <- 'additive'
par2 <- 'Double'
par1 <- '12'
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')