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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 computationMon, 19 Aug 2013 02:11:07 -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/2013/Aug/19/t1376892732jyz2g9dw5aiczc8.htm/, Retrieved Thu, 02 May 2024 15:50:27 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=211195, Retrieved Thu, 02 May 2024 15:50:27 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywordsStefanie Gubbi
Estimated Impact133
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [Tijdreeks 2 - Sta...] [2013-08-19 06:11:07] [3958f9c0a64aeec6b83979b094ee8a96] [Current]
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Dataseries X:
660
770
792
693
726
814
770
737
792
693
770
847
627
704
792
693
770
770
737
836
957
737
891
891
671
660
803
693
825
847
726
869
979
748
880
946
737
671
759
748
814
836
737
825
979
803
825
1034
814
704
704
825
847
858
704
803
1067
858
792
1155
869
671
583
825
803
957
737
825
1199
913
814
1111
858
704
649
847
715
968
770
869
1254
946
693
1166
924
792
627
869
627
880
869
858
1232
935
660
1155
891
825
605
814
550
825
902
891
1199
902
693
1188




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time3 seconds
R Server'Sir Maurice George Kendall' @ kendall.wessa.net

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input & view raw input (R code)  \tabularnewline
Raw Output & view raw output of R engine  \tabularnewline
Computing time & 3 seconds \tabularnewline
R Server & 'Sir Maurice George Kendall' @ kendall.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=211195&T=0

[TABLE]
[ROW][C]Summary of computational transaction[/C][/ROW]
[ROW][C]Raw Input[/C][C]view raw input (R code) [/C][/ROW]
[ROW][C]Raw Output[/C][C]view raw output of R engine [/C][/ROW]
[ROW][C]Computing time[/C][C]3 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Sir Maurice George Kendall' @ kendall.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=211195&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=211195&T=0

As an alternative you can also use a QR Code:  

The GUIDs for individual cells are displayed in the table below:

Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time3 seconds
R Server'Sir Maurice George Kendall' @ kendall.wessa.net







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.387631993675727
beta0.139129720645364
gammaFALSE

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.387631993675727 \tabularnewline
beta & 0.139129720645364 \tabularnewline
gamma & FALSE \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=211195&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]0.387631993675727[/C][/ROW]
[ROW][C]beta[/C][C]0.139129720645364[/C][/ROW]
[ROW][C]gamma[/C][C]FALSE[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=211195&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=211195&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
alpha0.387631993675727
beta0.139129720645364
gammaFALSE







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
3792880-88
4693951.142445029125-258.142445029125
5726942.410320864948-216.410320864948
6814938.183649827983-124.183649827983
7770963.009622469051-193.009622469051
8737950.747218886244-213.747218886244
9792918.918630198988-126.918630198988
10693913.902715181869-220.902715181869
11770860.542028659796-90.5420286597964
12847852.83028094316-5.83028094315978
13627877.641083236405-250.641083236405
14704794.038029071037-90.0380290710374
15792767.83400424199324.1659957580073
16693787.202412726032-94.2024127260318
17770755.60699638056614.3930036194337
18770766.8828687407263.11713125927372
19737773.955962631752-36.9559626317516
20836763.50236638336772.4976336166327
21957799.386365239006157.613634760994
22737876.764330894566-139.764330894566
23891831.33143441016259.6685655898384
24891866.42310242154124.5768975784594
25671889.237577082975-218.237577082975
26660806.159593480749-146.159593480749
27803743.13879018044159.8612098195591
28693763.206624350303-70.2066243503027
29825729.06968199338395.9303180066171
30847764.5063643721182.4936356278899
31726799.183533841146-73.1835338411456
32869769.56838098896599.4316190110351
33979812.226843645276166.773156354724
34748889.983305620844-141.983305620844
35880840.39856442625839.6014355737416
36946863.33762869147182.6623713085287
37737907.42656450036-170.42656450036
38671844.218834169572-173.218834169572
39759770.58684314392-11.5868431439199
40748758.983691485925-10.9836914859247
41814747.0219778032966.9780221967104
42836768.89291911459467.1070808854058
43737794.433048472508-57.4330484725084
44825768.60000993426556.3999900657346
45979789.934014323024189.065985676976
46803872.890145523467-69.8901455234675
47825851.697340718762-26.6973407187622
481034845.807631173475188.192368826525
49814933.36547545475-119.36547545475
50704895.266544293836-191.266544293836
51704818.981237416464-114.981237416464
52825766.06548795525158.9345120447487
53847783.74345207840963.2565479215907
54858806.50827275738951.4917272426106
55704827.489679628332-123.489679628332
56803773.9827568093529.0172431906499
571067781.15732927562285.84267072438
58858903.301472761725-45.3014727617249
59792894.640392052567-102.640392052567
601155858.217399314497296.782600685503
61869992.629358885516-123.629358885516
62671957.408721254228-286.408721254228
63583843.643248595104-260.643248595104
64825725.80851228832999.1914877116708
65803752.80674132712950.1932586728711
66957763.518668365506193.481331634494
67737840.20830383709-103.20830383709
68825796.32540385406428.6745961459359
691199805.110988724122393.889011275878
70913976.708245314058-63.7082453140581
71814967.490307308108-153.490307308108
721111915.192063745449195.807936254551
738581008.85313818209-150.853138182088
74704960.001608849032-256.001608849032
75649856.58471189806-207.58471189806
76847760.74047495020386.2595250497972
77715783.451739145448-68.4517391454476
78968742.500287846024225.499712153976
79770827.6552781728-57.6552781727999
80869799.94092072038369.059079279617
811254825.069536525492428.930463474508
829461012.82851946557-66.8285194655745
836931004.81132182856-311.811321828555
841166885.014614852574280.985385147426
859241010.15873685969-86.1587368596901
86792988.339412763065-196.339412763065
87627913.221727012601-286.221727012601
88869787.82651914075481.1734808592464
89627809.223225792582-182.223225792582
90880718.691437257098161.308562742902
91869770.02311403024198.9768859697585
92858802.53097406920655.4690259307945
931232821.165302884247410.834697115753
94935999.707515171373-64.7075151713725
95660990.424602155715-330.424602155715
961155860.321072456338294.678927543662
97891988.42003807039-97.42003807039
98825959.274927090729-134.274927090729
99605908.602083321369-303.602083321369
100814775.91901267343838.0809873265615
101550777.736982621873-227.736982621873
102825664.23328988256160.76671011744
103902709.996388612876192.003611387124
104891778.222881575519112.777118424481
1051199821.820848665916377.179151334084
106902988.251201123521-86.2512011235209
107693970.389497302017-277.389497302017
1081188863.476545349897324.523454650103

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
3 & 792 & 880 & -88 \tabularnewline
4 & 693 & 951.142445029125 & -258.142445029125 \tabularnewline
5 & 726 & 942.410320864948 & -216.410320864948 \tabularnewline
6 & 814 & 938.183649827983 & -124.183649827983 \tabularnewline
7 & 770 & 963.009622469051 & -193.009622469051 \tabularnewline
8 & 737 & 950.747218886244 & -213.747218886244 \tabularnewline
9 & 792 & 918.918630198988 & -126.918630198988 \tabularnewline
10 & 693 & 913.902715181869 & -220.902715181869 \tabularnewline
11 & 770 & 860.542028659796 & -90.5420286597964 \tabularnewline
12 & 847 & 852.83028094316 & -5.83028094315978 \tabularnewline
13 & 627 & 877.641083236405 & -250.641083236405 \tabularnewline
14 & 704 & 794.038029071037 & -90.0380290710374 \tabularnewline
15 & 792 & 767.834004241993 & 24.1659957580073 \tabularnewline
16 & 693 & 787.202412726032 & -94.2024127260318 \tabularnewline
17 & 770 & 755.606996380566 & 14.3930036194337 \tabularnewline
18 & 770 & 766.882868740726 & 3.11713125927372 \tabularnewline
19 & 737 & 773.955962631752 & -36.9559626317516 \tabularnewline
20 & 836 & 763.502366383367 & 72.4976336166327 \tabularnewline
21 & 957 & 799.386365239006 & 157.613634760994 \tabularnewline
22 & 737 & 876.764330894566 & -139.764330894566 \tabularnewline
23 & 891 & 831.331434410162 & 59.6685655898384 \tabularnewline
24 & 891 & 866.423102421541 & 24.5768975784594 \tabularnewline
25 & 671 & 889.237577082975 & -218.237577082975 \tabularnewline
26 & 660 & 806.159593480749 & -146.159593480749 \tabularnewline
27 & 803 & 743.138790180441 & 59.8612098195591 \tabularnewline
28 & 693 & 763.206624350303 & -70.2066243503027 \tabularnewline
29 & 825 & 729.069681993383 & 95.9303180066171 \tabularnewline
30 & 847 & 764.50636437211 & 82.4936356278899 \tabularnewline
31 & 726 & 799.183533841146 & -73.1835338411456 \tabularnewline
32 & 869 & 769.568380988965 & 99.4316190110351 \tabularnewline
33 & 979 & 812.226843645276 & 166.773156354724 \tabularnewline
34 & 748 & 889.983305620844 & -141.983305620844 \tabularnewline
35 & 880 & 840.398564426258 & 39.6014355737416 \tabularnewline
36 & 946 & 863.337628691471 & 82.6623713085287 \tabularnewline
37 & 737 & 907.42656450036 & -170.42656450036 \tabularnewline
38 & 671 & 844.218834169572 & -173.218834169572 \tabularnewline
39 & 759 & 770.58684314392 & -11.5868431439199 \tabularnewline
40 & 748 & 758.983691485925 & -10.9836914859247 \tabularnewline
41 & 814 & 747.02197780329 & 66.9780221967104 \tabularnewline
42 & 836 & 768.892919114594 & 67.1070808854058 \tabularnewline
43 & 737 & 794.433048472508 & -57.4330484725084 \tabularnewline
44 & 825 & 768.600009934265 & 56.3999900657346 \tabularnewline
45 & 979 & 789.934014323024 & 189.065985676976 \tabularnewline
46 & 803 & 872.890145523467 & -69.8901455234675 \tabularnewline
47 & 825 & 851.697340718762 & -26.6973407187622 \tabularnewline
48 & 1034 & 845.807631173475 & 188.192368826525 \tabularnewline
49 & 814 & 933.36547545475 & -119.36547545475 \tabularnewline
50 & 704 & 895.266544293836 & -191.266544293836 \tabularnewline
51 & 704 & 818.981237416464 & -114.981237416464 \tabularnewline
52 & 825 & 766.065487955251 & 58.9345120447487 \tabularnewline
53 & 847 & 783.743452078409 & 63.2565479215907 \tabularnewline
54 & 858 & 806.508272757389 & 51.4917272426106 \tabularnewline
55 & 704 & 827.489679628332 & -123.489679628332 \tabularnewline
56 & 803 & 773.98275680935 & 29.0172431906499 \tabularnewline
57 & 1067 & 781.15732927562 & 285.84267072438 \tabularnewline
58 & 858 & 903.301472761725 & -45.3014727617249 \tabularnewline
59 & 792 & 894.640392052567 & -102.640392052567 \tabularnewline
60 & 1155 & 858.217399314497 & 296.782600685503 \tabularnewline
61 & 869 & 992.629358885516 & -123.629358885516 \tabularnewline
62 & 671 & 957.408721254228 & -286.408721254228 \tabularnewline
63 & 583 & 843.643248595104 & -260.643248595104 \tabularnewline
64 & 825 & 725.808512288329 & 99.1914877116708 \tabularnewline
65 & 803 & 752.806741327129 & 50.1932586728711 \tabularnewline
66 & 957 & 763.518668365506 & 193.481331634494 \tabularnewline
67 & 737 & 840.20830383709 & -103.20830383709 \tabularnewline
68 & 825 & 796.325403854064 & 28.6745961459359 \tabularnewline
69 & 1199 & 805.110988724122 & 393.889011275878 \tabularnewline
70 & 913 & 976.708245314058 & -63.7082453140581 \tabularnewline
71 & 814 & 967.490307308108 & -153.490307308108 \tabularnewline
72 & 1111 & 915.192063745449 & 195.807936254551 \tabularnewline
73 & 858 & 1008.85313818209 & -150.853138182088 \tabularnewline
74 & 704 & 960.001608849032 & -256.001608849032 \tabularnewline
75 & 649 & 856.58471189806 & -207.58471189806 \tabularnewline
76 & 847 & 760.740474950203 & 86.2595250497972 \tabularnewline
77 & 715 & 783.451739145448 & -68.4517391454476 \tabularnewline
78 & 968 & 742.500287846024 & 225.499712153976 \tabularnewline
79 & 770 & 827.6552781728 & -57.6552781727999 \tabularnewline
80 & 869 & 799.940920720383 & 69.059079279617 \tabularnewline
81 & 1254 & 825.069536525492 & 428.930463474508 \tabularnewline
82 & 946 & 1012.82851946557 & -66.8285194655745 \tabularnewline
83 & 693 & 1004.81132182856 & -311.811321828555 \tabularnewline
84 & 1166 & 885.014614852574 & 280.985385147426 \tabularnewline
85 & 924 & 1010.15873685969 & -86.1587368596901 \tabularnewline
86 & 792 & 988.339412763065 & -196.339412763065 \tabularnewline
87 & 627 & 913.221727012601 & -286.221727012601 \tabularnewline
88 & 869 & 787.826519140754 & 81.1734808592464 \tabularnewline
89 & 627 & 809.223225792582 & -182.223225792582 \tabularnewline
90 & 880 & 718.691437257098 & 161.308562742902 \tabularnewline
91 & 869 & 770.023114030241 & 98.9768859697585 \tabularnewline
92 & 858 & 802.530974069206 & 55.4690259307945 \tabularnewline
93 & 1232 & 821.165302884247 & 410.834697115753 \tabularnewline
94 & 935 & 999.707515171373 & -64.7075151713725 \tabularnewline
95 & 660 & 990.424602155715 & -330.424602155715 \tabularnewline
96 & 1155 & 860.321072456338 & 294.678927543662 \tabularnewline
97 & 891 & 988.42003807039 & -97.42003807039 \tabularnewline
98 & 825 & 959.274927090729 & -134.274927090729 \tabularnewline
99 & 605 & 908.602083321369 & -303.602083321369 \tabularnewline
100 & 814 & 775.919012673438 & 38.0809873265615 \tabularnewline
101 & 550 & 777.736982621873 & -227.736982621873 \tabularnewline
102 & 825 & 664.23328988256 & 160.76671011744 \tabularnewline
103 & 902 & 709.996388612876 & 192.003611387124 \tabularnewline
104 & 891 & 778.222881575519 & 112.777118424481 \tabularnewline
105 & 1199 & 821.820848665916 & 377.179151334084 \tabularnewline
106 & 902 & 988.251201123521 & -86.2512011235209 \tabularnewline
107 & 693 & 970.389497302017 & -277.389497302017 \tabularnewline
108 & 1188 & 863.476545349897 & 324.523454650103 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=211195&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]792[/C][C]880[/C][C]-88[/C][/ROW]
[ROW][C]4[/C][C]693[/C][C]951.142445029125[/C][C]-258.142445029125[/C][/ROW]
[ROW][C]5[/C][C]726[/C][C]942.410320864948[/C][C]-216.410320864948[/C][/ROW]
[ROW][C]6[/C][C]814[/C][C]938.183649827983[/C][C]-124.183649827983[/C][/ROW]
[ROW][C]7[/C][C]770[/C][C]963.009622469051[/C][C]-193.009622469051[/C][/ROW]
[ROW][C]8[/C][C]737[/C][C]950.747218886244[/C][C]-213.747218886244[/C][/ROW]
[ROW][C]9[/C][C]792[/C][C]918.918630198988[/C][C]-126.918630198988[/C][/ROW]
[ROW][C]10[/C][C]693[/C][C]913.902715181869[/C][C]-220.902715181869[/C][/ROW]
[ROW][C]11[/C][C]770[/C][C]860.542028659796[/C][C]-90.5420286597964[/C][/ROW]
[ROW][C]12[/C][C]847[/C][C]852.83028094316[/C][C]-5.83028094315978[/C][/ROW]
[ROW][C]13[/C][C]627[/C][C]877.641083236405[/C][C]-250.641083236405[/C][/ROW]
[ROW][C]14[/C][C]704[/C][C]794.038029071037[/C][C]-90.0380290710374[/C][/ROW]
[ROW][C]15[/C][C]792[/C][C]767.834004241993[/C][C]24.1659957580073[/C][/ROW]
[ROW][C]16[/C][C]693[/C][C]787.202412726032[/C][C]-94.2024127260318[/C][/ROW]
[ROW][C]17[/C][C]770[/C][C]755.606996380566[/C][C]14.3930036194337[/C][/ROW]
[ROW][C]18[/C][C]770[/C][C]766.882868740726[/C][C]3.11713125927372[/C][/ROW]
[ROW][C]19[/C][C]737[/C][C]773.955962631752[/C][C]-36.9559626317516[/C][/ROW]
[ROW][C]20[/C][C]836[/C][C]763.502366383367[/C][C]72.4976336166327[/C][/ROW]
[ROW][C]21[/C][C]957[/C][C]799.386365239006[/C][C]157.613634760994[/C][/ROW]
[ROW][C]22[/C][C]737[/C][C]876.764330894566[/C][C]-139.764330894566[/C][/ROW]
[ROW][C]23[/C][C]891[/C][C]831.331434410162[/C][C]59.6685655898384[/C][/ROW]
[ROW][C]24[/C][C]891[/C][C]866.423102421541[/C][C]24.5768975784594[/C][/ROW]
[ROW][C]25[/C][C]671[/C][C]889.237577082975[/C][C]-218.237577082975[/C][/ROW]
[ROW][C]26[/C][C]660[/C][C]806.159593480749[/C][C]-146.159593480749[/C][/ROW]
[ROW][C]27[/C][C]803[/C][C]743.138790180441[/C][C]59.8612098195591[/C][/ROW]
[ROW][C]28[/C][C]693[/C][C]763.206624350303[/C][C]-70.2066243503027[/C][/ROW]
[ROW][C]29[/C][C]825[/C][C]729.069681993383[/C][C]95.9303180066171[/C][/ROW]
[ROW][C]30[/C][C]847[/C][C]764.50636437211[/C][C]82.4936356278899[/C][/ROW]
[ROW][C]31[/C][C]726[/C][C]799.183533841146[/C][C]-73.1835338411456[/C][/ROW]
[ROW][C]32[/C][C]869[/C][C]769.568380988965[/C][C]99.4316190110351[/C][/ROW]
[ROW][C]33[/C][C]979[/C][C]812.226843645276[/C][C]166.773156354724[/C][/ROW]
[ROW][C]34[/C][C]748[/C][C]889.983305620844[/C][C]-141.983305620844[/C][/ROW]
[ROW][C]35[/C][C]880[/C][C]840.398564426258[/C][C]39.6014355737416[/C][/ROW]
[ROW][C]36[/C][C]946[/C][C]863.337628691471[/C][C]82.6623713085287[/C][/ROW]
[ROW][C]37[/C][C]737[/C][C]907.42656450036[/C][C]-170.42656450036[/C][/ROW]
[ROW][C]38[/C][C]671[/C][C]844.218834169572[/C][C]-173.218834169572[/C][/ROW]
[ROW][C]39[/C][C]759[/C][C]770.58684314392[/C][C]-11.5868431439199[/C][/ROW]
[ROW][C]40[/C][C]748[/C][C]758.983691485925[/C][C]-10.9836914859247[/C][/ROW]
[ROW][C]41[/C][C]814[/C][C]747.02197780329[/C][C]66.9780221967104[/C][/ROW]
[ROW][C]42[/C][C]836[/C][C]768.892919114594[/C][C]67.1070808854058[/C][/ROW]
[ROW][C]43[/C][C]737[/C][C]794.433048472508[/C][C]-57.4330484725084[/C][/ROW]
[ROW][C]44[/C][C]825[/C][C]768.600009934265[/C][C]56.3999900657346[/C][/ROW]
[ROW][C]45[/C][C]979[/C][C]789.934014323024[/C][C]189.065985676976[/C][/ROW]
[ROW][C]46[/C][C]803[/C][C]872.890145523467[/C][C]-69.8901455234675[/C][/ROW]
[ROW][C]47[/C][C]825[/C][C]851.697340718762[/C][C]-26.6973407187622[/C][/ROW]
[ROW][C]48[/C][C]1034[/C][C]845.807631173475[/C][C]188.192368826525[/C][/ROW]
[ROW][C]49[/C][C]814[/C][C]933.36547545475[/C][C]-119.36547545475[/C][/ROW]
[ROW][C]50[/C][C]704[/C][C]895.266544293836[/C][C]-191.266544293836[/C][/ROW]
[ROW][C]51[/C][C]704[/C][C]818.981237416464[/C][C]-114.981237416464[/C][/ROW]
[ROW][C]52[/C][C]825[/C][C]766.065487955251[/C][C]58.9345120447487[/C][/ROW]
[ROW][C]53[/C][C]847[/C][C]783.743452078409[/C][C]63.2565479215907[/C][/ROW]
[ROW][C]54[/C][C]858[/C][C]806.508272757389[/C][C]51.4917272426106[/C][/ROW]
[ROW][C]55[/C][C]704[/C][C]827.489679628332[/C][C]-123.489679628332[/C][/ROW]
[ROW][C]56[/C][C]803[/C][C]773.98275680935[/C][C]29.0172431906499[/C][/ROW]
[ROW][C]57[/C][C]1067[/C][C]781.15732927562[/C][C]285.84267072438[/C][/ROW]
[ROW][C]58[/C][C]858[/C][C]903.301472761725[/C][C]-45.3014727617249[/C][/ROW]
[ROW][C]59[/C][C]792[/C][C]894.640392052567[/C][C]-102.640392052567[/C][/ROW]
[ROW][C]60[/C][C]1155[/C][C]858.217399314497[/C][C]296.782600685503[/C][/ROW]
[ROW][C]61[/C][C]869[/C][C]992.629358885516[/C][C]-123.629358885516[/C][/ROW]
[ROW][C]62[/C][C]671[/C][C]957.408721254228[/C][C]-286.408721254228[/C][/ROW]
[ROW][C]63[/C][C]583[/C][C]843.643248595104[/C][C]-260.643248595104[/C][/ROW]
[ROW][C]64[/C][C]825[/C][C]725.808512288329[/C][C]99.1914877116708[/C][/ROW]
[ROW][C]65[/C][C]803[/C][C]752.806741327129[/C][C]50.1932586728711[/C][/ROW]
[ROW][C]66[/C][C]957[/C][C]763.518668365506[/C][C]193.481331634494[/C][/ROW]
[ROW][C]67[/C][C]737[/C][C]840.20830383709[/C][C]-103.20830383709[/C][/ROW]
[ROW][C]68[/C][C]825[/C][C]796.325403854064[/C][C]28.6745961459359[/C][/ROW]
[ROW][C]69[/C][C]1199[/C][C]805.110988724122[/C][C]393.889011275878[/C][/ROW]
[ROW][C]70[/C][C]913[/C][C]976.708245314058[/C][C]-63.7082453140581[/C][/ROW]
[ROW][C]71[/C][C]814[/C][C]967.490307308108[/C][C]-153.490307308108[/C][/ROW]
[ROW][C]72[/C][C]1111[/C][C]915.192063745449[/C][C]195.807936254551[/C][/ROW]
[ROW][C]73[/C][C]858[/C][C]1008.85313818209[/C][C]-150.853138182088[/C][/ROW]
[ROW][C]74[/C][C]704[/C][C]960.001608849032[/C][C]-256.001608849032[/C][/ROW]
[ROW][C]75[/C][C]649[/C][C]856.58471189806[/C][C]-207.58471189806[/C][/ROW]
[ROW][C]76[/C][C]847[/C][C]760.740474950203[/C][C]86.2595250497972[/C][/ROW]
[ROW][C]77[/C][C]715[/C][C]783.451739145448[/C][C]-68.4517391454476[/C][/ROW]
[ROW][C]78[/C][C]968[/C][C]742.500287846024[/C][C]225.499712153976[/C][/ROW]
[ROW][C]79[/C][C]770[/C][C]827.6552781728[/C][C]-57.6552781727999[/C][/ROW]
[ROW][C]80[/C][C]869[/C][C]799.940920720383[/C][C]69.059079279617[/C][/ROW]
[ROW][C]81[/C][C]1254[/C][C]825.069536525492[/C][C]428.930463474508[/C][/ROW]
[ROW][C]82[/C][C]946[/C][C]1012.82851946557[/C][C]-66.8285194655745[/C][/ROW]
[ROW][C]83[/C][C]693[/C][C]1004.81132182856[/C][C]-311.811321828555[/C][/ROW]
[ROW][C]84[/C][C]1166[/C][C]885.014614852574[/C][C]280.985385147426[/C][/ROW]
[ROW][C]85[/C][C]924[/C][C]1010.15873685969[/C][C]-86.1587368596901[/C][/ROW]
[ROW][C]86[/C][C]792[/C][C]988.339412763065[/C][C]-196.339412763065[/C][/ROW]
[ROW][C]87[/C][C]627[/C][C]913.221727012601[/C][C]-286.221727012601[/C][/ROW]
[ROW][C]88[/C][C]869[/C][C]787.826519140754[/C][C]81.1734808592464[/C][/ROW]
[ROW][C]89[/C][C]627[/C][C]809.223225792582[/C][C]-182.223225792582[/C][/ROW]
[ROW][C]90[/C][C]880[/C][C]718.691437257098[/C][C]161.308562742902[/C][/ROW]
[ROW][C]91[/C][C]869[/C][C]770.023114030241[/C][C]98.9768859697585[/C][/ROW]
[ROW][C]92[/C][C]858[/C][C]802.530974069206[/C][C]55.4690259307945[/C][/ROW]
[ROW][C]93[/C][C]1232[/C][C]821.165302884247[/C][C]410.834697115753[/C][/ROW]
[ROW][C]94[/C][C]935[/C][C]999.707515171373[/C][C]-64.7075151713725[/C][/ROW]
[ROW][C]95[/C][C]660[/C][C]990.424602155715[/C][C]-330.424602155715[/C][/ROW]
[ROW][C]96[/C][C]1155[/C][C]860.321072456338[/C][C]294.678927543662[/C][/ROW]
[ROW][C]97[/C][C]891[/C][C]988.42003807039[/C][C]-97.42003807039[/C][/ROW]
[ROW][C]98[/C][C]825[/C][C]959.274927090729[/C][C]-134.274927090729[/C][/ROW]
[ROW][C]99[/C][C]605[/C][C]908.602083321369[/C][C]-303.602083321369[/C][/ROW]
[ROW][C]100[/C][C]814[/C][C]775.919012673438[/C][C]38.0809873265615[/C][/ROW]
[ROW][C]101[/C][C]550[/C][C]777.736982621873[/C][C]-227.736982621873[/C][/ROW]
[ROW][C]102[/C][C]825[/C][C]664.23328988256[/C][C]160.76671011744[/C][/ROW]
[ROW][C]103[/C][C]902[/C][C]709.996388612876[/C][C]192.003611387124[/C][/ROW]
[ROW][C]104[/C][C]891[/C][C]778.222881575519[/C][C]112.777118424481[/C][/ROW]
[ROW][C]105[/C][C]1199[/C][C]821.820848665916[/C][C]377.179151334084[/C][/ROW]
[ROW][C]106[/C][C]902[/C][C]988.251201123521[/C][C]-86.2512011235209[/C][/ROW]
[ROW][C]107[/C][C]693[/C][C]970.389497302017[/C][C]-277.389497302017[/C][/ROW]
[ROW][C]108[/C][C]1188[/C][C]863.476545349897[/C][C]324.523454650103[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=211195&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=211195&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
3792880-88
4693951.142445029125-258.142445029125
5726942.410320864948-216.410320864948
6814938.183649827983-124.183649827983
7770963.009622469051-193.009622469051
8737950.747218886244-213.747218886244
9792918.918630198988-126.918630198988
10693913.902715181869-220.902715181869
11770860.542028659796-90.5420286597964
12847852.83028094316-5.83028094315978
13627877.641083236405-250.641083236405
14704794.038029071037-90.0380290710374
15792767.83400424199324.1659957580073
16693787.202412726032-94.2024127260318
17770755.60699638056614.3930036194337
18770766.8828687407263.11713125927372
19737773.955962631752-36.9559626317516
20836763.50236638336772.4976336166327
21957799.386365239006157.613634760994
22737876.764330894566-139.764330894566
23891831.33143441016259.6685655898384
24891866.42310242154124.5768975784594
25671889.237577082975-218.237577082975
26660806.159593480749-146.159593480749
27803743.13879018044159.8612098195591
28693763.206624350303-70.2066243503027
29825729.06968199338395.9303180066171
30847764.5063643721182.4936356278899
31726799.183533841146-73.1835338411456
32869769.56838098896599.4316190110351
33979812.226843645276166.773156354724
34748889.983305620844-141.983305620844
35880840.39856442625839.6014355737416
36946863.33762869147182.6623713085287
37737907.42656450036-170.42656450036
38671844.218834169572-173.218834169572
39759770.58684314392-11.5868431439199
40748758.983691485925-10.9836914859247
41814747.0219778032966.9780221967104
42836768.89291911459467.1070808854058
43737794.433048472508-57.4330484725084
44825768.60000993426556.3999900657346
45979789.934014323024189.065985676976
46803872.890145523467-69.8901455234675
47825851.697340718762-26.6973407187622
481034845.807631173475188.192368826525
49814933.36547545475-119.36547545475
50704895.266544293836-191.266544293836
51704818.981237416464-114.981237416464
52825766.06548795525158.9345120447487
53847783.74345207840963.2565479215907
54858806.50827275738951.4917272426106
55704827.489679628332-123.489679628332
56803773.9827568093529.0172431906499
571067781.15732927562285.84267072438
58858903.301472761725-45.3014727617249
59792894.640392052567-102.640392052567
601155858.217399314497296.782600685503
61869992.629358885516-123.629358885516
62671957.408721254228-286.408721254228
63583843.643248595104-260.643248595104
64825725.80851228832999.1914877116708
65803752.80674132712950.1932586728711
66957763.518668365506193.481331634494
67737840.20830383709-103.20830383709
68825796.32540385406428.6745961459359
691199805.110988724122393.889011275878
70913976.708245314058-63.7082453140581
71814967.490307308108-153.490307308108
721111915.192063745449195.807936254551
738581008.85313818209-150.853138182088
74704960.001608849032-256.001608849032
75649856.58471189806-207.58471189806
76847760.74047495020386.2595250497972
77715783.451739145448-68.4517391454476
78968742.500287846024225.499712153976
79770827.6552781728-57.6552781727999
80869799.94092072038369.059079279617
811254825.069536525492428.930463474508
829461012.82851946557-66.8285194655745
836931004.81132182856-311.811321828555
841166885.014614852574280.985385147426
859241010.15873685969-86.1587368596901
86792988.339412763065-196.339412763065
87627913.221727012601-286.221727012601
88869787.82651914075481.1734808592464
89627809.223225792582-182.223225792582
90880718.691437257098161.308562742902
91869770.02311403024198.9768859697585
92858802.53097406920655.4690259307945
931232821.165302884247410.834697115753
94935999.707515171373-64.7075151713725
95660990.424602155715-330.424602155715
961155860.321072456338294.678927543662
97891988.42003807039-97.42003807039
98825959.274927090729-134.274927090729
99605908.602083321369-303.602083321369
100814775.91901267343838.0809873265615
101550777.736982621873-227.736982621873
102825664.23328988256160.76671011744
103902709.996388612876192.003611387124
104891778.222881575519112.777118424481
1051199821.820848665916377.179151334084
106902988.251201123521-86.2512011235209
107693970.389497302017-277.389497302017
1081188863.476545349897324.523454650103







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
1091007.38622792536667.3141088848141347.4583469659
1101025.50023678026653.750233327711397.25024023281
1111043.61424563517635.4579159705891451.77057529974
1121061.72825449007612.8381061724551510.61840280769
1131079.84226334498586.2805767504251573.40394993953
1141097.95627219988556.1383553028631639.7741890969
1151116.07028105479522.7190688546781709.42149325489
1161134.18428990969486.2854534442861782.0831263751
1171152.2982987646447.0599526252831857.53664490391
1181170.4123076195405.2305810286031935.5940342104
1191188.52631647441360.9566832735512016.09594967526
1201206.64032532931314.3740309412242098.9066197174

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
109 & 1007.38622792536 & 667.314108884814 & 1347.4583469659 \tabularnewline
110 & 1025.50023678026 & 653.75023332771 & 1397.25024023281 \tabularnewline
111 & 1043.61424563517 & 635.457915970589 & 1451.77057529974 \tabularnewline
112 & 1061.72825449007 & 612.838106172455 & 1510.61840280769 \tabularnewline
113 & 1079.84226334498 & 586.280576750425 & 1573.40394993953 \tabularnewline
114 & 1097.95627219988 & 556.138355302863 & 1639.7741890969 \tabularnewline
115 & 1116.07028105479 & 522.719068854678 & 1709.42149325489 \tabularnewline
116 & 1134.18428990969 & 486.285453444286 & 1782.0831263751 \tabularnewline
117 & 1152.2982987646 & 447.059952625283 & 1857.53664490391 \tabularnewline
118 & 1170.4123076195 & 405.230581028603 & 1935.5940342104 \tabularnewline
119 & 1188.52631647441 & 360.956683273551 & 2016.09594967526 \tabularnewline
120 & 1206.64032532931 & 314.374030941224 & 2098.9066197174 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=211195&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]1007.38622792536[/C][C]667.314108884814[/C][C]1347.4583469659[/C][/ROW]
[ROW][C]110[/C][C]1025.50023678026[/C][C]653.75023332771[/C][C]1397.25024023281[/C][/ROW]
[ROW][C]111[/C][C]1043.61424563517[/C][C]635.457915970589[/C][C]1451.77057529974[/C][/ROW]
[ROW][C]112[/C][C]1061.72825449007[/C][C]612.838106172455[/C][C]1510.61840280769[/C][/ROW]
[ROW][C]113[/C][C]1079.84226334498[/C][C]586.280576750425[/C][C]1573.40394993953[/C][/ROW]
[ROW][C]114[/C][C]1097.95627219988[/C][C]556.138355302863[/C][C]1639.7741890969[/C][/ROW]
[ROW][C]115[/C][C]1116.07028105479[/C][C]522.719068854678[/C][C]1709.42149325489[/C][/ROW]
[ROW][C]116[/C][C]1134.18428990969[/C][C]486.285453444286[/C][C]1782.0831263751[/C][/ROW]
[ROW][C]117[/C][C]1152.2982987646[/C][C]447.059952625283[/C][C]1857.53664490391[/C][/ROW]
[ROW][C]118[/C][C]1170.4123076195[/C][C]405.230581028603[/C][C]1935.5940342104[/C][/ROW]
[ROW][C]119[/C][C]1188.52631647441[/C][C]360.956683273551[/C][C]2016.09594967526[/C][/ROW]
[ROW][C]120[/C][C]1206.64032532931[/C][C]314.374030941224[/C][C]2098.9066197174[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=211195&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=211195&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
1091007.38622792536667.3141088848141347.4583469659
1101025.50023678026653.750233327711397.25024023281
1111043.61424563517635.4579159705891451.77057529974
1121061.72825449007612.8381061724551510.61840280769
1131079.84226334498586.2805767504251573.40394993953
1141097.95627219988556.1383553028631639.7741890969
1151116.07028105479522.7190688546781709.42149325489
1161134.18428990969486.2854534442861782.0831263751
1171152.2982987646447.0599526252831857.53664490391
1181170.4123076195405.2305810286031935.5940342104
1191188.52631647441360.9566832735512016.09594967526
1201206.64032532931314.3740309412242098.9066197174



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):
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')