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Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationFri, 17 Aug 2012 06:02:14 -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/2012/Aug/17/t13451977468ebft4psh7ygvn1.htm/, Retrieved Sat, 04 May 2024 11:41:32 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=169459, Retrieved Sat, 04 May 2024 11:41:32 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact162
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [Exponential Smoothing] [] [2012-08-17 09:53:12] [46972ec2bfa5b295f8450f947ab1f239]
- R  D    [Exponential Smoothing] [stap 27 reeks b] [2012-08-17 10:02:14] [7d6606cca1b3596736d7d387043cb02b] [Current]
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Dataseries X:
840
880
930
920
940
880
980
860
900
930
870
1000
870
860
930
980
1010
860
1140
880
800
900
900
1000
890
890
870
1000
1050
790
1160
830
730
950
980
910
840
860
880
1030
1060
770
1140
890
740
860
1050
840
810
830
920
1070
1040
740
1250
850
790
810
1080
760
840
820
900
1010
1080
780
1150
820
790
820
1130
800
890
810
950
1090
1090
850
1200
790
800
850
1230
800
930
700
1030
1040
1000
830
1190
720
810
870
1190
800
970
690
1010
1030
950
830
1150
750
840
880
1210
830




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'AstonUniversity' @ aston.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 & 2 seconds \tabularnewline
R Server & 'AstonUniversity' @ aston.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=169459&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]2 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'AstonUniversity' @ aston.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=169459&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=169459&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 time2 seconds
R Server'AstonUniversity' @ aston.wessa.net







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.043029055619011
betaFALSE
gammaFALSE

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.043029055619011 \tabularnewline
beta & FALSE \tabularnewline
gamma & FALSE \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=169459&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]0.043029055619011[/C][/ROW]
[ROW][C]beta[/C][C]FALSE[/C][/ROW]
[ROW][C]gamma[/C][C]FALSE[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=169459&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=169459&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
alpha0.043029055619011
betaFALSE
gammaFALSE







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
288084040
3930841.7211622247688.2788377752396
4920845.51971724537374.4802827546272
5940848.72453347454191.2754665254587
6880852.65203060031627.3479693996835
7980853.828787896682126.171212103318
8860859.2578159997940.742184000205839
9900859.28975147641940.7102485235814
10930861.04147502440468.9585249755964
11870864.0086952309835.99130476901655
121000864.26649541712135.73350458288
13870870.10697993518-0.106979935179993
14860870.1023766896-10.1023766895991
15930869.66768096113860.3323190388619
16980872.263723672685107.736276327315
171010876.899513898958133.100486101042
18860882.626702118317-22.6267021183174
191140881.653096494394258.346903505606
20880892.769519774336-12.7695197743355
21800892.220059397738-92.2200593977376
22900888.25191733272411.7480826672761
23900888.75742623523111.2425737647691
241000889.241183567056110.758816432944
25890894.007030839645-4.00703083964504
26890893.834612086779-3.83461208677886
27870893.66961235002-23.6696123500195
281000892.65113128373107.34886871627
291050897.27025172636152.72974827364
30790903.842068559504-113.842068559504
311160898.943551859674261.056448140326
32830910.176564286406-80.1765642864058
33730906.726642442385-176.726642442385
34950899.1222619153750.8777380846296
35980901.31148293718378.6885170628167
36910904.6973755144575.30262448554322
37840904.925542438372-64.925542438372
38860902.131857661697-42.1318576616968
39880900.318963615039-20.3189636150394
401030899.444657799527130.555342200473
411060905.06233088043154.93766911957
42770911.729152462456-141.729152462456
431140905.630680878314234.369319121686
44890915.71537134619-25.7153713461906
45740914.608863202272-174.608863202272
46860907.095608715969-47.0956087159691
471050905.069129149118144.930870850882
48840911.305367651873-71.3053676518728
49810908.237165021246-98.2371650212463
50830904.010112583693-74.010112583693
51920900.8255273329619.1744726670399
521070901.650586783815168.349413216185
531040908.894503048522131.105496951478
54740914.535848768806-174.535848768806
551250907.025736024621342.974263975379
56850921.783594705107-71.7835947051074
57790918.694814416009-128.694814416009
58810913.157198088624-103.157198088624
591080908.718441274567171.281558725433
60760916.088524991475-156.088524991475
61840909.372183168127-69.3721831681272
62820906.387163640174-86.3871636401736
63900902.670005571132-2.67000557113204
641010902.555117752909107.444882247091
651080907.178369567097172.821630432903
66780914.614721115162-134.614721115162
671150908.82237679316241.17762320684
68820919.200022156188-99.2000221561884
69790914.931538885423-124.931538885423
70820909.555852750153-89.5558527501532
711130905.702348981159224.297651018841
72800915.353665082062-115.353665082062
73890910.39010581139-20.3901058113894
74810909.512738814354-99.5127388143536
75950905.23079964111144.7692003588893
761090907.157176053372182.842823946628
771090915.024730094509174.975269905491
78850922.553750715223-72.5537507152234
791200919.43183134033280.56816865967
80790931.504414674511-141.504414674511
81800925.415613345146-125.415613345146
82850920.019097943025-70.0190979430254
831230917.006242283242312.993757716758
84800930.47406809244-130.47406809244
85930924.8598921596515.14010784034861
86700925.081066145802-225.081066145802
871030915.396040431827114.603959568173
881040920.327340582245119.672659417755
891000925.47674210040774.5232578995932
90830928.683407509478-98.6834075094783
911190924.43715367908265.56284632092
92720935.864072163765-215.864072163765
93810926.575644996484-116.575644996484
94870921.559505084109-51.5595050841087
951190919.340948272156270.659051727844
96800930.987151662742-130.987151662742
97970925.3508982284744.6491017715299
98690927.272106911936-237.272106911936
991010917.06251222678292.9374877732175
1001030921.061524557267108.938475442733
101950925.74904427614324.250955723857
102830926.792539998799-96.792539998799
1031150922.627648411685227.372351588315
104750932.411265974404-182.411265974404
105840924.562281465257-84.5622814652573
106880920.923646352818-40.9236463528183
1071210919.16274049777290.83725950223
108830931.677193112972-101.677193112972

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
2 & 880 & 840 & 40 \tabularnewline
3 & 930 & 841.72116222476 & 88.2788377752396 \tabularnewline
4 & 920 & 845.519717245373 & 74.4802827546272 \tabularnewline
5 & 940 & 848.724533474541 & 91.2754665254587 \tabularnewline
6 & 880 & 852.652030600316 & 27.3479693996835 \tabularnewline
7 & 980 & 853.828787896682 & 126.171212103318 \tabularnewline
8 & 860 & 859.257815999794 & 0.742184000205839 \tabularnewline
9 & 900 & 859.289751476419 & 40.7102485235814 \tabularnewline
10 & 930 & 861.041475024404 & 68.9585249755964 \tabularnewline
11 & 870 & 864.008695230983 & 5.99130476901655 \tabularnewline
12 & 1000 & 864.26649541712 & 135.73350458288 \tabularnewline
13 & 870 & 870.10697993518 & -0.106979935179993 \tabularnewline
14 & 860 & 870.1023766896 & -10.1023766895991 \tabularnewline
15 & 930 & 869.667680961138 & 60.3323190388619 \tabularnewline
16 & 980 & 872.263723672685 & 107.736276327315 \tabularnewline
17 & 1010 & 876.899513898958 & 133.100486101042 \tabularnewline
18 & 860 & 882.626702118317 & -22.6267021183174 \tabularnewline
19 & 1140 & 881.653096494394 & 258.346903505606 \tabularnewline
20 & 880 & 892.769519774336 & -12.7695197743355 \tabularnewline
21 & 800 & 892.220059397738 & -92.2200593977376 \tabularnewline
22 & 900 & 888.251917332724 & 11.7480826672761 \tabularnewline
23 & 900 & 888.757426235231 & 11.2425737647691 \tabularnewline
24 & 1000 & 889.241183567056 & 110.758816432944 \tabularnewline
25 & 890 & 894.007030839645 & -4.00703083964504 \tabularnewline
26 & 890 & 893.834612086779 & -3.83461208677886 \tabularnewline
27 & 870 & 893.66961235002 & -23.6696123500195 \tabularnewline
28 & 1000 & 892.65113128373 & 107.34886871627 \tabularnewline
29 & 1050 & 897.27025172636 & 152.72974827364 \tabularnewline
30 & 790 & 903.842068559504 & -113.842068559504 \tabularnewline
31 & 1160 & 898.943551859674 & 261.056448140326 \tabularnewline
32 & 830 & 910.176564286406 & -80.1765642864058 \tabularnewline
33 & 730 & 906.726642442385 & -176.726642442385 \tabularnewline
34 & 950 & 899.12226191537 & 50.8777380846296 \tabularnewline
35 & 980 & 901.311482937183 & 78.6885170628167 \tabularnewline
36 & 910 & 904.697375514457 & 5.30262448554322 \tabularnewline
37 & 840 & 904.925542438372 & -64.925542438372 \tabularnewline
38 & 860 & 902.131857661697 & -42.1318576616968 \tabularnewline
39 & 880 & 900.318963615039 & -20.3189636150394 \tabularnewline
40 & 1030 & 899.444657799527 & 130.555342200473 \tabularnewline
41 & 1060 & 905.06233088043 & 154.93766911957 \tabularnewline
42 & 770 & 911.729152462456 & -141.729152462456 \tabularnewline
43 & 1140 & 905.630680878314 & 234.369319121686 \tabularnewline
44 & 890 & 915.71537134619 & -25.7153713461906 \tabularnewline
45 & 740 & 914.608863202272 & -174.608863202272 \tabularnewline
46 & 860 & 907.095608715969 & -47.0956087159691 \tabularnewline
47 & 1050 & 905.069129149118 & 144.930870850882 \tabularnewline
48 & 840 & 911.305367651873 & -71.3053676518728 \tabularnewline
49 & 810 & 908.237165021246 & -98.2371650212463 \tabularnewline
50 & 830 & 904.010112583693 & -74.010112583693 \tabularnewline
51 & 920 & 900.82552733296 & 19.1744726670399 \tabularnewline
52 & 1070 & 901.650586783815 & 168.349413216185 \tabularnewline
53 & 1040 & 908.894503048522 & 131.105496951478 \tabularnewline
54 & 740 & 914.535848768806 & -174.535848768806 \tabularnewline
55 & 1250 & 907.025736024621 & 342.974263975379 \tabularnewline
56 & 850 & 921.783594705107 & -71.7835947051074 \tabularnewline
57 & 790 & 918.694814416009 & -128.694814416009 \tabularnewline
58 & 810 & 913.157198088624 & -103.157198088624 \tabularnewline
59 & 1080 & 908.718441274567 & 171.281558725433 \tabularnewline
60 & 760 & 916.088524991475 & -156.088524991475 \tabularnewline
61 & 840 & 909.372183168127 & -69.3721831681272 \tabularnewline
62 & 820 & 906.387163640174 & -86.3871636401736 \tabularnewline
63 & 900 & 902.670005571132 & -2.67000557113204 \tabularnewline
64 & 1010 & 902.555117752909 & 107.444882247091 \tabularnewline
65 & 1080 & 907.178369567097 & 172.821630432903 \tabularnewline
66 & 780 & 914.614721115162 & -134.614721115162 \tabularnewline
67 & 1150 & 908.82237679316 & 241.17762320684 \tabularnewline
68 & 820 & 919.200022156188 & -99.2000221561884 \tabularnewline
69 & 790 & 914.931538885423 & -124.931538885423 \tabularnewline
70 & 820 & 909.555852750153 & -89.5558527501532 \tabularnewline
71 & 1130 & 905.702348981159 & 224.297651018841 \tabularnewline
72 & 800 & 915.353665082062 & -115.353665082062 \tabularnewline
73 & 890 & 910.39010581139 & -20.3901058113894 \tabularnewline
74 & 810 & 909.512738814354 & -99.5127388143536 \tabularnewline
75 & 950 & 905.230799641111 & 44.7692003588893 \tabularnewline
76 & 1090 & 907.157176053372 & 182.842823946628 \tabularnewline
77 & 1090 & 915.024730094509 & 174.975269905491 \tabularnewline
78 & 850 & 922.553750715223 & -72.5537507152234 \tabularnewline
79 & 1200 & 919.43183134033 & 280.56816865967 \tabularnewline
80 & 790 & 931.504414674511 & -141.504414674511 \tabularnewline
81 & 800 & 925.415613345146 & -125.415613345146 \tabularnewline
82 & 850 & 920.019097943025 & -70.0190979430254 \tabularnewline
83 & 1230 & 917.006242283242 & 312.993757716758 \tabularnewline
84 & 800 & 930.47406809244 & -130.47406809244 \tabularnewline
85 & 930 & 924.859892159651 & 5.14010784034861 \tabularnewline
86 & 700 & 925.081066145802 & -225.081066145802 \tabularnewline
87 & 1030 & 915.396040431827 & 114.603959568173 \tabularnewline
88 & 1040 & 920.327340582245 & 119.672659417755 \tabularnewline
89 & 1000 & 925.476742100407 & 74.5232578995932 \tabularnewline
90 & 830 & 928.683407509478 & -98.6834075094783 \tabularnewline
91 & 1190 & 924.43715367908 & 265.56284632092 \tabularnewline
92 & 720 & 935.864072163765 & -215.864072163765 \tabularnewline
93 & 810 & 926.575644996484 & -116.575644996484 \tabularnewline
94 & 870 & 921.559505084109 & -51.5595050841087 \tabularnewline
95 & 1190 & 919.340948272156 & 270.659051727844 \tabularnewline
96 & 800 & 930.987151662742 & -130.987151662742 \tabularnewline
97 & 970 & 925.35089822847 & 44.6491017715299 \tabularnewline
98 & 690 & 927.272106911936 & -237.272106911936 \tabularnewline
99 & 1010 & 917.062512226782 & 92.9374877732175 \tabularnewline
100 & 1030 & 921.061524557267 & 108.938475442733 \tabularnewline
101 & 950 & 925.749044276143 & 24.250955723857 \tabularnewline
102 & 830 & 926.792539998799 & -96.792539998799 \tabularnewline
103 & 1150 & 922.627648411685 & 227.372351588315 \tabularnewline
104 & 750 & 932.411265974404 & -182.411265974404 \tabularnewline
105 & 840 & 924.562281465257 & -84.5622814652573 \tabularnewline
106 & 880 & 920.923646352818 & -40.9236463528183 \tabularnewline
107 & 1210 & 919.16274049777 & 290.83725950223 \tabularnewline
108 & 830 & 931.677193112972 & -101.677193112972 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=169459&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]2[/C][C]880[/C][C]840[/C][C]40[/C][/ROW]
[ROW][C]3[/C][C]930[/C][C]841.72116222476[/C][C]88.2788377752396[/C][/ROW]
[ROW][C]4[/C][C]920[/C][C]845.519717245373[/C][C]74.4802827546272[/C][/ROW]
[ROW][C]5[/C][C]940[/C][C]848.724533474541[/C][C]91.2754665254587[/C][/ROW]
[ROW][C]6[/C][C]880[/C][C]852.652030600316[/C][C]27.3479693996835[/C][/ROW]
[ROW][C]7[/C][C]980[/C][C]853.828787896682[/C][C]126.171212103318[/C][/ROW]
[ROW][C]8[/C][C]860[/C][C]859.257815999794[/C][C]0.742184000205839[/C][/ROW]
[ROW][C]9[/C][C]900[/C][C]859.289751476419[/C][C]40.7102485235814[/C][/ROW]
[ROW][C]10[/C][C]930[/C][C]861.041475024404[/C][C]68.9585249755964[/C][/ROW]
[ROW][C]11[/C][C]870[/C][C]864.008695230983[/C][C]5.99130476901655[/C][/ROW]
[ROW][C]12[/C][C]1000[/C][C]864.26649541712[/C][C]135.73350458288[/C][/ROW]
[ROW][C]13[/C][C]870[/C][C]870.10697993518[/C][C]-0.106979935179993[/C][/ROW]
[ROW][C]14[/C][C]860[/C][C]870.1023766896[/C][C]-10.1023766895991[/C][/ROW]
[ROW][C]15[/C][C]930[/C][C]869.667680961138[/C][C]60.3323190388619[/C][/ROW]
[ROW][C]16[/C][C]980[/C][C]872.263723672685[/C][C]107.736276327315[/C][/ROW]
[ROW][C]17[/C][C]1010[/C][C]876.899513898958[/C][C]133.100486101042[/C][/ROW]
[ROW][C]18[/C][C]860[/C][C]882.626702118317[/C][C]-22.6267021183174[/C][/ROW]
[ROW][C]19[/C][C]1140[/C][C]881.653096494394[/C][C]258.346903505606[/C][/ROW]
[ROW][C]20[/C][C]880[/C][C]892.769519774336[/C][C]-12.7695197743355[/C][/ROW]
[ROW][C]21[/C][C]800[/C][C]892.220059397738[/C][C]-92.2200593977376[/C][/ROW]
[ROW][C]22[/C][C]900[/C][C]888.251917332724[/C][C]11.7480826672761[/C][/ROW]
[ROW][C]23[/C][C]900[/C][C]888.757426235231[/C][C]11.2425737647691[/C][/ROW]
[ROW][C]24[/C][C]1000[/C][C]889.241183567056[/C][C]110.758816432944[/C][/ROW]
[ROW][C]25[/C][C]890[/C][C]894.007030839645[/C][C]-4.00703083964504[/C][/ROW]
[ROW][C]26[/C][C]890[/C][C]893.834612086779[/C][C]-3.83461208677886[/C][/ROW]
[ROW][C]27[/C][C]870[/C][C]893.66961235002[/C][C]-23.6696123500195[/C][/ROW]
[ROW][C]28[/C][C]1000[/C][C]892.65113128373[/C][C]107.34886871627[/C][/ROW]
[ROW][C]29[/C][C]1050[/C][C]897.27025172636[/C][C]152.72974827364[/C][/ROW]
[ROW][C]30[/C][C]790[/C][C]903.842068559504[/C][C]-113.842068559504[/C][/ROW]
[ROW][C]31[/C][C]1160[/C][C]898.943551859674[/C][C]261.056448140326[/C][/ROW]
[ROW][C]32[/C][C]830[/C][C]910.176564286406[/C][C]-80.1765642864058[/C][/ROW]
[ROW][C]33[/C][C]730[/C][C]906.726642442385[/C][C]-176.726642442385[/C][/ROW]
[ROW][C]34[/C][C]950[/C][C]899.12226191537[/C][C]50.8777380846296[/C][/ROW]
[ROW][C]35[/C][C]980[/C][C]901.311482937183[/C][C]78.6885170628167[/C][/ROW]
[ROW][C]36[/C][C]910[/C][C]904.697375514457[/C][C]5.30262448554322[/C][/ROW]
[ROW][C]37[/C][C]840[/C][C]904.925542438372[/C][C]-64.925542438372[/C][/ROW]
[ROW][C]38[/C][C]860[/C][C]902.131857661697[/C][C]-42.1318576616968[/C][/ROW]
[ROW][C]39[/C][C]880[/C][C]900.318963615039[/C][C]-20.3189636150394[/C][/ROW]
[ROW][C]40[/C][C]1030[/C][C]899.444657799527[/C][C]130.555342200473[/C][/ROW]
[ROW][C]41[/C][C]1060[/C][C]905.06233088043[/C][C]154.93766911957[/C][/ROW]
[ROW][C]42[/C][C]770[/C][C]911.729152462456[/C][C]-141.729152462456[/C][/ROW]
[ROW][C]43[/C][C]1140[/C][C]905.630680878314[/C][C]234.369319121686[/C][/ROW]
[ROW][C]44[/C][C]890[/C][C]915.71537134619[/C][C]-25.7153713461906[/C][/ROW]
[ROW][C]45[/C][C]740[/C][C]914.608863202272[/C][C]-174.608863202272[/C][/ROW]
[ROW][C]46[/C][C]860[/C][C]907.095608715969[/C][C]-47.0956087159691[/C][/ROW]
[ROW][C]47[/C][C]1050[/C][C]905.069129149118[/C][C]144.930870850882[/C][/ROW]
[ROW][C]48[/C][C]840[/C][C]911.305367651873[/C][C]-71.3053676518728[/C][/ROW]
[ROW][C]49[/C][C]810[/C][C]908.237165021246[/C][C]-98.2371650212463[/C][/ROW]
[ROW][C]50[/C][C]830[/C][C]904.010112583693[/C][C]-74.010112583693[/C][/ROW]
[ROW][C]51[/C][C]920[/C][C]900.82552733296[/C][C]19.1744726670399[/C][/ROW]
[ROW][C]52[/C][C]1070[/C][C]901.650586783815[/C][C]168.349413216185[/C][/ROW]
[ROW][C]53[/C][C]1040[/C][C]908.894503048522[/C][C]131.105496951478[/C][/ROW]
[ROW][C]54[/C][C]740[/C][C]914.535848768806[/C][C]-174.535848768806[/C][/ROW]
[ROW][C]55[/C][C]1250[/C][C]907.025736024621[/C][C]342.974263975379[/C][/ROW]
[ROW][C]56[/C][C]850[/C][C]921.783594705107[/C][C]-71.7835947051074[/C][/ROW]
[ROW][C]57[/C][C]790[/C][C]918.694814416009[/C][C]-128.694814416009[/C][/ROW]
[ROW][C]58[/C][C]810[/C][C]913.157198088624[/C][C]-103.157198088624[/C][/ROW]
[ROW][C]59[/C][C]1080[/C][C]908.718441274567[/C][C]171.281558725433[/C][/ROW]
[ROW][C]60[/C][C]760[/C][C]916.088524991475[/C][C]-156.088524991475[/C][/ROW]
[ROW][C]61[/C][C]840[/C][C]909.372183168127[/C][C]-69.3721831681272[/C][/ROW]
[ROW][C]62[/C][C]820[/C][C]906.387163640174[/C][C]-86.3871636401736[/C][/ROW]
[ROW][C]63[/C][C]900[/C][C]902.670005571132[/C][C]-2.67000557113204[/C][/ROW]
[ROW][C]64[/C][C]1010[/C][C]902.555117752909[/C][C]107.444882247091[/C][/ROW]
[ROW][C]65[/C][C]1080[/C][C]907.178369567097[/C][C]172.821630432903[/C][/ROW]
[ROW][C]66[/C][C]780[/C][C]914.614721115162[/C][C]-134.614721115162[/C][/ROW]
[ROW][C]67[/C][C]1150[/C][C]908.82237679316[/C][C]241.17762320684[/C][/ROW]
[ROW][C]68[/C][C]820[/C][C]919.200022156188[/C][C]-99.2000221561884[/C][/ROW]
[ROW][C]69[/C][C]790[/C][C]914.931538885423[/C][C]-124.931538885423[/C][/ROW]
[ROW][C]70[/C][C]820[/C][C]909.555852750153[/C][C]-89.5558527501532[/C][/ROW]
[ROW][C]71[/C][C]1130[/C][C]905.702348981159[/C][C]224.297651018841[/C][/ROW]
[ROW][C]72[/C][C]800[/C][C]915.353665082062[/C][C]-115.353665082062[/C][/ROW]
[ROW][C]73[/C][C]890[/C][C]910.39010581139[/C][C]-20.3901058113894[/C][/ROW]
[ROW][C]74[/C][C]810[/C][C]909.512738814354[/C][C]-99.5127388143536[/C][/ROW]
[ROW][C]75[/C][C]950[/C][C]905.230799641111[/C][C]44.7692003588893[/C][/ROW]
[ROW][C]76[/C][C]1090[/C][C]907.157176053372[/C][C]182.842823946628[/C][/ROW]
[ROW][C]77[/C][C]1090[/C][C]915.024730094509[/C][C]174.975269905491[/C][/ROW]
[ROW][C]78[/C][C]850[/C][C]922.553750715223[/C][C]-72.5537507152234[/C][/ROW]
[ROW][C]79[/C][C]1200[/C][C]919.43183134033[/C][C]280.56816865967[/C][/ROW]
[ROW][C]80[/C][C]790[/C][C]931.504414674511[/C][C]-141.504414674511[/C][/ROW]
[ROW][C]81[/C][C]800[/C][C]925.415613345146[/C][C]-125.415613345146[/C][/ROW]
[ROW][C]82[/C][C]850[/C][C]920.019097943025[/C][C]-70.0190979430254[/C][/ROW]
[ROW][C]83[/C][C]1230[/C][C]917.006242283242[/C][C]312.993757716758[/C][/ROW]
[ROW][C]84[/C][C]800[/C][C]930.47406809244[/C][C]-130.47406809244[/C][/ROW]
[ROW][C]85[/C][C]930[/C][C]924.859892159651[/C][C]5.14010784034861[/C][/ROW]
[ROW][C]86[/C][C]700[/C][C]925.081066145802[/C][C]-225.081066145802[/C][/ROW]
[ROW][C]87[/C][C]1030[/C][C]915.396040431827[/C][C]114.603959568173[/C][/ROW]
[ROW][C]88[/C][C]1040[/C][C]920.327340582245[/C][C]119.672659417755[/C][/ROW]
[ROW][C]89[/C][C]1000[/C][C]925.476742100407[/C][C]74.5232578995932[/C][/ROW]
[ROW][C]90[/C][C]830[/C][C]928.683407509478[/C][C]-98.6834075094783[/C][/ROW]
[ROW][C]91[/C][C]1190[/C][C]924.43715367908[/C][C]265.56284632092[/C][/ROW]
[ROW][C]92[/C][C]720[/C][C]935.864072163765[/C][C]-215.864072163765[/C][/ROW]
[ROW][C]93[/C][C]810[/C][C]926.575644996484[/C][C]-116.575644996484[/C][/ROW]
[ROW][C]94[/C][C]870[/C][C]921.559505084109[/C][C]-51.5595050841087[/C][/ROW]
[ROW][C]95[/C][C]1190[/C][C]919.340948272156[/C][C]270.659051727844[/C][/ROW]
[ROW][C]96[/C][C]800[/C][C]930.987151662742[/C][C]-130.987151662742[/C][/ROW]
[ROW][C]97[/C][C]970[/C][C]925.35089822847[/C][C]44.6491017715299[/C][/ROW]
[ROW][C]98[/C][C]690[/C][C]927.272106911936[/C][C]-237.272106911936[/C][/ROW]
[ROW][C]99[/C][C]1010[/C][C]917.062512226782[/C][C]92.9374877732175[/C][/ROW]
[ROW][C]100[/C][C]1030[/C][C]921.061524557267[/C][C]108.938475442733[/C][/ROW]
[ROW][C]101[/C][C]950[/C][C]925.749044276143[/C][C]24.250955723857[/C][/ROW]
[ROW][C]102[/C][C]830[/C][C]926.792539998799[/C][C]-96.792539998799[/C][/ROW]
[ROW][C]103[/C][C]1150[/C][C]922.627648411685[/C][C]227.372351588315[/C][/ROW]
[ROW][C]104[/C][C]750[/C][C]932.411265974404[/C][C]-182.411265974404[/C][/ROW]
[ROW][C]105[/C][C]840[/C][C]924.562281465257[/C][C]-84.5622814652573[/C][/ROW]
[ROW][C]106[/C][C]880[/C][C]920.923646352818[/C][C]-40.9236463528183[/C][/ROW]
[ROW][C]107[/C][C]1210[/C][C]919.16274049777[/C][C]290.83725950223[/C][/ROW]
[ROW][C]108[/C][C]830[/C][C]931.677193112972[/C][C]-101.677193112972[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=169459&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=169459&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
288084040
3930841.7211622247688.2788377752396
4920845.51971724537374.4802827546272
5940848.72453347454191.2754665254587
6880852.65203060031627.3479693996835
7980853.828787896682126.171212103318
8860859.2578159997940.742184000205839
9900859.28975147641940.7102485235814
10930861.04147502440468.9585249755964
11870864.0086952309835.99130476901655
121000864.26649541712135.73350458288
13870870.10697993518-0.106979935179993
14860870.1023766896-10.1023766895991
15930869.66768096113860.3323190388619
16980872.263723672685107.736276327315
171010876.899513898958133.100486101042
18860882.626702118317-22.6267021183174
191140881.653096494394258.346903505606
20880892.769519774336-12.7695197743355
21800892.220059397738-92.2200593977376
22900888.25191733272411.7480826672761
23900888.75742623523111.2425737647691
241000889.241183567056110.758816432944
25890894.007030839645-4.00703083964504
26890893.834612086779-3.83461208677886
27870893.66961235002-23.6696123500195
281000892.65113128373107.34886871627
291050897.27025172636152.72974827364
30790903.842068559504-113.842068559504
311160898.943551859674261.056448140326
32830910.176564286406-80.1765642864058
33730906.726642442385-176.726642442385
34950899.1222619153750.8777380846296
35980901.31148293718378.6885170628167
36910904.6973755144575.30262448554322
37840904.925542438372-64.925542438372
38860902.131857661697-42.1318576616968
39880900.318963615039-20.3189636150394
401030899.444657799527130.555342200473
411060905.06233088043154.93766911957
42770911.729152462456-141.729152462456
431140905.630680878314234.369319121686
44890915.71537134619-25.7153713461906
45740914.608863202272-174.608863202272
46860907.095608715969-47.0956087159691
471050905.069129149118144.930870850882
48840911.305367651873-71.3053676518728
49810908.237165021246-98.2371650212463
50830904.010112583693-74.010112583693
51920900.8255273329619.1744726670399
521070901.650586783815168.349413216185
531040908.894503048522131.105496951478
54740914.535848768806-174.535848768806
551250907.025736024621342.974263975379
56850921.783594705107-71.7835947051074
57790918.694814416009-128.694814416009
58810913.157198088624-103.157198088624
591080908.718441274567171.281558725433
60760916.088524991475-156.088524991475
61840909.372183168127-69.3721831681272
62820906.387163640174-86.3871636401736
63900902.670005571132-2.67000557113204
641010902.555117752909107.444882247091
651080907.178369567097172.821630432903
66780914.614721115162-134.614721115162
671150908.82237679316241.17762320684
68820919.200022156188-99.2000221561884
69790914.931538885423-124.931538885423
70820909.555852750153-89.5558527501532
711130905.702348981159224.297651018841
72800915.353665082062-115.353665082062
73890910.39010581139-20.3901058113894
74810909.512738814354-99.5127388143536
75950905.23079964111144.7692003588893
761090907.157176053372182.842823946628
771090915.024730094509174.975269905491
78850922.553750715223-72.5537507152234
791200919.43183134033280.56816865967
80790931.504414674511-141.504414674511
81800925.415613345146-125.415613345146
82850920.019097943025-70.0190979430254
831230917.006242283242312.993757716758
84800930.47406809244-130.47406809244
85930924.8598921596515.14010784034861
86700925.081066145802-225.081066145802
871030915.396040431827114.603959568173
881040920.327340582245119.672659417755
891000925.47674210040774.5232578995932
90830928.683407509478-98.6834075094783
911190924.43715367908265.56284632092
92720935.864072163765-215.864072163765
93810926.575644996484-116.575644996484
94870921.559505084109-51.5595050841087
951190919.340948272156270.659051727844
96800930.987151662742-130.987151662742
97970925.3508982284744.6491017715299
98690927.272106911936-237.272106911936
991010917.06251222678292.9374877732175
1001030921.061524557267108.938475442733
101950925.74904427614324.250955723857
102830926.792539998799-96.792539998799
1031150922.627648411685227.372351588315
104750932.411265974404-182.411265974404
105840924.562281465257-84.5622814652573
106880920.923646352818-40.9236463528183
1071210919.16274049777290.83725950223
108830931.677193112972-101.677193112972







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
109927.30211951533663.1255834219651191.47865560869
110927.30211951533662.8811351395341191.72310389112
111927.30211951533662.6369126326721191.96732639799
112927.30211951533662.3929152769421192.21132375372
113927.30211951533662.1491424507841192.45509657987
114927.30211951533661.9055935354921192.69864549517
115927.30211951533661.6622679151941192.94197111547
116927.30211951533661.4191649768371193.18507405382
117927.30211951533661.1762841101711193.42795492049
118927.30211951533660.9336247077251193.67061432293
119927.30211951533660.6911861647921193.91305286587
120927.30211951533660.4489678794161194.15527115124

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
109 & 927.30211951533 & 663.125583421965 & 1191.47865560869 \tabularnewline
110 & 927.30211951533 & 662.881135139534 & 1191.72310389112 \tabularnewline
111 & 927.30211951533 & 662.636912632672 & 1191.96732639799 \tabularnewline
112 & 927.30211951533 & 662.392915276942 & 1192.21132375372 \tabularnewline
113 & 927.30211951533 & 662.149142450784 & 1192.45509657987 \tabularnewline
114 & 927.30211951533 & 661.905593535492 & 1192.69864549517 \tabularnewline
115 & 927.30211951533 & 661.662267915194 & 1192.94197111547 \tabularnewline
116 & 927.30211951533 & 661.419164976837 & 1193.18507405382 \tabularnewline
117 & 927.30211951533 & 661.176284110171 & 1193.42795492049 \tabularnewline
118 & 927.30211951533 & 660.933624707725 & 1193.67061432293 \tabularnewline
119 & 927.30211951533 & 660.691186164792 & 1193.91305286587 \tabularnewline
120 & 927.30211951533 & 660.448967879416 & 1194.15527115124 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=169459&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]927.30211951533[/C][C]663.125583421965[/C][C]1191.47865560869[/C][/ROW]
[ROW][C]110[/C][C]927.30211951533[/C][C]662.881135139534[/C][C]1191.72310389112[/C][/ROW]
[ROW][C]111[/C][C]927.30211951533[/C][C]662.636912632672[/C][C]1191.96732639799[/C][/ROW]
[ROW][C]112[/C][C]927.30211951533[/C][C]662.392915276942[/C][C]1192.21132375372[/C][/ROW]
[ROW][C]113[/C][C]927.30211951533[/C][C]662.149142450784[/C][C]1192.45509657987[/C][/ROW]
[ROW][C]114[/C][C]927.30211951533[/C][C]661.905593535492[/C][C]1192.69864549517[/C][/ROW]
[ROW][C]115[/C][C]927.30211951533[/C][C]661.662267915194[/C][C]1192.94197111547[/C][/ROW]
[ROW][C]116[/C][C]927.30211951533[/C][C]661.419164976837[/C][C]1193.18507405382[/C][/ROW]
[ROW][C]117[/C][C]927.30211951533[/C][C]661.176284110171[/C][C]1193.42795492049[/C][/ROW]
[ROW][C]118[/C][C]927.30211951533[/C][C]660.933624707725[/C][C]1193.67061432293[/C][/ROW]
[ROW][C]119[/C][C]927.30211951533[/C][C]660.691186164792[/C][C]1193.91305286587[/C][/ROW]
[ROW][C]120[/C][C]927.30211951533[/C][C]660.448967879416[/C][C]1194.15527115124[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=169459&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=169459&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
109927.30211951533663.1255834219651191.47865560869
110927.30211951533662.8811351395341191.72310389112
111927.30211951533662.6369126326721191.96732639799
112927.30211951533662.3929152769421192.21132375372
113927.30211951533662.1491424507841192.45509657987
114927.30211951533661.9055935354921192.69864549517
115927.30211951533661.6622679151941192.94197111547
116927.30211951533661.4191649768371193.18507405382
117927.30211951533661.1762841101711193.42795492049
118927.30211951533660.9336247077251193.67061432293
119927.30211951533660.6911861647921193.91305286587
120927.30211951533660.4489678794161194.15527115124



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