Free Statistics

of Irreproducible Research!

Author's title

Author*The author of this computation has been verified*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationTue, 20 Dec 2016 17:19:34 +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/2016/Dec/20/t1482250879ecgworbcguroqje.htm/, Retrieved Sun, 28 Apr 2024 00:23:23 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=301735, Retrieved Sun, 28 Apr 2024 00:23:23 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact61
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [Exponential smoot...] [2016-12-20 16:19:34] [63af9ed1c5670c0e3049894fd77d93e0] [Current]
Feedback Forum

Post a new message
Dataseries X:
5610
3530
2370
11610
4630
8760
4130
5400
5630
7050
5620
5510
4240
3620
4220
3480
3400
4830
3060
8030
8480
7270
10030
7810
6470
5150
4580
2640
2180
6250
4310
6160
8560
6250
8940
8040
6290
2630
4760
3820
2350
2420
4780
6120
4290
5540
6120
5110
4800
2670
5120
2370
3280
4090
2250
2520
3670
6440
5490
2000
2130
1210
6770
2380
2380
3760
3860
4590
4580
8030
5880
1770
5440
4090
3360
1240
1890
3390
2980
5030
3720
3530
1620
2290
2050
2070
2760
1500
1850
2760
3360
2120
3970
3760
3630
1850
3160
2700
1080
1150
1230
2180
2310
2940
4370
4750
7810
2880




Summary of computational transaction
Raw Input view raw input (R code)
Raw Outputview raw output of R engine
Computing time1 seconds
R ServerBig Analytics Cloud Computing Center

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input view raw input (R code)  \tabularnewline
Raw Outputview raw output of R engine  \tabularnewline
Computing time1 seconds \tabularnewline
R ServerBig Analytics Cloud Computing Center \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=301735&T=0

[TABLE]
[ROW]
Summary of computational transaction[/C][/ROW] [ROW]Raw Input[/C] view raw input (R code) [/C][/ROW] [ROW]Raw Output[/C]view raw output of R engine [/C][/ROW] [ROW]Computing time[/C]1 seconds[/C][/ROW] [ROW]R Server[/C]Big Analytics Cloud Computing Center[/C][/ROW] [/TABLE] Source: https://freestatistics.org/blog/index.php?pk=301735&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=301735&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 Input view raw input (R code)
Raw Outputview raw output of R engine
Computing time1 seconds
R ServerBig Analytics Cloud Computing Center







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.136565811798447
betaFALSE
gammaFALSE

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.136565811798447 \tabularnewline
beta & FALSE \tabularnewline
gamma & FALSE \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=301735&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]0.136565811798447[/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=301735&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=301735&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
alpha0.136565811798447
betaFALSE
gammaFALSE







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
235305610-2080
323705325.94311145923-2955.94311145923
4116104922.262340812776687.73765918723
546305835.57866333472-1205.57866333472
687605670.937834489533089.06216551047
741306092.79811681834-1962.79811681834
854005824.74699859858-424.746998598576
956305766.74107992601-136.741079926009
1070505748.066923339721301.93307666028
1156205925.86647086108-305.866470861078
1255105884.09556796601-374.095567966008
1342405833.00690303653-1593.00690303653
1436205615.45662212282-1995.45662212282
1542205342.94546861403-1122.94546861403
1634805189.58950908737-1709.58950908737
1734004956.11802993674-1556.11802993674
1848304743.6055079242386.3944920757694
1930604755.40404186947-1695.40404186947
2080304523.86981256523506.1301874348
2184805002.687327883273477.31267211673
2272705477.569355827921792.43064417208
23100305722.354101841694307.64589815831
2478106310.631260863931499.36873913607
2564706515.39376990926-45.3937699092621
2651506509.19453287101-1359.19453287101
2745806323.57502809747-1743.57502809747
2826406085.46228895384-3445.46228895384
2921805614.92993444193-3434.92993444193
3062505145.835939474081104.16406052592
3143105296.62700075847-986.62700075847
3261605161.88748345762998.112516542377
3385605298.195529545423261.80447045458
3462505743.64650498085506.353495019146
3589405812.797081085123127.20291891488
3680406239.866086365211800.13391363479
3762906485.70283562666-195.702835626657
3826306458.97651900805-3828.97651900805
3947605936.06923233252-1176.06923233252
4038205775.45838288785-1955.45838288785
4123505508.4096213907-3158.4096213907
4224205077.07884745345-2657.07884745345
4347804714.2127176384965.7872823615116
4461204723.19701126021396.8029887398
4542904913.95254533995-623.952545339949
4655404828.74195946189711.258040538108
4761204925.875491166151194.12450883385
4851105088.9520741034721.0479258965315
4948005091.8265011902-291.826501190202
5026705051.97297815086-2381.97297815086
5151204726.67690470773393.323095292274
5223704780.39139251539-2410.39139251539
5332804451.21433524454-1171.21433524454
5440904291.26649876189-201.266498761892
5522504263.78037597064-2013.78037597064
5625203988.76682414243-1468.76682414243
5736703788.18349046079-118.183490460794
5864403772.043666144842667.95633385516
5954904136.395288720581353.60471127942
6020004321.25141497066-2321.25141497066
6121304004.24783109689-1874.24783109689
6212103748.28965453167-2538.28965453167
6367703401.646067280953368.35393271905
6423803861.64805652722-1481.64805652722
6523803659.30558688799-1279.30558688799
6637603484.59618087634275.403819123657
6738603522.20692700736337.793072992642
6845903568.337912240491021.66208775951
6945803707.86202463906872.137975360937
7080303826.966255244484203.03374475552
7158804400.956970613291479.04302938671
7217704602.94368260632-2832.94368260632
7354404216.06042881191223.9395711881
7440904383.20872994345-293.208729943449
7533604343.16644171233-983.16644171233
7612404208.8995184669-2968.8995184669
7718903803.44934557945-1913.44934557945
7833903542.13758236518-152.137582365183
7929803521.36078992443-541.360789924429
8050303447.429414172551582.57058582745
8137203663.5544509544256.4455490455803
8235303671.26298318224-141.262983182238
8316203651.97128920689-2031.97128920689
8422903374.47348054521-1084.47348054521
8520503226.37147930067-1176.37147930067
8620703065.71935325343-995.719353253432
8727602929.73813145295-169.738131452953
8815002906.55770573793-1406.55770573793
8918502714.47001081247-864.470010812468
9027602596.41296201045163.587037989549
9133602618.7533586532741.246641346803
9221202719.9823079716-599.982307971595
9339702638.045237018751331.95476298125
9437602819.94472050409940.055279495909
9536302948.32413288387681.675867116135
9618503041.41775105999-1191.41775105999
9731602878.7108186954281.289181304597
9827002917.12530409039-217.125304090386
9910802887.4734106753-1807.4734106753
10011502640.63433704232-1490.63433704232
10112302437.06464870949-1207.06464870949
10221802272.22088506528-92.2208850652755
10323102259.6266650315750.3733349684348
10429402266.50594041452673.494059585475
10543702358.482203403252011.51779659675
10647502633.18676424252116.8132357575
10778102922.271082209424887.72891779058
10828803589.76774971824-709.767749718238

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
2 & 3530 & 5610 & -2080 \tabularnewline
3 & 2370 & 5325.94311145923 & -2955.94311145923 \tabularnewline
4 & 11610 & 4922.26234081277 & 6687.73765918723 \tabularnewline
5 & 4630 & 5835.57866333472 & -1205.57866333472 \tabularnewline
6 & 8760 & 5670.93783448953 & 3089.06216551047 \tabularnewline
7 & 4130 & 6092.79811681834 & -1962.79811681834 \tabularnewline
8 & 5400 & 5824.74699859858 & -424.746998598576 \tabularnewline
9 & 5630 & 5766.74107992601 & -136.741079926009 \tabularnewline
10 & 7050 & 5748.06692333972 & 1301.93307666028 \tabularnewline
11 & 5620 & 5925.86647086108 & -305.866470861078 \tabularnewline
12 & 5510 & 5884.09556796601 & -374.095567966008 \tabularnewline
13 & 4240 & 5833.00690303653 & -1593.00690303653 \tabularnewline
14 & 3620 & 5615.45662212282 & -1995.45662212282 \tabularnewline
15 & 4220 & 5342.94546861403 & -1122.94546861403 \tabularnewline
16 & 3480 & 5189.58950908737 & -1709.58950908737 \tabularnewline
17 & 3400 & 4956.11802993674 & -1556.11802993674 \tabularnewline
18 & 4830 & 4743.60550792423 & 86.3944920757694 \tabularnewline
19 & 3060 & 4755.40404186947 & -1695.40404186947 \tabularnewline
20 & 8030 & 4523.8698125652 & 3506.1301874348 \tabularnewline
21 & 8480 & 5002.68732788327 & 3477.31267211673 \tabularnewline
22 & 7270 & 5477.56935582792 & 1792.43064417208 \tabularnewline
23 & 10030 & 5722.35410184169 & 4307.64589815831 \tabularnewline
24 & 7810 & 6310.63126086393 & 1499.36873913607 \tabularnewline
25 & 6470 & 6515.39376990926 & -45.3937699092621 \tabularnewline
26 & 5150 & 6509.19453287101 & -1359.19453287101 \tabularnewline
27 & 4580 & 6323.57502809747 & -1743.57502809747 \tabularnewline
28 & 2640 & 6085.46228895384 & -3445.46228895384 \tabularnewline
29 & 2180 & 5614.92993444193 & -3434.92993444193 \tabularnewline
30 & 6250 & 5145.83593947408 & 1104.16406052592 \tabularnewline
31 & 4310 & 5296.62700075847 & -986.62700075847 \tabularnewline
32 & 6160 & 5161.88748345762 & 998.112516542377 \tabularnewline
33 & 8560 & 5298.19552954542 & 3261.80447045458 \tabularnewline
34 & 6250 & 5743.64650498085 & 506.353495019146 \tabularnewline
35 & 8940 & 5812.79708108512 & 3127.20291891488 \tabularnewline
36 & 8040 & 6239.86608636521 & 1800.13391363479 \tabularnewline
37 & 6290 & 6485.70283562666 & -195.702835626657 \tabularnewline
38 & 2630 & 6458.97651900805 & -3828.97651900805 \tabularnewline
39 & 4760 & 5936.06923233252 & -1176.06923233252 \tabularnewline
40 & 3820 & 5775.45838288785 & -1955.45838288785 \tabularnewline
41 & 2350 & 5508.4096213907 & -3158.4096213907 \tabularnewline
42 & 2420 & 5077.07884745345 & -2657.07884745345 \tabularnewline
43 & 4780 & 4714.21271763849 & 65.7872823615116 \tabularnewline
44 & 6120 & 4723.1970112602 & 1396.8029887398 \tabularnewline
45 & 4290 & 4913.95254533995 & -623.952545339949 \tabularnewline
46 & 5540 & 4828.74195946189 & 711.258040538108 \tabularnewline
47 & 6120 & 4925.87549116615 & 1194.12450883385 \tabularnewline
48 & 5110 & 5088.95207410347 & 21.0479258965315 \tabularnewline
49 & 4800 & 5091.8265011902 & -291.826501190202 \tabularnewline
50 & 2670 & 5051.97297815086 & -2381.97297815086 \tabularnewline
51 & 5120 & 4726.67690470773 & 393.323095292274 \tabularnewline
52 & 2370 & 4780.39139251539 & -2410.39139251539 \tabularnewline
53 & 3280 & 4451.21433524454 & -1171.21433524454 \tabularnewline
54 & 4090 & 4291.26649876189 & -201.266498761892 \tabularnewline
55 & 2250 & 4263.78037597064 & -2013.78037597064 \tabularnewline
56 & 2520 & 3988.76682414243 & -1468.76682414243 \tabularnewline
57 & 3670 & 3788.18349046079 & -118.183490460794 \tabularnewline
58 & 6440 & 3772.04366614484 & 2667.95633385516 \tabularnewline
59 & 5490 & 4136.39528872058 & 1353.60471127942 \tabularnewline
60 & 2000 & 4321.25141497066 & -2321.25141497066 \tabularnewline
61 & 2130 & 4004.24783109689 & -1874.24783109689 \tabularnewline
62 & 1210 & 3748.28965453167 & -2538.28965453167 \tabularnewline
63 & 6770 & 3401.64606728095 & 3368.35393271905 \tabularnewline
64 & 2380 & 3861.64805652722 & -1481.64805652722 \tabularnewline
65 & 2380 & 3659.30558688799 & -1279.30558688799 \tabularnewline
66 & 3760 & 3484.59618087634 & 275.403819123657 \tabularnewline
67 & 3860 & 3522.20692700736 & 337.793072992642 \tabularnewline
68 & 4590 & 3568.33791224049 & 1021.66208775951 \tabularnewline
69 & 4580 & 3707.86202463906 & 872.137975360937 \tabularnewline
70 & 8030 & 3826.96625524448 & 4203.03374475552 \tabularnewline
71 & 5880 & 4400.95697061329 & 1479.04302938671 \tabularnewline
72 & 1770 & 4602.94368260632 & -2832.94368260632 \tabularnewline
73 & 5440 & 4216.0604288119 & 1223.9395711881 \tabularnewline
74 & 4090 & 4383.20872994345 & -293.208729943449 \tabularnewline
75 & 3360 & 4343.16644171233 & -983.16644171233 \tabularnewline
76 & 1240 & 4208.8995184669 & -2968.8995184669 \tabularnewline
77 & 1890 & 3803.44934557945 & -1913.44934557945 \tabularnewline
78 & 3390 & 3542.13758236518 & -152.137582365183 \tabularnewline
79 & 2980 & 3521.36078992443 & -541.360789924429 \tabularnewline
80 & 5030 & 3447.42941417255 & 1582.57058582745 \tabularnewline
81 & 3720 & 3663.55445095442 & 56.4455490455803 \tabularnewline
82 & 3530 & 3671.26298318224 & -141.262983182238 \tabularnewline
83 & 1620 & 3651.97128920689 & -2031.97128920689 \tabularnewline
84 & 2290 & 3374.47348054521 & -1084.47348054521 \tabularnewline
85 & 2050 & 3226.37147930067 & -1176.37147930067 \tabularnewline
86 & 2070 & 3065.71935325343 & -995.719353253432 \tabularnewline
87 & 2760 & 2929.73813145295 & -169.738131452953 \tabularnewline
88 & 1500 & 2906.55770573793 & -1406.55770573793 \tabularnewline
89 & 1850 & 2714.47001081247 & -864.470010812468 \tabularnewline
90 & 2760 & 2596.41296201045 & 163.587037989549 \tabularnewline
91 & 3360 & 2618.7533586532 & 741.246641346803 \tabularnewline
92 & 2120 & 2719.9823079716 & -599.982307971595 \tabularnewline
93 & 3970 & 2638.04523701875 & 1331.95476298125 \tabularnewline
94 & 3760 & 2819.94472050409 & 940.055279495909 \tabularnewline
95 & 3630 & 2948.32413288387 & 681.675867116135 \tabularnewline
96 & 1850 & 3041.41775105999 & -1191.41775105999 \tabularnewline
97 & 3160 & 2878.7108186954 & 281.289181304597 \tabularnewline
98 & 2700 & 2917.12530409039 & -217.125304090386 \tabularnewline
99 & 1080 & 2887.4734106753 & -1807.4734106753 \tabularnewline
100 & 1150 & 2640.63433704232 & -1490.63433704232 \tabularnewline
101 & 1230 & 2437.06464870949 & -1207.06464870949 \tabularnewline
102 & 2180 & 2272.22088506528 & -92.2208850652755 \tabularnewline
103 & 2310 & 2259.62666503157 & 50.3733349684348 \tabularnewline
104 & 2940 & 2266.50594041452 & 673.494059585475 \tabularnewline
105 & 4370 & 2358.48220340325 & 2011.51779659675 \tabularnewline
106 & 4750 & 2633.1867642425 & 2116.8132357575 \tabularnewline
107 & 7810 & 2922.27108220942 & 4887.72891779058 \tabularnewline
108 & 2880 & 3589.76774971824 & -709.767749718238 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=301735&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]3530[/C][C]5610[/C][C]-2080[/C][/ROW]
[ROW][C]3[/C][C]2370[/C][C]5325.94311145923[/C][C]-2955.94311145923[/C][/ROW]
[ROW][C]4[/C][C]11610[/C][C]4922.26234081277[/C][C]6687.73765918723[/C][/ROW]
[ROW][C]5[/C][C]4630[/C][C]5835.57866333472[/C][C]-1205.57866333472[/C][/ROW]
[ROW][C]6[/C][C]8760[/C][C]5670.93783448953[/C][C]3089.06216551047[/C][/ROW]
[ROW][C]7[/C][C]4130[/C][C]6092.79811681834[/C][C]-1962.79811681834[/C][/ROW]
[ROW][C]8[/C][C]5400[/C][C]5824.74699859858[/C][C]-424.746998598576[/C][/ROW]
[ROW][C]9[/C][C]5630[/C][C]5766.74107992601[/C][C]-136.741079926009[/C][/ROW]
[ROW][C]10[/C][C]7050[/C][C]5748.06692333972[/C][C]1301.93307666028[/C][/ROW]
[ROW][C]11[/C][C]5620[/C][C]5925.86647086108[/C][C]-305.866470861078[/C][/ROW]
[ROW][C]12[/C][C]5510[/C][C]5884.09556796601[/C][C]-374.095567966008[/C][/ROW]
[ROW][C]13[/C][C]4240[/C][C]5833.00690303653[/C][C]-1593.00690303653[/C][/ROW]
[ROW][C]14[/C][C]3620[/C][C]5615.45662212282[/C][C]-1995.45662212282[/C][/ROW]
[ROW][C]15[/C][C]4220[/C][C]5342.94546861403[/C][C]-1122.94546861403[/C][/ROW]
[ROW][C]16[/C][C]3480[/C][C]5189.58950908737[/C][C]-1709.58950908737[/C][/ROW]
[ROW][C]17[/C][C]3400[/C][C]4956.11802993674[/C][C]-1556.11802993674[/C][/ROW]
[ROW][C]18[/C][C]4830[/C][C]4743.60550792423[/C][C]86.3944920757694[/C][/ROW]
[ROW][C]19[/C][C]3060[/C][C]4755.40404186947[/C][C]-1695.40404186947[/C][/ROW]
[ROW][C]20[/C][C]8030[/C][C]4523.8698125652[/C][C]3506.1301874348[/C][/ROW]
[ROW][C]21[/C][C]8480[/C][C]5002.68732788327[/C][C]3477.31267211673[/C][/ROW]
[ROW][C]22[/C][C]7270[/C][C]5477.56935582792[/C][C]1792.43064417208[/C][/ROW]
[ROW][C]23[/C][C]10030[/C][C]5722.35410184169[/C][C]4307.64589815831[/C][/ROW]
[ROW][C]24[/C][C]7810[/C][C]6310.63126086393[/C][C]1499.36873913607[/C][/ROW]
[ROW][C]25[/C][C]6470[/C][C]6515.39376990926[/C][C]-45.3937699092621[/C][/ROW]
[ROW][C]26[/C][C]5150[/C][C]6509.19453287101[/C][C]-1359.19453287101[/C][/ROW]
[ROW][C]27[/C][C]4580[/C][C]6323.57502809747[/C][C]-1743.57502809747[/C][/ROW]
[ROW][C]28[/C][C]2640[/C][C]6085.46228895384[/C][C]-3445.46228895384[/C][/ROW]
[ROW][C]29[/C][C]2180[/C][C]5614.92993444193[/C][C]-3434.92993444193[/C][/ROW]
[ROW][C]30[/C][C]6250[/C][C]5145.83593947408[/C][C]1104.16406052592[/C][/ROW]
[ROW][C]31[/C][C]4310[/C][C]5296.62700075847[/C][C]-986.62700075847[/C][/ROW]
[ROW][C]32[/C][C]6160[/C][C]5161.88748345762[/C][C]998.112516542377[/C][/ROW]
[ROW][C]33[/C][C]8560[/C][C]5298.19552954542[/C][C]3261.80447045458[/C][/ROW]
[ROW][C]34[/C][C]6250[/C][C]5743.64650498085[/C][C]506.353495019146[/C][/ROW]
[ROW][C]35[/C][C]8940[/C][C]5812.79708108512[/C][C]3127.20291891488[/C][/ROW]
[ROW][C]36[/C][C]8040[/C][C]6239.86608636521[/C][C]1800.13391363479[/C][/ROW]
[ROW][C]37[/C][C]6290[/C][C]6485.70283562666[/C][C]-195.702835626657[/C][/ROW]
[ROW][C]38[/C][C]2630[/C][C]6458.97651900805[/C][C]-3828.97651900805[/C][/ROW]
[ROW][C]39[/C][C]4760[/C][C]5936.06923233252[/C][C]-1176.06923233252[/C][/ROW]
[ROW][C]40[/C][C]3820[/C][C]5775.45838288785[/C][C]-1955.45838288785[/C][/ROW]
[ROW][C]41[/C][C]2350[/C][C]5508.4096213907[/C][C]-3158.4096213907[/C][/ROW]
[ROW][C]42[/C][C]2420[/C][C]5077.07884745345[/C][C]-2657.07884745345[/C][/ROW]
[ROW][C]43[/C][C]4780[/C][C]4714.21271763849[/C][C]65.7872823615116[/C][/ROW]
[ROW][C]44[/C][C]6120[/C][C]4723.1970112602[/C][C]1396.8029887398[/C][/ROW]
[ROW][C]45[/C][C]4290[/C][C]4913.95254533995[/C][C]-623.952545339949[/C][/ROW]
[ROW][C]46[/C][C]5540[/C][C]4828.74195946189[/C][C]711.258040538108[/C][/ROW]
[ROW][C]47[/C][C]6120[/C][C]4925.87549116615[/C][C]1194.12450883385[/C][/ROW]
[ROW][C]48[/C][C]5110[/C][C]5088.95207410347[/C][C]21.0479258965315[/C][/ROW]
[ROW][C]49[/C][C]4800[/C][C]5091.8265011902[/C][C]-291.826501190202[/C][/ROW]
[ROW][C]50[/C][C]2670[/C][C]5051.97297815086[/C][C]-2381.97297815086[/C][/ROW]
[ROW][C]51[/C][C]5120[/C][C]4726.67690470773[/C][C]393.323095292274[/C][/ROW]
[ROW][C]52[/C][C]2370[/C][C]4780.39139251539[/C][C]-2410.39139251539[/C][/ROW]
[ROW][C]53[/C][C]3280[/C][C]4451.21433524454[/C][C]-1171.21433524454[/C][/ROW]
[ROW][C]54[/C][C]4090[/C][C]4291.26649876189[/C][C]-201.266498761892[/C][/ROW]
[ROW][C]55[/C][C]2250[/C][C]4263.78037597064[/C][C]-2013.78037597064[/C][/ROW]
[ROW][C]56[/C][C]2520[/C][C]3988.76682414243[/C][C]-1468.76682414243[/C][/ROW]
[ROW][C]57[/C][C]3670[/C][C]3788.18349046079[/C][C]-118.183490460794[/C][/ROW]
[ROW][C]58[/C][C]6440[/C][C]3772.04366614484[/C][C]2667.95633385516[/C][/ROW]
[ROW][C]59[/C][C]5490[/C][C]4136.39528872058[/C][C]1353.60471127942[/C][/ROW]
[ROW][C]60[/C][C]2000[/C][C]4321.25141497066[/C][C]-2321.25141497066[/C][/ROW]
[ROW][C]61[/C][C]2130[/C][C]4004.24783109689[/C][C]-1874.24783109689[/C][/ROW]
[ROW][C]62[/C][C]1210[/C][C]3748.28965453167[/C][C]-2538.28965453167[/C][/ROW]
[ROW][C]63[/C][C]6770[/C][C]3401.64606728095[/C][C]3368.35393271905[/C][/ROW]
[ROW][C]64[/C][C]2380[/C][C]3861.64805652722[/C][C]-1481.64805652722[/C][/ROW]
[ROW][C]65[/C][C]2380[/C][C]3659.30558688799[/C][C]-1279.30558688799[/C][/ROW]
[ROW][C]66[/C][C]3760[/C][C]3484.59618087634[/C][C]275.403819123657[/C][/ROW]
[ROW][C]67[/C][C]3860[/C][C]3522.20692700736[/C][C]337.793072992642[/C][/ROW]
[ROW][C]68[/C][C]4590[/C][C]3568.33791224049[/C][C]1021.66208775951[/C][/ROW]
[ROW][C]69[/C][C]4580[/C][C]3707.86202463906[/C][C]872.137975360937[/C][/ROW]
[ROW][C]70[/C][C]8030[/C][C]3826.96625524448[/C][C]4203.03374475552[/C][/ROW]
[ROW][C]71[/C][C]5880[/C][C]4400.95697061329[/C][C]1479.04302938671[/C][/ROW]
[ROW][C]72[/C][C]1770[/C][C]4602.94368260632[/C][C]-2832.94368260632[/C][/ROW]
[ROW][C]73[/C][C]5440[/C][C]4216.0604288119[/C][C]1223.9395711881[/C][/ROW]
[ROW][C]74[/C][C]4090[/C][C]4383.20872994345[/C][C]-293.208729943449[/C][/ROW]
[ROW][C]75[/C][C]3360[/C][C]4343.16644171233[/C][C]-983.16644171233[/C][/ROW]
[ROW][C]76[/C][C]1240[/C][C]4208.8995184669[/C][C]-2968.8995184669[/C][/ROW]
[ROW][C]77[/C][C]1890[/C][C]3803.44934557945[/C][C]-1913.44934557945[/C][/ROW]
[ROW][C]78[/C][C]3390[/C][C]3542.13758236518[/C][C]-152.137582365183[/C][/ROW]
[ROW][C]79[/C][C]2980[/C][C]3521.36078992443[/C][C]-541.360789924429[/C][/ROW]
[ROW][C]80[/C][C]5030[/C][C]3447.42941417255[/C][C]1582.57058582745[/C][/ROW]
[ROW][C]81[/C][C]3720[/C][C]3663.55445095442[/C][C]56.4455490455803[/C][/ROW]
[ROW][C]82[/C][C]3530[/C][C]3671.26298318224[/C][C]-141.262983182238[/C][/ROW]
[ROW][C]83[/C][C]1620[/C][C]3651.97128920689[/C][C]-2031.97128920689[/C][/ROW]
[ROW][C]84[/C][C]2290[/C][C]3374.47348054521[/C][C]-1084.47348054521[/C][/ROW]
[ROW][C]85[/C][C]2050[/C][C]3226.37147930067[/C][C]-1176.37147930067[/C][/ROW]
[ROW][C]86[/C][C]2070[/C][C]3065.71935325343[/C][C]-995.719353253432[/C][/ROW]
[ROW][C]87[/C][C]2760[/C][C]2929.73813145295[/C][C]-169.738131452953[/C][/ROW]
[ROW][C]88[/C][C]1500[/C][C]2906.55770573793[/C][C]-1406.55770573793[/C][/ROW]
[ROW][C]89[/C][C]1850[/C][C]2714.47001081247[/C][C]-864.470010812468[/C][/ROW]
[ROW][C]90[/C][C]2760[/C][C]2596.41296201045[/C][C]163.587037989549[/C][/ROW]
[ROW][C]91[/C][C]3360[/C][C]2618.7533586532[/C][C]741.246641346803[/C][/ROW]
[ROW][C]92[/C][C]2120[/C][C]2719.9823079716[/C][C]-599.982307971595[/C][/ROW]
[ROW][C]93[/C][C]3970[/C][C]2638.04523701875[/C][C]1331.95476298125[/C][/ROW]
[ROW][C]94[/C][C]3760[/C][C]2819.94472050409[/C][C]940.055279495909[/C][/ROW]
[ROW][C]95[/C][C]3630[/C][C]2948.32413288387[/C][C]681.675867116135[/C][/ROW]
[ROW][C]96[/C][C]1850[/C][C]3041.41775105999[/C][C]-1191.41775105999[/C][/ROW]
[ROW][C]97[/C][C]3160[/C][C]2878.7108186954[/C][C]281.289181304597[/C][/ROW]
[ROW][C]98[/C][C]2700[/C][C]2917.12530409039[/C][C]-217.125304090386[/C][/ROW]
[ROW][C]99[/C][C]1080[/C][C]2887.4734106753[/C][C]-1807.4734106753[/C][/ROW]
[ROW][C]100[/C][C]1150[/C][C]2640.63433704232[/C][C]-1490.63433704232[/C][/ROW]
[ROW][C]101[/C][C]1230[/C][C]2437.06464870949[/C][C]-1207.06464870949[/C][/ROW]
[ROW][C]102[/C][C]2180[/C][C]2272.22088506528[/C][C]-92.2208850652755[/C][/ROW]
[ROW][C]103[/C][C]2310[/C][C]2259.62666503157[/C][C]50.3733349684348[/C][/ROW]
[ROW][C]104[/C][C]2940[/C][C]2266.50594041452[/C][C]673.494059585475[/C][/ROW]
[ROW][C]105[/C][C]4370[/C][C]2358.48220340325[/C][C]2011.51779659675[/C][/ROW]
[ROW][C]106[/C][C]4750[/C][C]2633.1867642425[/C][C]2116.8132357575[/C][/ROW]
[ROW][C]107[/C][C]7810[/C][C]2922.27108220942[/C][C]4887.72891779058[/C][/ROW]
[ROW][C]108[/C][C]2880[/C][C]3589.76774971824[/C][C]-709.767749718238[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=301735&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=301735&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
235305610-2080
323705325.94311145923-2955.94311145923
4116104922.262340812776687.73765918723
546305835.57866333472-1205.57866333472
687605670.937834489533089.06216551047
741306092.79811681834-1962.79811681834
854005824.74699859858-424.746998598576
956305766.74107992601-136.741079926009
1070505748.066923339721301.93307666028
1156205925.86647086108-305.866470861078
1255105884.09556796601-374.095567966008
1342405833.00690303653-1593.00690303653
1436205615.45662212282-1995.45662212282
1542205342.94546861403-1122.94546861403
1634805189.58950908737-1709.58950908737
1734004956.11802993674-1556.11802993674
1848304743.6055079242386.3944920757694
1930604755.40404186947-1695.40404186947
2080304523.86981256523506.1301874348
2184805002.687327883273477.31267211673
2272705477.569355827921792.43064417208
23100305722.354101841694307.64589815831
2478106310.631260863931499.36873913607
2564706515.39376990926-45.3937699092621
2651506509.19453287101-1359.19453287101
2745806323.57502809747-1743.57502809747
2826406085.46228895384-3445.46228895384
2921805614.92993444193-3434.92993444193
3062505145.835939474081104.16406052592
3143105296.62700075847-986.62700075847
3261605161.88748345762998.112516542377
3385605298.195529545423261.80447045458
3462505743.64650498085506.353495019146
3589405812.797081085123127.20291891488
3680406239.866086365211800.13391363479
3762906485.70283562666-195.702835626657
3826306458.97651900805-3828.97651900805
3947605936.06923233252-1176.06923233252
4038205775.45838288785-1955.45838288785
4123505508.4096213907-3158.4096213907
4224205077.07884745345-2657.07884745345
4347804714.2127176384965.7872823615116
4461204723.19701126021396.8029887398
4542904913.95254533995-623.952545339949
4655404828.74195946189711.258040538108
4761204925.875491166151194.12450883385
4851105088.9520741034721.0479258965315
4948005091.8265011902-291.826501190202
5026705051.97297815086-2381.97297815086
5151204726.67690470773393.323095292274
5223704780.39139251539-2410.39139251539
5332804451.21433524454-1171.21433524454
5440904291.26649876189-201.266498761892
5522504263.78037597064-2013.78037597064
5625203988.76682414243-1468.76682414243
5736703788.18349046079-118.183490460794
5864403772.043666144842667.95633385516
5954904136.395288720581353.60471127942
6020004321.25141497066-2321.25141497066
6121304004.24783109689-1874.24783109689
6212103748.28965453167-2538.28965453167
6367703401.646067280953368.35393271905
6423803861.64805652722-1481.64805652722
6523803659.30558688799-1279.30558688799
6637603484.59618087634275.403819123657
6738603522.20692700736337.793072992642
6845903568.337912240491021.66208775951
6945803707.86202463906872.137975360937
7080303826.966255244484203.03374475552
7158804400.956970613291479.04302938671
7217704602.94368260632-2832.94368260632
7354404216.06042881191223.9395711881
7440904383.20872994345-293.208729943449
7533604343.16644171233-983.16644171233
7612404208.8995184669-2968.8995184669
7718903803.44934557945-1913.44934557945
7833903542.13758236518-152.137582365183
7929803521.36078992443-541.360789924429
8050303447.429414172551582.57058582745
8137203663.5544509544256.4455490455803
8235303671.26298318224-141.262983182238
8316203651.97128920689-2031.97128920689
8422903374.47348054521-1084.47348054521
8520503226.37147930067-1176.37147930067
8620703065.71935325343-995.719353253432
8727602929.73813145295-169.738131452953
8815002906.55770573793-1406.55770573793
8918502714.47001081247-864.470010812468
9027602596.41296201045163.587037989549
9133602618.7533586532741.246641346803
9221202719.9823079716-599.982307971595
9339702638.045237018751331.95476298125
9437602819.94472050409940.055279495909
9536302948.32413288387681.675867116135
9618503041.41775105999-1191.41775105999
9731602878.7108186954281.289181304597
9827002917.12530409039-217.125304090386
9910802887.4734106753-1807.4734106753
10011502640.63433704232-1490.63433704232
10112302437.06464870949-1207.06464870949
10221802272.22088506528-92.2208850652755
10323102259.6266650315750.3733349684348
10429402266.50594041452673.494059585475
10543702358.482203403252011.51779659675
10647502633.18676424252116.8132357575
10778102922.271082209424887.72891779058
10828803589.76774971824-709.767749718238







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
1093492.83774078961-299.0746458870997284.75012746632
1103492.83774078961-334.2712995683397319.94678114756
1113492.83774078961-369.1471977292897354.82267930851
1123492.83774078961-403.7109531065817389.3864346858
1133492.83774078961-437.9707997604637423.64628133968
1143492.83774078961-471.9346159817967457.61009756102
1153492.83774078961-505.6099454476347491.28542702685
1163492.83774078961-539.0040167863567524.67949836557
1173492.83774078961-572.1237616960587557.79924327528
1183492.83774078961-604.9758317448737590.65131332409
1193492.83774078961-637.5666139685437623.24209554776
1203492.83774078961-669.9022453688337655.57772694805

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
109 & 3492.83774078961 & -299.074645887099 & 7284.75012746632 \tabularnewline
110 & 3492.83774078961 & -334.271299568339 & 7319.94678114756 \tabularnewline
111 & 3492.83774078961 & -369.147197729289 & 7354.82267930851 \tabularnewline
112 & 3492.83774078961 & -403.710953106581 & 7389.3864346858 \tabularnewline
113 & 3492.83774078961 & -437.970799760463 & 7423.64628133968 \tabularnewline
114 & 3492.83774078961 & -471.934615981796 & 7457.61009756102 \tabularnewline
115 & 3492.83774078961 & -505.609945447634 & 7491.28542702685 \tabularnewline
116 & 3492.83774078961 & -539.004016786356 & 7524.67949836557 \tabularnewline
117 & 3492.83774078961 & -572.123761696058 & 7557.79924327528 \tabularnewline
118 & 3492.83774078961 & -604.975831744873 & 7590.65131332409 \tabularnewline
119 & 3492.83774078961 & -637.566613968543 & 7623.24209554776 \tabularnewline
120 & 3492.83774078961 & -669.902245368833 & 7655.57772694805 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=301735&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]3492.83774078961[/C][C]-299.074645887099[/C][C]7284.75012746632[/C][/ROW]
[ROW][C]110[/C][C]3492.83774078961[/C][C]-334.271299568339[/C][C]7319.94678114756[/C][/ROW]
[ROW][C]111[/C][C]3492.83774078961[/C][C]-369.147197729289[/C][C]7354.82267930851[/C][/ROW]
[ROW][C]112[/C][C]3492.83774078961[/C][C]-403.710953106581[/C][C]7389.3864346858[/C][/ROW]
[ROW][C]113[/C][C]3492.83774078961[/C][C]-437.970799760463[/C][C]7423.64628133968[/C][/ROW]
[ROW][C]114[/C][C]3492.83774078961[/C][C]-471.934615981796[/C][C]7457.61009756102[/C][/ROW]
[ROW][C]115[/C][C]3492.83774078961[/C][C]-505.609945447634[/C][C]7491.28542702685[/C][/ROW]
[ROW][C]116[/C][C]3492.83774078961[/C][C]-539.004016786356[/C][C]7524.67949836557[/C][/ROW]
[ROW][C]117[/C][C]3492.83774078961[/C][C]-572.123761696058[/C][C]7557.79924327528[/C][/ROW]
[ROW][C]118[/C][C]3492.83774078961[/C][C]-604.975831744873[/C][C]7590.65131332409[/C][/ROW]
[ROW][C]119[/C][C]3492.83774078961[/C][C]-637.566613968543[/C][C]7623.24209554776[/C][/ROW]
[ROW][C]120[/C][C]3492.83774078961[/C][C]-669.902245368833[/C][C]7655.57772694805[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=301735&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=301735&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
1093492.83774078961-299.0746458870997284.75012746632
1103492.83774078961-334.2712995683397319.94678114756
1113492.83774078961-369.1471977292897354.82267930851
1123492.83774078961-403.7109531065817389.3864346858
1133492.83774078961-437.9707997604637423.64628133968
1143492.83774078961-471.9346159817967457.61009756102
1153492.83774078961-505.6099454476347491.28542702685
1163492.83774078961-539.0040167863567524.67949836557
1173492.83774078961-572.1237616960587557.79924327528
1183492.83774078961-604.9758317448737590.65131332409
1193492.83774078961-637.5666139685437623.24209554776
1203492.83774078961-669.9022453688337655.57772694805



Parameters (Session):
par1 = 12 ; par2 = Single ; par3 = additive ; par4 = 12 ;
Parameters (R input):
par1 = 12 ; par2 = Single ; par3 = additive ; par4 = 12 ;
R code (references can be found in the software module):
par4 <- '12'
par3 <- 'additive'
par2 <- 'Single'
par1 <- '12'
par1 <- as.numeric(par1)
par4 <- as.numeric(par4)
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$fitted[,'xhat']
bitmap(file='test1.png')
op <- par(mfrow=c(2,1))
plot(fit,ylab='Observed (black) / Fitted (red)',main='Interpolation Fit of Exponential Smoothing')
plot(myresid,ylab='Residuals',main='Interpolation Prediction Errors')
par(op)
dev.off()
bitmap(file='test2.png')
p <- predict(fit, par4, prediction.interval=TRUE)
np <- length(p[,1])
plot(fit,p,ylab='Observed (black) / Fitted (red)',main='Extrapolation Fit of Exponential Smoothing')
dev.off()
bitmap(file='test3.png')
op <- par(mfrow = c(2,2))
acf(as.numeric(myresid),lag.max = nx/2,main='Residual ACF')
spectrum(myresid,main='Residals Periodogram')
cpgram(myresid,main='Residal Cumulative Periodogram')
qqnorm(myresid,main='Residual Normal QQ Plot')
qqline(myresid)
par(op)
dev.off()
load(file='createtable')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Estimated Parameters of Exponential Smoothing',2,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'Parameter',header=TRUE)
a<-table.element(a,'Value',header=TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'alpha',header=TRUE)
a<-table.element(a,fit$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')