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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 computationFri, 26 Jul 2013 13:33:03 -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/Jul/26/t1374860067s01oykg9tnua30o.htm/, Retrieved Sun, 28 Apr 2024 23:23:54 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=210855, Retrieved Sun, 28 Apr 2024 23:23:54 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywordsJeroen Biesemans
Estimated Impact173
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [Tijdreeks B stap 28] [2013-07-26 17:33:03] [09688f513f3d2798cb35a3603f8bd204] [Current]
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Dataseries X:
2240
2240
2380
2380
2380
2380
2140
2400
2180
2260
2280
2480
2360
2160
2380
2280
2320
2400
1960
2520
2200
2420
2300
2280
2220
2240
2200
2340
2240
2500
1820
2520
2180
2480
2260
2400
2240
2240
2240
2140
2200
2460
1860
2480
1960
2540
2280
2320
2320
2440
2320
2180
2120
2460
2140
2480
2100
2700
2200
2260
2340
2720
2300
2360
2020
2380
2000
2540
1980
2940
2260
2300
2300
2820
2380
2360
1980
2340
2160
2700
1920
2980
2240
2180
2440
2740
2360
2380
2000
2500
2180
2740
1960
3060
2300
2240
2580
2740
2260
2400
1820
2440
2080
2680
1900
3000
2240
2300




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time4 seconds
R Server'Gwilym Jenkins' @ jenkins.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 & 4 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ jenkins.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=210855&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]4 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Gwilym Jenkins' @ jenkins.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=210855&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=210855&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 time4 seconds
R Server'Gwilym Jenkins' @ jenkins.wessa.net







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.00622700651239415
beta0.442874882632437
gamma1

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.00622700651239415 \tabularnewline
beta & 0.442874882632437 \tabularnewline
gamma & 1 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=210855&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]0.00622700651239415[/C][/ROW]
[ROW][C]beta[/C][C]0.442874882632437[/C][/ROW]
[ROW][C]gamma[/C][C]1[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=210855&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=210855&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
alpha0.00622700651239415
beta0.442874882632437
gamma1







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
1323602381.05987486467-21.0598748646744
1421602180.476957968-20.476957967996
1523802395.10664181067-15.1066418106684
1622802285.71689453454-5.71689453453973
1723202317.005330169262.99466983073808
1824002403.43853612701-3.4385361270115
1919602132.65485182856-172.654851828559
2025202387.02521543823132.974784561773
2122002170.7742545894329.2257454105693
2224202253.39992842702166.600071572983
2323002280.135852010319.8641479896974
2422802481.23081389417-201.230813894168
2522202344.7008480563-124.700848056302
2622402144.9195908334395.0804091665677
2722002363.93629052775-163.936290527747
2823402263.089497204176.9105027959049
2922402302.90388349635-62.9038834963458
3025002381.37163861337118.628361386625
3118201946.18977096798-126.189770967976
3225202500.244163996819.7558360031994
3321802182.28213638723-2.28213638722946
3424802398.8589635460281.1410364539815
3522602279.50609342375-19.5060934237517
3624002259.84578174065140.154218259347
3722402201.9873185847538.0126814152522
3822402221.9156945731418.0843054268589
3922402183.5312431075556.468756892451
4021402323.2317187126-183.231718712599
4122002223.37071440498-23.3707144049763
4224602480.77639050381-20.776390503805
4318601806.5451985923353.4548014076681
4424802502.22905290481-22.2290529048123
4519602164.87202542108-204.872025421077
4625402460.5832296722979.4167703277126
4722802242.6496280492737.350371950733
4823202380.82774351284-60.8277435128384
4923202220.906346396799.0936536032959
5024402220.9708016645219.029198335503
5123202222.0914604084397.9085395915749
5221802124.7331690888955.2668309111073
5321202185.65772723671-65.6577272367135
5424602444.459307230515.5406927694994
5521401848.68312734158291.316872658423
5624802469.2734021934910.7265978065116
5721001954.22840767499145.771592325013
5827002536.32228574824163.677714251759
5922002280.39867371078-80.3986737107839
6022602323.01181135031-63.0118113503113
6123402324.7141785757615.2858214242351
6227202446.18482196431273.815178035692
6323002329.44915101345-29.4491510134471
6423602190.44069563007169.55930436993
6520202133.91360545637-113.913605456372
6623802477.77497001961-97.7749700196055
6720002154.76669680155-154.766696801554
6825402496.6048990208543.3951009791458
6919802113.95612686743-133.956126867433
7029402715.58010192006224.419898079943
7122602214.2674461217245.7325538782775
7223002275.6300703782824.3699296217164
7323002356.79643478247-56.7964347824736
7428202737.6149940561582.3850059438487
7523802315.3360508935464.6639491064643
7623602375.09029755361-15.090297553606
7719802033.1167340484-53.1167340484049
7823402395.36815261024-55.3681526102391
7921602013.37641147782146.623588522181
8027002558.70048917066141.299510829342
8119201996.90550179448-76.9055017944768
8229802964.3364159320415.6635840679633
8322402279.13331335627-39.1333133562739
8421802319.48226595812-139.482265958115
8524402318.92188321346121.078116786539
8627402844.13988437373-104.13988437373
8723602399.43043500578-39.4304350057751
8823802378.84879661841.15120338160341
8920001995.956705901194.04329409880916
9025002359.18827699578140.811723004221
9121802177.9944458872.0055541129982
9227402721.6088144885718.391185511432
9319601935.6795555958224.3204444041805
9430603004.5341604976455.465839502358
9523002259.0713235621640.9286764378385
9622402199.9705311676440.0294688323593
9725802462.73972692774117.260273072261
9827402767.97090930031-27.9709093003144
9922602385.20655271317-125.206552713165
10024002405.41618635118-5.41618635117538
10118202021.95179058215-201.951790582153
10224402525.02879360445-85.0287936044497
10320802200.8718420793-120.871842079305
10426802764.14504271822-84.1450427182172
10519001975.80707169735-75.8070716973502
10630003081.69736849845-81.6973684984514
10722402313.96062175932-73.9606217593241
10823002250.9256192789849.0743807210201

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 2360 & 2381.05987486467 & -21.0598748646744 \tabularnewline
14 & 2160 & 2180.476957968 & -20.476957967996 \tabularnewline
15 & 2380 & 2395.10664181067 & -15.1066418106684 \tabularnewline
16 & 2280 & 2285.71689453454 & -5.71689453453973 \tabularnewline
17 & 2320 & 2317.00533016926 & 2.99466983073808 \tabularnewline
18 & 2400 & 2403.43853612701 & -3.4385361270115 \tabularnewline
19 & 1960 & 2132.65485182856 & -172.654851828559 \tabularnewline
20 & 2520 & 2387.02521543823 & 132.974784561773 \tabularnewline
21 & 2200 & 2170.77425458943 & 29.2257454105693 \tabularnewline
22 & 2420 & 2253.39992842702 & 166.600071572983 \tabularnewline
23 & 2300 & 2280.1358520103 & 19.8641479896974 \tabularnewline
24 & 2280 & 2481.23081389417 & -201.230813894168 \tabularnewline
25 & 2220 & 2344.7008480563 & -124.700848056302 \tabularnewline
26 & 2240 & 2144.91959083343 & 95.0804091665677 \tabularnewline
27 & 2200 & 2363.93629052775 & -163.936290527747 \tabularnewline
28 & 2340 & 2263.0894972041 & 76.9105027959049 \tabularnewline
29 & 2240 & 2302.90388349635 & -62.9038834963458 \tabularnewline
30 & 2500 & 2381.37163861337 & 118.628361386625 \tabularnewline
31 & 1820 & 1946.18977096798 & -126.189770967976 \tabularnewline
32 & 2520 & 2500.2441639968 & 19.7558360031994 \tabularnewline
33 & 2180 & 2182.28213638723 & -2.28213638722946 \tabularnewline
34 & 2480 & 2398.85896354602 & 81.1410364539815 \tabularnewline
35 & 2260 & 2279.50609342375 & -19.5060934237517 \tabularnewline
36 & 2400 & 2259.84578174065 & 140.154218259347 \tabularnewline
37 & 2240 & 2201.98731858475 & 38.0126814152522 \tabularnewline
38 & 2240 & 2221.91569457314 & 18.0843054268589 \tabularnewline
39 & 2240 & 2183.53124310755 & 56.468756892451 \tabularnewline
40 & 2140 & 2323.2317187126 & -183.231718712599 \tabularnewline
41 & 2200 & 2223.37071440498 & -23.3707144049763 \tabularnewline
42 & 2460 & 2480.77639050381 & -20.776390503805 \tabularnewline
43 & 1860 & 1806.54519859233 & 53.4548014076681 \tabularnewline
44 & 2480 & 2502.22905290481 & -22.2290529048123 \tabularnewline
45 & 1960 & 2164.87202542108 & -204.872025421077 \tabularnewline
46 & 2540 & 2460.58322967229 & 79.4167703277126 \tabularnewline
47 & 2280 & 2242.64962804927 & 37.350371950733 \tabularnewline
48 & 2320 & 2380.82774351284 & -60.8277435128384 \tabularnewline
49 & 2320 & 2220.9063463967 & 99.0936536032959 \tabularnewline
50 & 2440 & 2220.9708016645 & 219.029198335503 \tabularnewline
51 & 2320 & 2222.09146040843 & 97.9085395915749 \tabularnewline
52 & 2180 & 2124.73316908889 & 55.2668309111073 \tabularnewline
53 & 2120 & 2185.65772723671 & -65.6577272367135 \tabularnewline
54 & 2460 & 2444.4593072305 & 15.5406927694994 \tabularnewline
55 & 2140 & 1848.68312734158 & 291.316872658423 \tabularnewline
56 & 2480 & 2469.27340219349 & 10.7265978065116 \tabularnewline
57 & 2100 & 1954.22840767499 & 145.771592325013 \tabularnewline
58 & 2700 & 2536.32228574824 & 163.677714251759 \tabularnewline
59 & 2200 & 2280.39867371078 & -80.3986737107839 \tabularnewline
60 & 2260 & 2323.01181135031 & -63.0118113503113 \tabularnewline
61 & 2340 & 2324.71417857576 & 15.2858214242351 \tabularnewline
62 & 2720 & 2446.18482196431 & 273.815178035692 \tabularnewline
63 & 2300 & 2329.44915101345 & -29.4491510134471 \tabularnewline
64 & 2360 & 2190.44069563007 & 169.55930436993 \tabularnewline
65 & 2020 & 2133.91360545637 & -113.913605456372 \tabularnewline
66 & 2380 & 2477.77497001961 & -97.7749700196055 \tabularnewline
67 & 2000 & 2154.76669680155 & -154.766696801554 \tabularnewline
68 & 2540 & 2496.60489902085 & 43.3951009791458 \tabularnewline
69 & 1980 & 2113.95612686743 & -133.956126867433 \tabularnewline
70 & 2940 & 2715.58010192006 & 224.419898079943 \tabularnewline
71 & 2260 & 2214.26744612172 & 45.7325538782775 \tabularnewline
72 & 2300 & 2275.63007037828 & 24.3699296217164 \tabularnewline
73 & 2300 & 2356.79643478247 & -56.7964347824736 \tabularnewline
74 & 2820 & 2737.61499405615 & 82.3850059438487 \tabularnewline
75 & 2380 & 2315.33605089354 & 64.6639491064643 \tabularnewline
76 & 2360 & 2375.09029755361 & -15.090297553606 \tabularnewline
77 & 1980 & 2033.1167340484 & -53.1167340484049 \tabularnewline
78 & 2340 & 2395.36815261024 & -55.3681526102391 \tabularnewline
79 & 2160 & 2013.37641147782 & 146.623588522181 \tabularnewline
80 & 2700 & 2558.70048917066 & 141.299510829342 \tabularnewline
81 & 1920 & 1996.90550179448 & -76.9055017944768 \tabularnewline
82 & 2980 & 2964.33641593204 & 15.6635840679633 \tabularnewline
83 & 2240 & 2279.13331335627 & -39.1333133562739 \tabularnewline
84 & 2180 & 2319.48226595812 & -139.482265958115 \tabularnewline
85 & 2440 & 2318.92188321346 & 121.078116786539 \tabularnewline
86 & 2740 & 2844.13988437373 & -104.13988437373 \tabularnewline
87 & 2360 & 2399.43043500578 & -39.4304350057751 \tabularnewline
88 & 2380 & 2378.8487966184 & 1.15120338160341 \tabularnewline
89 & 2000 & 1995.95670590119 & 4.04329409880916 \tabularnewline
90 & 2500 & 2359.18827699578 & 140.811723004221 \tabularnewline
91 & 2180 & 2177.994445887 & 2.0055541129982 \tabularnewline
92 & 2740 & 2721.60881448857 & 18.391185511432 \tabularnewline
93 & 1960 & 1935.67955559582 & 24.3204444041805 \tabularnewline
94 & 3060 & 3004.53416049764 & 55.465839502358 \tabularnewline
95 & 2300 & 2259.07132356216 & 40.9286764378385 \tabularnewline
96 & 2240 & 2199.97053116764 & 40.0294688323593 \tabularnewline
97 & 2580 & 2462.73972692774 & 117.260273072261 \tabularnewline
98 & 2740 & 2767.97090930031 & -27.9709093003144 \tabularnewline
99 & 2260 & 2385.20655271317 & -125.206552713165 \tabularnewline
100 & 2400 & 2405.41618635118 & -5.41618635117538 \tabularnewline
101 & 1820 & 2021.95179058215 & -201.951790582153 \tabularnewline
102 & 2440 & 2525.02879360445 & -85.0287936044497 \tabularnewline
103 & 2080 & 2200.8718420793 & -120.871842079305 \tabularnewline
104 & 2680 & 2764.14504271822 & -84.1450427182172 \tabularnewline
105 & 1900 & 1975.80707169735 & -75.8070716973502 \tabularnewline
106 & 3000 & 3081.69736849845 & -81.6973684984514 \tabularnewline
107 & 2240 & 2313.96062175932 & -73.9606217593241 \tabularnewline
108 & 2300 & 2250.92561927898 & 49.0743807210201 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=210855&T=2

[TABLE]
[ROW][C]Interpolation Forecasts of Exponential Smoothing[/C][/ROW]
[ROW][C]t[/C][C]Observed[/C][C]Fitted[/C][C]Residuals[/C][/ROW]
[ROW][C]13[/C][C]2360[/C][C]2381.05987486467[/C][C]-21.0598748646744[/C][/ROW]
[ROW][C]14[/C][C]2160[/C][C]2180.476957968[/C][C]-20.476957967996[/C][/ROW]
[ROW][C]15[/C][C]2380[/C][C]2395.10664181067[/C][C]-15.1066418106684[/C][/ROW]
[ROW][C]16[/C][C]2280[/C][C]2285.71689453454[/C][C]-5.71689453453973[/C][/ROW]
[ROW][C]17[/C][C]2320[/C][C]2317.00533016926[/C][C]2.99466983073808[/C][/ROW]
[ROW][C]18[/C][C]2400[/C][C]2403.43853612701[/C][C]-3.4385361270115[/C][/ROW]
[ROW][C]19[/C][C]1960[/C][C]2132.65485182856[/C][C]-172.654851828559[/C][/ROW]
[ROW][C]20[/C][C]2520[/C][C]2387.02521543823[/C][C]132.974784561773[/C][/ROW]
[ROW][C]21[/C][C]2200[/C][C]2170.77425458943[/C][C]29.2257454105693[/C][/ROW]
[ROW][C]22[/C][C]2420[/C][C]2253.39992842702[/C][C]166.600071572983[/C][/ROW]
[ROW][C]23[/C][C]2300[/C][C]2280.1358520103[/C][C]19.8641479896974[/C][/ROW]
[ROW][C]24[/C][C]2280[/C][C]2481.23081389417[/C][C]-201.230813894168[/C][/ROW]
[ROW][C]25[/C][C]2220[/C][C]2344.7008480563[/C][C]-124.700848056302[/C][/ROW]
[ROW][C]26[/C][C]2240[/C][C]2144.91959083343[/C][C]95.0804091665677[/C][/ROW]
[ROW][C]27[/C][C]2200[/C][C]2363.93629052775[/C][C]-163.936290527747[/C][/ROW]
[ROW][C]28[/C][C]2340[/C][C]2263.0894972041[/C][C]76.9105027959049[/C][/ROW]
[ROW][C]29[/C][C]2240[/C][C]2302.90388349635[/C][C]-62.9038834963458[/C][/ROW]
[ROW][C]30[/C][C]2500[/C][C]2381.37163861337[/C][C]118.628361386625[/C][/ROW]
[ROW][C]31[/C][C]1820[/C][C]1946.18977096798[/C][C]-126.189770967976[/C][/ROW]
[ROW][C]32[/C][C]2520[/C][C]2500.2441639968[/C][C]19.7558360031994[/C][/ROW]
[ROW][C]33[/C][C]2180[/C][C]2182.28213638723[/C][C]-2.28213638722946[/C][/ROW]
[ROW][C]34[/C][C]2480[/C][C]2398.85896354602[/C][C]81.1410364539815[/C][/ROW]
[ROW][C]35[/C][C]2260[/C][C]2279.50609342375[/C][C]-19.5060934237517[/C][/ROW]
[ROW][C]36[/C][C]2400[/C][C]2259.84578174065[/C][C]140.154218259347[/C][/ROW]
[ROW][C]37[/C][C]2240[/C][C]2201.98731858475[/C][C]38.0126814152522[/C][/ROW]
[ROW][C]38[/C][C]2240[/C][C]2221.91569457314[/C][C]18.0843054268589[/C][/ROW]
[ROW][C]39[/C][C]2240[/C][C]2183.53124310755[/C][C]56.468756892451[/C][/ROW]
[ROW][C]40[/C][C]2140[/C][C]2323.2317187126[/C][C]-183.231718712599[/C][/ROW]
[ROW][C]41[/C][C]2200[/C][C]2223.37071440498[/C][C]-23.3707144049763[/C][/ROW]
[ROW][C]42[/C][C]2460[/C][C]2480.77639050381[/C][C]-20.776390503805[/C][/ROW]
[ROW][C]43[/C][C]1860[/C][C]1806.54519859233[/C][C]53.4548014076681[/C][/ROW]
[ROW][C]44[/C][C]2480[/C][C]2502.22905290481[/C][C]-22.2290529048123[/C][/ROW]
[ROW][C]45[/C][C]1960[/C][C]2164.87202542108[/C][C]-204.872025421077[/C][/ROW]
[ROW][C]46[/C][C]2540[/C][C]2460.58322967229[/C][C]79.4167703277126[/C][/ROW]
[ROW][C]47[/C][C]2280[/C][C]2242.64962804927[/C][C]37.350371950733[/C][/ROW]
[ROW][C]48[/C][C]2320[/C][C]2380.82774351284[/C][C]-60.8277435128384[/C][/ROW]
[ROW][C]49[/C][C]2320[/C][C]2220.9063463967[/C][C]99.0936536032959[/C][/ROW]
[ROW][C]50[/C][C]2440[/C][C]2220.9708016645[/C][C]219.029198335503[/C][/ROW]
[ROW][C]51[/C][C]2320[/C][C]2222.09146040843[/C][C]97.9085395915749[/C][/ROW]
[ROW][C]52[/C][C]2180[/C][C]2124.73316908889[/C][C]55.2668309111073[/C][/ROW]
[ROW][C]53[/C][C]2120[/C][C]2185.65772723671[/C][C]-65.6577272367135[/C][/ROW]
[ROW][C]54[/C][C]2460[/C][C]2444.4593072305[/C][C]15.5406927694994[/C][/ROW]
[ROW][C]55[/C][C]2140[/C][C]1848.68312734158[/C][C]291.316872658423[/C][/ROW]
[ROW][C]56[/C][C]2480[/C][C]2469.27340219349[/C][C]10.7265978065116[/C][/ROW]
[ROW][C]57[/C][C]2100[/C][C]1954.22840767499[/C][C]145.771592325013[/C][/ROW]
[ROW][C]58[/C][C]2700[/C][C]2536.32228574824[/C][C]163.677714251759[/C][/ROW]
[ROW][C]59[/C][C]2200[/C][C]2280.39867371078[/C][C]-80.3986737107839[/C][/ROW]
[ROW][C]60[/C][C]2260[/C][C]2323.01181135031[/C][C]-63.0118113503113[/C][/ROW]
[ROW][C]61[/C][C]2340[/C][C]2324.71417857576[/C][C]15.2858214242351[/C][/ROW]
[ROW][C]62[/C][C]2720[/C][C]2446.18482196431[/C][C]273.815178035692[/C][/ROW]
[ROW][C]63[/C][C]2300[/C][C]2329.44915101345[/C][C]-29.4491510134471[/C][/ROW]
[ROW][C]64[/C][C]2360[/C][C]2190.44069563007[/C][C]169.55930436993[/C][/ROW]
[ROW][C]65[/C][C]2020[/C][C]2133.91360545637[/C][C]-113.913605456372[/C][/ROW]
[ROW][C]66[/C][C]2380[/C][C]2477.77497001961[/C][C]-97.7749700196055[/C][/ROW]
[ROW][C]67[/C][C]2000[/C][C]2154.76669680155[/C][C]-154.766696801554[/C][/ROW]
[ROW][C]68[/C][C]2540[/C][C]2496.60489902085[/C][C]43.3951009791458[/C][/ROW]
[ROW][C]69[/C][C]1980[/C][C]2113.95612686743[/C][C]-133.956126867433[/C][/ROW]
[ROW][C]70[/C][C]2940[/C][C]2715.58010192006[/C][C]224.419898079943[/C][/ROW]
[ROW][C]71[/C][C]2260[/C][C]2214.26744612172[/C][C]45.7325538782775[/C][/ROW]
[ROW][C]72[/C][C]2300[/C][C]2275.63007037828[/C][C]24.3699296217164[/C][/ROW]
[ROW][C]73[/C][C]2300[/C][C]2356.79643478247[/C][C]-56.7964347824736[/C][/ROW]
[ROW][C]74[/C][C]2820[/C][C]2737.61499405615[/C][C]82.3850059438487[/C][/ROW]
[ROW][C]75[/C][C]2380[/C][C]2315.33605089354[/C][C]64.6639491064643[/C][/ROW]
[ROW][C]76[/C][C]2360[/C][C]2375.09029755361[/C][C]-15.090297553606[/C][/ROW]
[ROW][C]77[/C][C]1980[/C][C]2033.1167340484[/C][C]-53.1167340484049[/C][/ROW]
[ROW][C]78[/C][C]2340[/C][C]2395.36815261024[/C][C]-55.3681526102391[/C][/ROW]
[ROW][C]79[/C][C]2160[/C][C]2013.37641147782[/C][C]146.623588522181[/C][/ROW]
[ROW][C]80[/C][C]2700[/C][C]2558.70048917066[/C][C]141.299510829342[/C][/ROW]
[ROW][C]81[/C][C]1920[/C][C]1996.90550179448[/C][C]-76.9055017944768[/C][/ROW]
[ROW][C]82[/C][C]2980[/C][C]2964.33641593204[/C][C]15.6635840679633[/C][/ROW]
[ROW][C]83[/C][C]2240[/C][C]2279.13331335627[/C][C]-39.1333133562739[/C][/ROW]
[ROW][C]84[/C][C]2180[/C][C]2319.48226595812[/C][C]-139.482265958115[/C][/ROW]
[ROW][C]85[/C][C]2440[/C][C]2318.92188321346[/C][C]121.078116786539[/C][/ROW]
[ROW][C]86[/C][C]2740[/C][C]2844.13988437373[/C][C]-104.13988437373[/C][/ROW]
[ROW][C]87[/C][C]2360[/C][C]2399.43043500578[/C][C]-39.4304350057751[/C][/ROW]
[ROW][C]88[/C][C]2380[/C][C]2378.8487966184[/C][C]1.15120338160341[/C][/ROW]
[ROW][C]89[/C][C]2000[/C][C]1995.95670590119[/C][C]4.04329409880916[/C][/ROW]
[ROW][C]90[/C][C]2500[/C][C]2359.18827699578[/C][C]140.811723004221[/C][/ROW]
[ROW][C]91[/C][C]2180[/C][C]2177.994445887[/C][C]2.0055541129982[/C][/ROW]
[ROW][C]92[/C][C]2740[/C][C]2721.60881448857[/C][C]18.391185511432[/C][/ROW]
[ROW][C]93[/C][C]1960[/C][C]1935.67955559582[/C][C]24.3204444041805[/C][/ROW]
[ROW][C]94[/C][C]3060[/C][C]3004.53416049764[/C][C]55.465839502358[/C][/ROW]
[ROW][C]95[/C][C]2300[/C][C]2259.07132356216[/C][C]40.9286764378385[/C][/ROW]
[ROW][C]96[/C][C]2240[/C][C]2199.97053116764[/C][C]40.0294688323593[/C][/ROW]
[ROW][C]97[/C][C]2580[/C][C]2462.73972692774[/C][C]117.260273072261[/C][/ROW]
[ROW][C]98[/C][C]2740[/C][C]2767.97090930031[/C][C]-27.9709093003144[/C][/ROW]
[ROW][C]99[/C][C]2260[/C][C]2385.20655271317[/C][C]-125.206552713165[/C][/ROW]
[ROW][C]100[/C][C]2400[/C][C]2405.41618635118[/C][C]-5.41618635117538[/C][/ROW]
[ROW][C]101[/C][C]1820[/C][C]2021.95179058215[/C][C]-201.951790582153[/C][/ROW]
[ROW][C]102[/C][C]2440[/C][C]2525.02879360445[/C][C]-85.0287936044497[/C][/ROW]
[ROW][C]103[/C][C]2080[/C][C]2200.8718420793[/C][C]-120.871842079305[/C][/ROW]
[ROW][C]104[/C][C]2680[/C][C]2764.14504271822[/C][C]-84.1450427182172[/C][/ROW]
[ROW][C]105[/C][C]1900[/C][C]1975.80707169735[/C][C]-75.8070716973502[/C][/ROW]
[ROW][C]106[/C][C]3000[/C][C]3081.69736849845[/C][C]-81.6973684984514[/C][/ROW]
[ROW][C]107[/C][C]2240[/C][C]2313.96062175932[/C][C]-73.9606217593241[/C][/ROW]
[ROW][C]108[/C][C]2300[/C][C]2250.92561927898[/C][C]49.0743807210201[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=210855&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=210855&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
1323602381.05987486467-21.0598748646744
1421602180.476957968-20.476957967996
1523802395.10664181067-15.1066418106684
1622802285.71689453454-5.71689453453973
1723202317.005330169262.99466983073808
1824002403.43853612701-3.4385361270115
1919602132.65485182856-172.654851828559
2025202387.02521543823132.974784561773
2122002170.7742545894329.2257454105693
2224202253.39992842702166.600071572983
2323002280.135852010319.8641479896974
2422802481.23081389417-201.230813894168
2522202344.7008480563-124.700848056302
2622402144.9195908334395.0804091665677
2722002363.93629052775-163.936290527747
2823402263.089497204176.9105027959049
2922402302.90388349635-62.9038834963458
3025002381.37163861337118.628361386625
3118201946.18977096798-126.189770967976
3225202500.244163996819.7558360031994
3321802182.28213638723-2.28213638722946
3424802398.8589635460281.1410364539815
3522602279.50609342375-19.5060934237517
3624002259.84578174065140.154218259347
3722402201.9873185847538.0126814152522
3822402221.9156945731418.0843054268589
3922402183.5312431075556.468756892451
4021402323.2317187126-183.231718712599
4122002223.37071440498-23.3707144049763
4224602480.77639050381-20.776390503805
4318601806.5451985923353.4548014076681
4424802502.22905290481-22.2290529048123
4519602164.87202542108-204.872025421077
4625402460.5832296722979.4167703277126
4722802242.6496280492737.350371950733
4823202380.82774351284-60.8277435128384
4923202220.906346396799.0936536032959
5024402220.9708016645219.029198335503
5123202222.0914604084397.9085395915749
5221802124.7331690888955.2668309111073
5321202185.65772723671-65.6577272367135
5424602444.459307230515.5406927694994
5521401848.68312734158291.316872658423
5624802469.2734021934910.7265978065116
5721001954.22840767499145.771592325013
5827002536.32228574824163.677714251759
5922002280.39867371078-80.3986737107839
6022602323.01181135031-63.0118113503113
6123402324.7141785757615.2858214242351
6227202446.18482196431273.815178035692
6323002329.44915101345-29.4491510134471
6423602190.44069563007169.55930436993
6520202133.91360545637-113.913605456372
6623802477.77497001961-97.7749700196055
6720002154.76669680155-154.766696801554
6825402496.6048990208543.3951009791458
6919802113.95612686743-133.956126867433
7029402715.58010192006224.419898079943
7122602214.2674461217245.7325538782775
7223002275.6300703782824.3699296217164
7323002356.79643478247-56.7964347824736
7428202737.6149940561582.3850059438487
7523802315.3360508935464.6639491064643
7623602375.09029755361-15.090297553606
7719802033.1167340484-53.1167340484049
7823402395.36815261024-55.3681526102391
7921602013.37641147782146.623588522181
8027002558.70048917066141.299510829342
8119201996.90550179448-76.9055017944768
8229802964.3364159320415.6635840679633
8322402279.13331335627-39.1333133562739
8421802319.48226595812-139.482265958115
8524402318.92188321346121.078116786539
8627402844.13988437373-104.13988437373
8723602399.43043500578-39.4304350057751
8823802378.84879661841.15120338160341
8920001995.956705901194.04329409880916
9025002359.18827699578140.811723004221
9121802177.9944458872.0055541129982
9227402721.6088144885718.391185511432
9319601935.6795555958224.3204444041805
9430603004.5341604976455.465839502358
9523002259.0713235621640.9286764378385
9622402199.9705311676440.0294688323593
9725802462.73972692774117.260273072261
9827402767.97090930031-27.9709093003144
9922602385.20655271317-125.206552713165
10024002405.41618635118-5.41618635117538
10118202021.95179058215-201.951790582153
10224402525.02879360445-85.0287936044497
10320802200.8718420793-120.871842079305
10426802764.14504271822-84.1450427182172
10519001975.80707169735-75.8070716973502
10630003081.69736849845-81.6973684984514
10722402313.96062175932-73.9606217593241
10823002250.9256192789849.0743807210201







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
1092589.932328894192385.218545663462794.64611212492
1102747.992400893652543.269317106072952.71548468123
1112265.149487712592060.419299179122469.87967624607
1122403.534681566622198.782279728262608.28708340498
1131822.335777393471617.583572572162027.08798221478
1142442.335350284732237.506677985162647.1640225843
1152081.781541044361876.943726086182286.61935600253
1162682.023347635422477.01507908562887.03161618524
1171901.495154540911696.580304917092106.41000416474
1183002.552586838082797.169620791183207.93555288498
1192242.289223429222037.095247205222447.48319965321
1202302.176240754911202.778660911433401.57382059839

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
109 & 2589.93232889419 & 2385.21854566346 & 2794.64611212492 \tabularnewline
110 & 2747.99240089365 & 2543.26931710607 & 2952.71548468123 \tabularnewline
111 & 2265.14948771259 & 2060.41929917912 & 2469.87967624607 \tabularnewline
112 & 2403.53468156662 & 2198.78227972826 & 2608.28708340498 \tabularnewline
113 & 1822.33577739347 & 1617.58357257216 & 2027.08798221478 \tabularnewline
114 & 2442.33535028473 & 2237.50667798516 & 2647.1640225843 \tabularnewline
115 & 2081.78154104436 & 1876.94372608618 & 2286.61935600253 \tabularnewline
116 & 2682.02334763542 & 2477.0150790856 & 2887.03161618524 \tabularnewline
117 & 1901.49515454091 & 1696.58030491709 & 2106.41000416474 \tabularnewline
118 & 3002.55258683808 & 2797.16962079118 & 3207.93555288498 \tabularnewline
119 & 2242.28922342922 & 2037.09524720522 & 2447.48319965321 \tabularnewline
120 & 2302.17624075491 & 1202.77866091143 & 3401.57382059839 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=210855&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]2589.93232889419[/C][C]2385.21854566346[/C][C]2794.64611212492[/C][/ROW]
[ROW][C]110[/C][C]2747.99240089365[/C][C]2543.26931710607[/C][C]2952.71548468123[/C][/ROW]
[ROW][C]111[/C][C]2265.14948771259[/C][C]2060.41929917912[/C][C]2469.87967624607[/C][/ROW]
[ROW][C]112[/C][C]2403.53468156662[/C][C]2198.78227972826[/C][C]2608.28708340498[/C][/ROW]
[ROW][C]113[/C][C]1822.33577739347[/C][C]1617.58357257216[/C][C]2027.08798221478[/C][/ROW]
[ROW][C]114[/C][C]2442.33535028473[/C][C]2237.50667798516[/C][C]2647.1640225843[/C][/ROW]
[ROW][C]115[/C][C]2081.78154104436[/C][C]1876.94372608618[/C][C]2286.61935600253[/C][/ROW]
[ROW][C]116[/C][C]2682.02334763542[/C][C]2477.0150790856[/C][C]2887.03161618524[/C][/ROW]
[ROW][C]117[/C][C]1901.49515454091[/C][C]1696.58030491709[/C][C]2106.41000416474[/C][/ROW]
[ROW][C]118[/C][C]3002.55258683808[/C][C]2797.16962079118[/C][C]3207.93555288498[/C][/ROW]
[ROW][C]119[/C][C]2242.28922342922[/C][C]2037.09524720522[/C][C]2447.48319965321[/C][/ROW]
[ROW][C]120[/C][C]2302.17624075491[/C][C]1202.77866091143[/C][C]3401.57382059839[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=210855&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=210855&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
1092589.932328894192385.218545663462794.64611212492
1102747.992400893652543.269317106072952.71548468123
1112265.149487712592060.419299179122469.87967624607
1122403.534681566622198.782279728262608.28708340498
1131822.335777393471617.583572572162027.08798221478
1142442.335350284732237.506677985162647.1640225843
1152081.781541044361876.943726086182286.61935600253
1162682.023347635422477.01507908562887.03161618524
1171901.495154540911696.580304917092106.41000416474
1183002.552586838082797.169620791183207.93555288498
1192242.289223429222037.095247205222447.48319965321
1202302.176240754911202.778660911433401.57382059839



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