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Author's title

Author*The author of this computation has been verified*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationFri, 16 Dec 2016 16:09:36 +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/16/t1481901046uo66rq0xykp2rmv.htm/, Retrieved Thu, 02 May 2024 18:48:37 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=300344, Retrieved Thu, 02 May 2024 18:48:37 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact58
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [] [2016-12-16 15:09:36] [1a4fa2544711480e714211476e711237] [Current]
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Dataseries X:
1100
680
860
440
1480
1620
1240
1440
1540
860
1180
1180
1480
940
1300
860
1220
2180
940
920
2060
1160
980
1020
740
720
1340
1140
1200
1900
1020
2140
2020
1340
1400
2320
1280
1160
2120
1540
2400
1420
1480
3380
1880
2200
1980
1340
1960
1340
3300
1780
2040
4460
800
1420
1960
1940
1880
940
1880
720
1660
4260
2540
2320
2860
5880
3140
4440
3600
2920
2260
3740
3380
4560
3320
4760
4000
4840
6160
3440
3280
2000
3600
4320
3480
5620
4200
8540
3800
5380
5140
2720
3120
3440
5020
5800
2260
5800
5660
4880
3440
5900
5960
5520
5920
3840




Summary of computational transaction
Raw Input view raw input (R code)
Raw Outputview raw output of R engine
Computing time2 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 time2 seconds \tabularnewline
R ServerBig Analytics Cloud Computing Center \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=300344&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]2 seconds[/C][/ROW] [ROW]R Server[/C]Big Analytics Cloud Computing Center[/C][/ROW] [/TABLE] Source: https://freestatistics.org/blog/index.php?pk=300344&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=300344&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 time2 seconds
R ServerBig Analytics Cloud Computing Center







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.0972409779681732
beta0.0213076495618894
gamma0.236568574865812

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.0972409779681732 \tabularnewline
beta & 0.0213076495618894 \tabularnewline
gamma & 0.236568574865812 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=300344&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]0.0972409779681732[/C][/ROW]
[ROW][C]beta[/C][C]0.0213076495618894[/C][/ROW]
[ROW][C]gamma[/C][C]0.236568574865812[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=300344&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=300344&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
alpha0.0972409779681732
beta0.0213076495618894
gamma0.236568574865812







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
1314801329.37141169351150.628588306491
14940883.84637846631156.1536215336895
1513001239.2645247823560.735475217652
16860807.72561486891552.2743851310852
1712201158.0901408126261.9098591873837
1821802121.0039606058858.9960393941237
199401336.35089472584-396.350894725843
209201483.58055065506-563.580550655063
2120601500.88592098162559.114079018379
221160849.42587606807310.57412393193
239801209.49322017473-229.493220174725
2410201183.86028333101-163.86028333101
257401497.46965111504-757.469651115044
26720925.434163697482-205.434163697482
2713401255.6458688100484.3541311899617
281140821.075975517805318.924024482195
2912001209.66527682724-9.66527682723881
3019002187.52859194977-287.528591949772
3110201259.04820703788-239.048207037875
3221401382.00609865566757.993901344345
3320201797.93243113462222.067568865383
341340992.092992670004347.907007329996
3514001257.07761076383142.922389236168
3623201282.408124938861037.59187506114
3712801622.66206423328-342.662064233282
3811601110.8276438073549.1723561926542
3921201652.40674390866467.593256091336
4015401177.15573686727362.844263132732
4124001594.40617776931805.593822230688
4214202954.06624981273-1534.06624981273
4314801617.07526152777-137.075261527774
4433802083.574704540081296.42529545992
4518802525.62976027258-645.629760272585
4622001405.92945584594794.070544154063
4719801738.53440481441241.465595185589
4813402018.01641243512-678.016412435118
4919601883.5351563500776.4648436499303
5013401399.45610534793-59.4561053479267
5133002166.550297711161133.44970228884
5217801587.42729950716192.572700492841
5320402190.73046804201-150.730468042014
5444603077.195147320571382.80485267943
558002060.37733403948-1260.37733403948
5614202886.86933070075-1466.86933070075
5719602628.64085000687-668.640850006869
5819401725.71410769935214.285892300654
5918801888.11076207318-8.11076207318456
609401941.04275601125-1001.04275601125
6118801934.27537786983-54.2753778698263
627201399.64185477641-679.641854776409
6316602308.40272768167-648.402727681672
6442601445.953671581852814.04632841815
6525402250.26982295134289.730177048656
6623203567.56962055611-1247.56962055611
6728601740.067374260851119.93262573915
6858802832.709861647563047.29013835244
6931403200.04644602982-60.0464460298181
7044402341.06458311482098.9354168852
7136002685.82071382305914.179286176949
7229202532.59386404833387.406135951675
7322603043.44106281481-783.441062814809
7437401937.009104503331802.99089549667
7533803869.74208063786-489.742080637857
7645603558.802739804211001.19726019579
7733203652.57391116071-332.573911160706
7847605105.63614351796-345.636143517958
7940003144.05516455989855.944835440108
8048405301.48181950371-461.48181950371
8161604437.118357297021722.88164270298
8234403990.96045306335-550.960453063345
8332803782.53570167609-502.535701676093
8420003285.69046420352-1285.69046420352
8536003418.66291731183181.337082688175
8643202809.356306287611510.64369371239
8734804451.92508769923-971.925087699229
8856204411.439007142691208.56099285731
8942004187.1266520268712.8733479731263
9085405933.071264748322606.92873525168
9138004111.2736565443-311.273656544302
9253806222.22694766372-842.226947663725
9351405700.85011128812-560.850111288119
9427204391.49909258838-1671.49909258838
9531204061.86718455345-941.867184553447
9634403279.95023123117160.049768768827
9750203943.875190640661076.12480935934
9858003627.754104973922172.24589502608
9922604961.36003353438-2701.36003353438
10058005274.45062518772525.549374812282
10156604655.951809893751004.04819010625
10248807328.65560319804-2448.65560319804
10334404245.26101006669-805.261010066685
10459006257.74915711116-357.749157111162
10559605815.57367297738144.426327022625
10655204234.704140547381285.29585945262
10759204338.723796975531581.27620302447
10838403950.11271787407-110.112717874072

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 1480 & 1329.37141169351 & 150.628588306491 \tabularnewline
14 & 940 & 883.846378466311 & 56.1536215336895 \tabularnewline
15 & 1300 & 1239.26452478235 & 60.735475217652 \tabularnewline
16 & 860 & 807.725614868915 & 52.2743851310852 \tabularnewline
17 & 1220 & 1158.09014081262 & 61.9098591873837 \tabularnewline
18 & 2180 & 2121.00396060588 & 58.9960393941237 \tabularnewline
19 & 940 & 1336.35089472584 & -396.350894725843 \tabularnewline
20 & 920 & 1483.58055065506 & -563.580550655063 \tabularnewline
21 & 2060 & 1500.88592098162 & 559.114079018379 \tabularnewline
22 & 1160 & 849.42587606807 & 310.57412393193 \tabularnewline
23 & 980 & 1209.49322017473 & -229.493220174725 \tabularnewline
24 & 1020 & 1183.86028333101 & -163.86028333101 \tabularnewline
25 & 740 & 1497.46965111504 & -757.469651115044 \tabularnewline
26 & 720 & 925.434163697482 & -205.434163697482 \tabularnewline
27 & 1340 & 1255.64586881004 & 84.3541311899617 \tabularnewline
28 & 1140 & 821.075975517805 & 318.924024482195 \tabularnewline
29 & 1200 & 1209.66527682724 & -9.66527682723881 \tabularnewline
30 & 1900 & 2187.52859194977 & -287.528591949772 \tabularnewline
31 & 1020 & 1259.04820703788 & -239.048207037875 \tabularnewline
32 & 2140 & 1382.00609865566 & 757.993901344345 \tabularnewline
33 & 2020 & 1797.93243113462 & 222.067568865383 \tabularnewline
34 & 1340 & 992.092992670004 & 347.907007329996 \tabularnewline
35 & 1400 & 1257.07761076383 & 142.922389236168 \tabularnewline
36 & 2320 & 1282.40812493886 & 1037.59187506114 \tabularnewline
37 & 1280 & 1622.66206423328 & -342.662064233282 \tabularnewline
38 & 1160 & 1110.82764380735 & 49.1723561926542 \tabularnewline
39 & 2120 & 1652.40674390866 & 467.593256091336 \tabularnewline
40 & 1540 & 1177.15573686727 & 362.844263132732 \tabularnewline
41 & 2400 & 1594.40617776931 & 805.593822230688 \tabularnewline
42 & 1420 & 2954.06624981273 & -1534.06624981273 \tabularnewline
43 & 1480 & 1617.07526152777 & -137.075261527774 \tabularnewline
44 & 3380 & 2083.57470454008 & 1296.42529545992 \tabularnewline
45 & 1880 & 2525.62976027258 & -645.629760272585 \tabularnewline
46 & 2200 & 1405.92945584594 & 794.070544154063 \tabularnewline
47 & 1980 & 1738.53440481441 & 241.465595185589 \tabularnewline
48 & 1340 & 2018.01641243512 & -678.016412435118 \tabularnewline
49 & 1960 & 1883.53515635007 & 76.4648436499303 \tabularnewline
50 & 1340 & 1399.45610534793 & -59.4561053479267 \tabularnewline
51 & 3300 & 2166.55029771116 & 1133.44970228884 \tabularnewline
52 & 1780 & 1587.42729950716 & 192.572700492841 \tabularnewline
53 & 2040 & 2190.73046804201 & -150.730468042014 \tabularnewline
54 & 4460 & 3077.19514732057 & 1382.80485267943 \tabularnewline
55 & 800 & 2060.37733403948 & -1260.37733403948 \tabularnewline
56 & 1420 & 2886.86933070075 & -1466.86933070075 \tabularnewline
57 & 1960 & 2628.64085000687 & -668.640850006869 \tabularnewline
58 & 1940 & 1725.71410769935 & 214.285892300654 \tabularnewline
59 & 1880 & 1888.11076207318 & -8.11076207318456 \tabularnewline
60 & 940 & 1941.04275601125 & -1001.04275601125 \tabularnewline
61 & 1880 & 1934.27537786983 & -54.2753778698263 \tabularnewline
62 & 720 & 1399.64185477641 & -679.641854776409 \tabularnewline
63 & 1660 & 2308.40272768167 & -648.402727681672 \tabularnewline
64 & 4260 & 1445.95367158185 & 2814.04632841815 \tabularnewline
65 & 2540 & 2250.26982295134 & 289.730177048656 \tabularnewline
66 & 2320 & 3567.56962055611 & -1247.56962055611 \tabularnewline
67 & 2860 & 1740.06737426085 & 1119.93262573915 \tabularnewline
68 & 5880 & 2832.70986164756 & 3047.29013835244 \tabularnewline
69 & 3140 & 3200.04644602982 & -60.0464460298181 \tabularnewline
70 & 4440 & 2341.0645831148 & 2098.9354168852 \tabularnewline
71 & 3600 & 2685.82071382305 & 914.179286176949 \tabularnewline
72 & 2920 & 2532.59386404833 & 387.406135951675 \tabularnewline
73 & 2260 & 3043.44106281481 & -783.441062814809 \tabularnewline
74 & 3740 & 1937.00910450333 & 1802.99089549667 \tabularnewline
75 & 3380 & 3869.74208063786 & -489.742080637857 \tabularnewline
76 & 4560 & 3558.80273980421 & 1001.19726019579 \tabularnewline
77 & 3320 & 3652.57391116071 & -332.573911160706 \tabularnewline
78 & 4760 & 5105.63614351796 & -345.636143517958 \tabularnewline
79 & 4000 & 3144.05516455989 & 855.944835440108 \tabularnewline
80 & 4840 & 5301.48181950371 & -461.48181950371 \tabularnewline
81 & 6160 & 4437.11835729702 & 1722.88164270298 \tabularnewline
82 & 3440 & 3990.96045306335 & -550.960453063345 \tabularnewline
83 & 3280 & 3782.53570167609 & -502.535701676093 \tabularnewline
84 & 2000 & 3285.69046420352 & -1285.69046420352 \tabularnewline
85 & 3600 & 3418.66291731183 & 181.337082688175 \tabularnewline
86 & 4320 & 2809.35630628761 & 1510.64369371239 \tabularnewline
87 & 3480 & 4451.92508769923 & -971.925087699229 \tabularnewline
88 & 5620 & 4411.43900714269 & 1208.56099285731 \tabularnewline
89 & 4200 & 4187.12665202687 & 12.8733479731263 \tabularnewline
90 & 8540 & 5933.07126474832 & 2606.92873525168 \tabularnewline
91 & 3800 & 4111.2736565443 & -311.273656544302 \tabularnewline
92 & 5380 & 6222.22694766372 & -842.226947663725 \tabularnewline
93 & 5140 & 5700.85011128812 & -560.850111288119 \tabularnewline
94 & 2720 & 4391.49909258838 & -1671.49909258838 \tabularnewline
95 & 3120 & 4061.86718455345 & -941.867184553447 \tabularnewline
96 & 3440 & 3279.95023123117 & 160.049768768827 \tabularnewline
97 & 5020 & 3943.87519064066 & 1076.12480935934 \tabularnewline
98 & 5800 & 3627.75410497392 & 2172.24589502608 \tabularnewline
99 & 2260 & 4961.36003353438 & -2701.36003353438 \tabularnewline
100 & 5800 & 5274.45062518772 & 525.549374812282 \tabularnewline
101 & 5660 & 4655.95180989375 & 1004.04819010625 \tabularnewline
102 & 4880 & 7328.65560319804 & -2448.65560319804 \tabularnewline
103 & 3440 & 4245.26101006669 & -805.261010066685 \tabularnewline
104 & 5900 & 6257.74915711116 & -357.749157111162 \tabularnewline
105 & 5960 & 5815.57367297738 & 144.426327022625 \tabularnewline
106 & 5520 & 4234.70414054738 & 1285.29585945262 \tabularnewline
107 & 5920 & 4338.72379697553 & 1581.27620302447 \tabularnewline
108 & 3840 & 3950.11271787407 & -110.112717874072 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=300344&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]1480[/C][C]1329.37141169351[/C][C]150.628588306491[/C][/ROW]
[ROW][C]14[/C][C]940[/C][C]883.846378466311[/C][C]56.1536215336895[/C][/ROW]
[ROW][C]15[/C][C]1300[/C][C]1239.26452478235[/C][C]60.735475217652[/C][/ROW]
[ROW][C]16[/C][C]860[/C][C]807.725614868915[/C][C]52.2743851310852[/C][/ROW]
[ROW][C]17[/C][C]1220[/C][C]1158.09014081262[/C][C]61.9098591873837[/C][/ROW]
[ROW][C]18[/C][C]2180[/C][C]2121.00396060588[/C][C]58.9960393941237[/C][/ROW]
[ROW][C]19[/C][C]940[/C][C]1336.35089472584[/C][C]-396.350894725843[/C][/ROW]
[ROW][C]20[/C][C]920[/C][C]1483.58055065506[/C][C]-563.580550655063[/C][/ROW]
[ROW][C]21[/C][C]2060[/C][C]1500.88592098162[/C][C]559.114079018379[/C][/ROW]
[ROW][C]22[/C][C]1160[/C][C]849.42587606807[/C][C]310.57412393193[/C][/ROW]
[ROW][C]23[/C][C]980[/C][C]1209.49322017473[/C][C]-229.493220174725[/C][/ROW]
[ROW][C]24[/C][C]1020[/C][C]1183.86028333101[/C][C]-163.86028333101[/C][/ROW]
[ROW][C]25[/C][C]740[/C][C]1497.46965111504[/C][C]-757.469651115044[/C][/ROW]
[ROW][C]26[/C][C]720[/C][C]925.434163697482[/C][C]-205.434163697482[/C][/ROW]
[ROW][C]27[/C][C]1340[/C][C]1255.64586881004[/C][C]84.3541311899617[/C][/ROW]
[ROW][C]28[/C][C]1140[/C][C]821.075975517805[/C][C]318.924024482195[/C][/ROW]
[ROW][C]29[/C][C]1200[/C][C]1209.66527682724[/C][C]-9.66527682723881[/C][/ROW]
[ROW][C]30[/C][C]1900[/C][C]2187.52859194977[/C][C]-287.528591949772[/C][/ROW]
[ROW][C]31[/C][C]1020[/C][C]1259.04820703788[/C][C]-239.048207037875[/C][/ROW]
[ROW][C]32[/C][C]2140[/C][C]1382.00609865566[/C][C]757.993901344345[/C][/ROW]
[ROW][C]33[/C][C]2020[/C][C]1797.93243113462[/C][C]222.067568865383[/C][/ROW]
[ROW][C]34[/C][C]1340[/C][C]992.092992670004[/C][C]347.907007329996[/C][/ROW]
[ROW][C]35[/C][C]1400[/C][C]1257.07761076383[/C][C]142.922389236168[/C][/ROW]
[ROW][C]36[/C][C]2320[/C][C]1282.40812493886[/C][C]1037.59187506114[/C][/ROW]
[ROW][C]37[/C][C]1280[/C][C]1622.66206423328[/C][C]-342.662064233282[/C][/ROW]
[ROW][C]38[/C][C]1160[/C][C]1110.82764380735[/C][C]49.1723561926542[/C][/ROW]
[ROW][C]39[/C][C]2120[/C][C]1652.40674390866[/C][C]467.593256091336[/C][/ROW]
[ROW][C]40[/C][C]1540[/C][C]1177.15573686727[/C][C]362.844263132732[/C][/ROW]
[ROW][C]41[/C][C]2400[/C][C]1594.40617776931[/C][C]805.593822230688[/C][/ROW]
[ROW][C]42[/C][C]1420[/C][C]2954.06624981273[/C][C]-1534.06624981273[/C][/ROW]
[ROW][C]43[/C][C]1480[/C][C]1617.07526152777[/C][C]-137.075261527774[/C][/ROW]
[ROW][C]44[/C][C]3380[/C][C]2083.57470454008[/C][C]1296.42529545992[/C][/ROW]
[ROW][C]45[/C][C]1880[/C][C]2525.62976027258[/C][C]-645.629760272585[/C][/ROW]
[ROW][C]46[/C][C]2200[/C][C]1405.92945584594[/C][C]794.070544154063[/C][/ROW]
[ROW][C]47[/C][C]1980[/C][C]1738.53440481441[/C][C]241.465595185589[/C][/ROW]
[ROW][C]48[/C][C]1340[/C][C]2018.01641243512[/C][C]-678.016412435118[/C][/ROW]
[ROW][C]49[/C][C]1960[/C][C]1883.53515635007[/C][C]76.4648436499303[/C][/ROW]
[ROW][C]50[/C][C]1340[/C][C]1399.45610534793[/C][C]-59.4561053479267[/C][/ROW]
[ROW][C]51[/C][C]3300[/C][C]2166.55029771116[/C][C]1133.44970228884[/C][/ROW]
[ROW][C]52[/C][C]1780[/C][C]1587.42729950716[/C][C]192.572700492841[/C][/ROW]
[ROW][C]53[/C][C]2040[/C][C]2190.73046804201[/C][C]-150.730468042014[/C][/ROW]
[ROW][C]54[/C][C]4460[/C][C]3077.19514732057[/C][C]1382.80485267943[/C][/ROW]
[ROW][C]55[/C][C]800[/C][C]2060.37733403948[/C][C]-1260.37733403948[/C][/ROW]
[ROW][C]56[/C][C]1420[/C][C]2886.86933070075[/C][C]-1466.86933070075[/C][/ROW]
[ROW][C]57[/C][C]1960[/C][C]2628.64085000687[/C][C]-668.640850006869[/C][/ROW]
[ROW][C]58[/C][C]1940[/C][C]1725.71410769935[/C][C]214.285892300654[/C][/ROW]
[ROW][C]59[/C][C]1880[/C][C]1888.11076207318[/C][C]-8.11076207318456[/C][/ROW]
[ROW][C]60[/C][C]940[/C][C]1941.04275601125[/C][C]-1001.04275601125[/C][/ROW]
[ROW][C]61[/C][C]1880[/C][C]1934.27537786983[/C][C]-54.2753778698263[/C][/ROW]
[ROW][C]62[/C][C]720[/C][C]1399.64185477641[/C][C]-679.641854776409[/C][/ROW]
[ROW][C]63[/C][C]1660[/C][C]2308.40272768167[/C][C]-648.402727681672[/C][/ROW]
[ROW][C]64[/C][C]4260[/C][C]1445.95367158185[/C][C]2814.04632841815[/C][/ROW]
[ROW][C]65[/C][C]2540[/C][C]2250.26982295134[/C][C]289.730177048656[/C][/ROW]
[ROW][C]66[/C][C]2320[/C][C]3567.56962055611[/C][C]-1247.56962055611[/C][/ROW]
[ROW][C]67[/C][C]2860[/C][C]1740.06737426085[/C][C]1119.93262573915[/C][/ROW]
[ROW][C]68[/C][C]5880[/C][C]2832.70986164756[/C][C]3047.29013835244[/C][/ROW]
[ROW][C]69[/C][C]3140[/C][C]3200.04644602982[/C][C]-60.0464460298181[/C][/ROW]
[ROW][C]70[/C][C]4440[/C][C]2341.0645831148[/C][C]2098.9354168852[/C][/ROW]
[ROW][C]71[/C][C]3600[/C][C]2685.82071382305[/C][C]914.179286176949[/C][/ROW]
[ROW][C]72[/C][C]2920[/C][C]2532.59386404833[/C][C]387.406135951675[/C][/ROW]
[ROW][C]73[/C][C]2260[/C][C]3043.44106281481[/C][C]-783.441062814809[/C][/ROW]
[ROW][C]74[/C][C]3740[/C][C]1937.00910450333[/C][C]1802.99089549667[/C][/ROW]
[ROW][C]75[/C][C]3380[/C][C]3869.74208063786[/C][C]-489.742080637857[/C][/ROW]
[ROW][C]76[/C][C]4560[/C][C]3558.80273980421[/C][C]1001.19726019579[/C][/ROW]
[ROW][C]77[/C][C]3320[/C][C]3652.57391116071[/C][C]-332.573911160706[/C][/ROW]
[ROW][C]78[/C][C]4760[/C][C]5105.63614351796[/C][C]-345.636143517958[/C][/ROW]
[ROW][C]79[/C][C]4000[/C][C]3144.05516455989[/C][C]855.944835440108[/C][/ROW]
[ROW][C]80[/C][C]4840[/C][C]5301.48181950371[/C][C]-461.48181950371[/C][/ROW]
[ROW][C]81[/C][C]6160[/C][C]4437.11835729702[/C][C]1722.88164270298[/C][/ROW]
[ROW][C]82[/C][C]3440[/C][C]3990.96045306335[/C][C]-550.960453063345[/C][/ROW]
[ROW][C]83[/C][C]3280[/C][C]3782.53570167609[/C][C]-502.535701676093[/C][/ROW]
[ROW][C]84[/C][C]2000[/C][C]3285.69046420352[/C][C]-1285.69046420352[/C][/ROW]
[ROW][C]85[/C][C]3600[/C][C]3418.66291731183[/C][C]181.337082688175[/C][/ROW]
[ROW][C]86[/C][C]4320[/C][C]2809.35630628761[/C][C]1510.64369371239[/C][/ROW]
[ROW][C]87[/C][C]3480[/C][C]4451.92508769923[/C][C]-971.925087699229[/C][/ROW]
[ROW][C]88[/C][C]5620[/C][C]4411.43900714269[/C][C]1208.56099285731[/C][/ROW]
[ROW][C]89[/C][C]4200[/C][C]4187.12665202687[/C][C]12.8733479731263[/C][/ROW]
[ROW][C]90[/C][C]8540[/C][C]5933.07126474832[/C][C]2606.92873525168[/C][/ROW]
[ROW][C]91[/C][C]3800[/C][C]4111.2736565443[/C][C]-311.273656544302[/C][/ROW]
[ROW][C]92[/C][C]5380[/C][C]6222.22694766372[/C][C]-842.226947663725[/C][/ROW]
[ROW][C]93[/C][C]5140[/C][C]5700.85011128812[/C][C]-560.850111288119[/C][/ROW]
[ROW][C]94[/C][C]2720[/C][C]4391.49909258838[/C][C]-1671.49909258838[/C][/ROW]
[ROW][C]95[/C][C]3120[/C][C]4061.86718455345[/C][C]-941.867184553447[/C][/ROW]
[ROW][C]96[/C][C]3440[/C][C]3279.95023123117[/C][C]160.049768768827[/C][/ROW]
[ROW][C]97[/C][C]5020[/C][C]3943.87519064066[/C][C]1076.12480935934[/C][/ROW]
[ROW][C]98[/C][C]5800[/C][C]3627.75410497392[/C][C]2172.24589502608[/C][/ROW]
[ROW][C]99[/C][C]2260[/C][C]4961.36003353438[/C][C]-2701.36003353438[/C][/ROW]
[ROW][C]100[/C][C]5800[/C][C]5274.45062518772[/C][C]525.549374812282[/C][/ROW]
[ROW][C]101[/C][C]5660[/C][C]4655.95180989375[/C][C]1004.04819010625[/C][/ROW]
[ROW][C]102[/C][C]4880[/C][C]7328.65560319804[/C][C]-2448.65560319804[/C][/ROW]
[ROW][C]103[/C][C]3440[/C][C]4245.26101006669[/C][C]-805.261010066685[/C][/ROW]
[ROW][C]104[/C][C]5900[/C][C]6257.74915711116[/C][C]-357.749157111162[/C][/ROW]
[ROW][C]105[/C][C]5960[/C][C]5815.57367297738[/C][C]144.426327022625[/C][/ROW]
[ROW][C]106[/C][C]5520[/C][C]4234.70414054738[/C][C]1285.29585945262[/C][/ROW]
[ROW][C]107[/C][C]5920[/C][C]4338.72379697553[/C][C]1581.27620302447[/C][/ROW]
[ROW][C]108[/C][C]3840[/C][C]3950.11271787407[/C][C]-110.112717874072[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=300344&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=300344&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
1314801329.37141169351150.628588306491
14940883.84637846631156.1536215336895
1513001239.2645247823560.735475217652
16860807.72561486891552.2743851310852
1712201158.0901408126261.9098591873837
1821802121.0039606058858.9960393941237
199401336.35089472584-396.350894725843
209201483.58055065506-563.580550655063
2120601500.88592098162559.114079018379
221160849.42587606807310.57412393193
239801209.49322017473-229.493220174725
2410201183.86028333101-163.86028333101
257401497.46965111504-757.469651115044
26720925.434163697482-205.434163697482
2713401255.6458688100484.3541311899617
281140821.075975517805318.924024482195
2912001209.66527682724-9.66527682723881
3019002187.52859194977-287.528591949772
3110201259.04820703788-239.048207037875
3221401382.00609865566757.993901344345
3320201797.93243113462222.067568865383
341340992.092992670004347.907007329996
3514001257.07761076383142.922389236168
3623201282.408124938861037.59187506114
3712801622.66206423328-342.662064233282
3811601110.8276438073549.1723561926542
3921201652.40674390866467.593256091336
4015401177.15573686727362.844263132732
4124001594.40617776931805.593822230688
4214202954.06624981273-1534.06624981273
4314801617.07526152777-137.075261527774
4433802083.574704540081296.42529545992
4518802525.62976027258-645.629760272585
4622001405.92945584594794.070544154063
4719801738.53440481441241.465595185589
4813402018.01641243512-678.016412435118
4919601883.5351563500776.4648436499303
5013401399.45610534793-59.4561053479267
5133002166.550297711161133.44970228884
5217801587.42729950716192.572700492841
5320402190.73046804201-150.730468042014
5444603077.195147320571382.80485267943
558002060.37733403948-1260.37733403948
5614202886.86933070075-1466.86933070075
5719602628.64085000687-668.640850006869
5819401725.71410769935214.285892300654
5918801888.11076207318-8.11076207318456
609401941.04275601125-1001.04275601125
6118801934.27537786983-54.2753778698263
627201399.64185477641-679.641854776409
6316602308.40272768167-648.402727681672
6442601445.953671581852814.04632841815
6525402250.26982295134289.730177048656
6623203567.56962055611-1247.56962055611
6728601740.067374260851119.93262573915
6858802832.709861647563047.29013835244
6931403200.04644602982-60.0464460298181
7044402341.06458311482098.9354168852
7136002685.82071382305914.179286176949
7229202532.59386404833387.406135951675
7322603043.44106281481-783.441062814809
7437401937.009104503331802.99089549667
7533803869.74208063786-489.742080637857
7645603558.802739804211001.19726019579
7733203652.57391116071-332.573911160706
7847605105.63614351796-345.636143517958
7940003144.05516455989855.944835440108
8048405301.48181950371-461.48181950371
8161604437.118357297021722.88164270298
8234403990.96045306335-550.960453063345
8332803782.53570167609-502.535701676093
8420003285.69046420352-1285.69046420352
8536003418.66291731183181.337082688175
8643202809.356306287611510.64369371239
8734804451.92508769923-971.925087699229
8856204411.439007142691208.56099285731
8942004187.1266520268712.8733479731263
9085405933.071264748322606.92873525168
9138004111.2736565443-311.273656544302
9253806222.22694766372-842.226947663725
9351405700.85011128812-560.850111288119
9427204391.49909258838-1671.49909258838
9531204061.86718455345-941.867184553447
9634403279.95023123117160.049768768827
9750203943.875190640661076.12480935934
9858003627.754104973922172.24589502608
9922604961.36003353438-2701.36003353438
10058005274.45062518772525.549374812282
10156604655.951809893751004.04819010625
10248807328.65560319804-2448.65560319804
10334404245.26101006669-805.261010066685
10459006257.74915711116-357.749157111162
10559605815.57367297738144.426327022625
10655204234.704140547381285.29585945262
10759204338.723796975531581.27620302447
10838403950.11271787407-110.112717874072







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
1094930.633872189544314.027227858145547.24051652093
1104684.281399176314040.347128174555328.21567017806
1114732.932598890754058.239959792375407.62523798914
1126181.825634401475422.598006886946941.053261916
1135529.030760743814773.042743755356285.01877773226
1147549.0947377456645.475917475368452.71355801465
1154676.818297024233924.316104478285429.32048957018
1167235.315730387056272.406324627228198.22513614688
1176881.937737823055922.256026554137841.61944909197
1185285.750660873384431.961634870556139.53968687621
1195318.577193084114435.498633223126201.65575294509
1204319.893315651873776.951590980624862.83504032311

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
109 & 4930.63387218954 & 4314.02722785814 & 5547.24051652093 \tabularnewline
110 & 4684.28139917631 & 4040.34712817455 & 5328.21567017806 \tabularnewline
111 & 4732.93259889075 & 4058.23995979237 & 5407.62523798914 \tabularnewline
112 & 6181.82563440147 & 5422.59800688694 & 6941.053261916 \tabularnewline
113 & 5529.03076074381 & 4773.04274375535 & 6285.01877773226 \tabularnewline
114 & 7549.094737745 & 6645.47591747536 & 8452.71355801465 \tabularnewline
115 & 4676.81829702423 & 3924.31610447828 & 5429.32048957018 \tabularnewline
116 & 7235.31573038705 & 6272.40632462722 & 8198.22513614688 \tabularnewline
117 & 6881.93773782305 & 5922.25602655413 & 7841.61944909197 \tabularnewline
118 & 5285.75066087338 & 4431.96163487055 & 6139.53968687621 \tabularnewline
119 & 5318.57719308411 & 4435.49863322312 & 6201.65575294509 \tabularnewline
120 & 4319.89331565187 & 3776.95159098062 & 4862.83504032311 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=300344&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]4930.63387218954[/C][C]4314.02722785814[/C][C]5547.24051652093[/C][/ROW]
[ROW][C]110[/C][C]4684.28139917631[/C][C]4040.34712817455[/C][C]5328.21567017806[/C][/ROW]
[ROW][C]111[/C][C]4732.93259889075[/C][C]4058.23995979237[/C][C]5407.62523798914[/C][/ROW]
[ROW][C]112[/C][C]6181.82563440147[/C][C]5422.59800688694[/C][C]6941.053261916[/C][/ROW]
[ROW][C]113[/C][C]5529.03076074381[/C][C]4773.04274375535[/C][C]6285.01877773226[/C][/ROW]
[ROW][C]114[/C][C]7549.094737745[/C][C]6645.47591747536[/C][C]8452.71355801465[/C][/ROW]
[ROW][C]115[/C][C]4676.81829702423[/C][C]3924.31610447828[/C][C]5429.32048957018[/C][/ROW]
[ROW][C]116[/C][C]7235.31573038705[/C][C]6272.40632462722[/C][C]8198.22513614688[/C][/ROW]
[ROW][C]117[/C][C]6881.93773782305[/C][C]5922.25602655413[/C][C]7841.61944909197[/C][/ROW]
[ROW][C]118[/C][C]5285.75066087338[/C][C]4431.96163487055[/C][C]6139.53968687621[/C][/ROW]
[ROW][C]119[/C][C]5318.57719308411[/C][C]4435.49863322312[/C][C]6201.65575294509[/C][/ROW]
[ROW][C]120[/C][C]4319.89331565187[/C][C]3776.95159098062[/C][C]4862.83504032311[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=300344&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=300344&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
1094930.633872189544314.027227858145547.24051652093
1104684.281399176314040.347128174555328.21567017806
1114732.932598890754058.239959792375407.62523798914
1126181.825634401475422.598006886946941.053261916
1135529.030760743814773.042743755356285.01877773226
1147549.0947377456645.475917475368452.71355801465
1154676.818297024233924.316104478285429.32048957018
1167235.315730387056272.406324627228198.22513614688
1176881.937737823055922.256026554137841.61944909197
1185285.750660873384431.961634870556139.53968687621
1195318.577193084114435.498633223126201.65575294509
1204319.893315651873776.951590980624862.83504032311



Parameters (Session):
Parameters (R input):
par1 = 12 ; par2 = Triple ; par3 = multiplicative ; par4 = 12 ;
R code (references can be found in the software module):
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')