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 11:33:19 +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/t1482230034ssexocxbma9z3kf.htm/, Retrieved Sun, 28 Apr 2024 04:49:35 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=301585, Retrieved Sun, 28 Apr 2024 04:49:35 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact113
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [meh] [2016-12-20 10:33:19] [34b674d558c9d5fa20516c65c4cfbe6a] [Current]
Feedback Forum

Post a new message
Dataseries X:
3650
3700
3750
3850
3950
3900
3700
3700
4000
4350
4350
4200
4050
4100
4150
4350
4350
4350
4000
4050
4350
4750
4750
4700
4300
4400
4450
4600
4500
4500
4200
4150
4500
4850
4900
4850
4500
4650
4600
4700
4750
4800
4400
4450
4750
5100
5200
4850
4600
4650
4850
5000
5050
5150
4650
4700
5100
5450
5550
5300
5200
5400
5500
5500
5650
5500
4850
5050
5550
6050
6050
5850
5600
5700
5700
5750
5950
5850
5150
5250
5900
6350
6400
6200
5850
5950
6150
6250
6250
6200
5200
5750
6200
6650
6700
6550
6100
6250
6300
6500
6250
6500
5400
6100
6550
6950
7150
7150
6700
6950
7050
7050
7100
7250




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=301585&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=301585&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=301585&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
alpha0.393783482668539
beta0
gamma1

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.393783482668539 \tabularnewline
beta & 0 \tabularnewline
gamma & 1 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=301585&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]0.393783482668539[/C][/ROW]
[ROW][C]beta[/C][C]0[/C][/ROW]
[ROW][C]gamma[/C][C]1[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=301585&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=301585&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
alpha0.393783482668539
beta0
gamma1







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
1340503835.26976495727214.730235042734
1441003975.66177495642124.338225043582
1541504078.3755711193671.6244288806397
1643504308.2482117112541.7517882887523
1743504324.2741665210225.7258334789776
1843504329.8226983660520.1773016339512
1940004087.35297668411-87.3529766841089
2040504052.53960751377-2.53960751376735
2143504351.12434223217-1.12434223217406
2247504696.099718375453.9002816246002
2347504712.7428825334737.2571174665272
2447004574.91557688009125.08442311991
2543004606.01289544033-306.012895440328
2644004486.54773244587-86.5477324458661
2744504474.2621478975-24.2621478975043
2846004648.26695020142-48.2669502014214
2945004619.12981415141-119.129814151413
3045004564.27297293694-64.272972936943
3142004223.3614971925-23.3614971925044
3241504265.16218095907-115.162180959072
3345004520.2559636692-20.2559636692013
3448504891.05445913579-41.0544591357866
3549004860.2166537680639.7833462319368
3648504776.6264986357473.373501364259
3745004526.02259524652-26.0225952465198
3846504649.856394561870.14360543813018
3946004709.46697710753-109.466977107525
4047004835.36741737303-135.367417373031
4147504728.9733174262321.0266825737672
4248004762.5629128436737.4370871563333
4344004486.50439112987-86.504391129869
4444504447.78935541442.21064458560431
4547504806.63633465672-56.6363346567223
4651005150.50044944758-50.5004494475806
4752005164.9481819563735.0518180436347
4848505099.85773603665-249.857736036649
4946004661.71515475271-61.7151547527083
5046504787.3561967312-137.356196731202
5148504726.37388269888123.626117301117
5250004928.361258771571.6387412284957
5350504998.2914514935951.7085485064126
5451505053.9113172467996.0886827532086
5546504725.81345379162-75.813453791623
5647004745.08885260057-45.0888526005656
5751005049.6360603006950.3639396993085
5854505439.3547907361910.645209263811
5955505529.7438713307420.2561286692589
6053005286.1102496916913.8897503083072
6152005065.88221251344134.117787486555
6254005222.78418347262177.215816527383
6355005443.886921869156.1130781309048
6455005587.77317218379-87.7731721837881
6556505582.847574441867.1524255581999
6655005671.45295430816-171.452954308158
6748505133.79169871408-283.791698714077
6850505089.79446064861-39.7944606486053
6955505454.2915717677895.7084282322212
7060505837.78806238016212.211937619844
7160506013.3770893471736.6229106528253
7258505772.329032399777.6709676002993
7356005650.10120707933-50.1012070793277
7457005760.58751785363-60.5875178536307
7557005814.63275073735-114.632750737346
7657505804.05589235152-54.0558923515173
7759505906.3260587966343.6739412033667
7858505841.039476926838.96052307316768
7951505306.32046638117-156.320466381168
8052505460.43445002235-210.434450022345
8159005839.8804412290960.119558770908
8263506279.9889745986170.0110254013862
8364006293.13666270404106.863337295961
8462006104.6321357101495.3678642898567
8558505911.91545325446-61.915453254459
8659506011.39253422756-61.3925342275616
8761506032.35765210281117.642347897188
8862506149.96958311601100.030416883994
8962506372.16183238045-122.16183238045
9062006220.52801459422-20.5280145942215
9152005574.00083917898-374.000839178984
9257505609.59109680936140.408903190635
9362006291.20771447614-91.2077144761397
9466506677.72243761573-27.7224376157346
9567006674.7247824533625.2752175466367
9665506447.12345590936102.876544090637
9761006162.01582253982-62.01582253982
9862506261.77038189751-11.7703818975115
9963006410.80978645731-110.809786457312
10065006427.7843968990372.2156031009717
10162506504.32702039508-254.327020395081
10265006362.26083364638137.739166353623
10354005563.77559524583-163.775595245826
10461005993.99276407773106.007235922268
10565506521.6527540799228.3472459200793
10669506993.73206933478-43.7320693347765
10771507016.55813957711133.441860422893
10871506878.59425629129271.405743708712
10967006559.89016184543140.109838154566
11069506769.698083846180.301916153995
11170506934.33306394585115.666936054146
11270507151.44348116275-101.443481162745
11371006961.64649368435138.353506315653
11472507211.8884106141438.1115893858632

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 4050 & 3835.26976495727 & 214.730235042734 \tabularnewline
14 & 4100 & 3975.66177495642 & 124.338225043582 \tabularnewline
15 & 4150 & 4078.37557111936 & 71.6244288806397 \tabularnewline
16 & 4350 & 4308.24821171125 & 41.7517882887523 \tabularnewline
17 & 4350 & 4324.27416652102 & 25.7258334789776 \tabularnewline
18 & 4350 & 4329.82269836605 & 20.1773016339512 \tabularnewline
19 & 4000 & 4087.35297668411 & -87.3529766841089 \tabularnewline
20 & 4050 & 4052.53960751377 & -2.53960751376735 \tabularnewline
21 & 4350 & 4351.12434223217 & -1.12434223217406 \tabularnewline
22 & 4750 & 4696.0997183754 & 53.9002816246002 \tabularnewline
23 & 4750 & 4712.74288253347 & 37.2571174665272 \tabularnewline
24 & 4700 & 4574.91557688009 & 125.08442311991 \tabularnewline
25 & 4300 & 4606.01289544033 & -306.012895440328 \tabularnewline
26 & 4400 & 4486.54773244587 & -86.5477324458661 \tabularnewline
27 & 4450 & 4474.2621478975 & -24.2621478975043 \tabularnewline
28 & 4600 & 4648.26695020142 & -48.2669502014214 \tabularnewline
29 & 4500 & 4619.12981415141 & -119.129814151413 \tabularnewline
30 & 4500 & 4564.27297293694 & -64.272972936943 \tabularnewline
31 & 4200 & 4223.3614971925 & -23.3614971925044 \tabularnewline
32 & 4150 & 4265.16218095907 & -115.162180959072 \tabularnewline
33 & 4500 & 4520.2559636692 & -20.2559636692013 \tabularnewline
34 & 4850 & 4891.05445913579 & -41.0544591357866 \tabularnewline
35 & 4900 & 4860.21665376806 & 39.7833462319368 \tabularnewline
36 & 4850 & 4776.62649863574 & 73.373501364259 \tabularnewline
37 & 4500 & 4526.02259524652 & -26.0225952465198 \tabularnewline
38 & 4650 & 4649.85639456187 & 0.14360543813018 \tabularnewline
39 & 4600 & 4709.46697710753 & -109.466977107525 \tabularnewline
40 & 4700 & 4835.36741737303 & -135.367417373031 \tabularnewline
41 & 4750 & 4728.97331742623 & 21.0266825737672 \tabularnewline
42 & 4800 & 4762.56291284367 & 37.4370871563333 \tabularnewline
43 & 4400 & 4486.50439112987 & -86.504391129869 \tabularnewline
44 & 4450 & 4447.7893554144 & 2.21064458560431 \tabularnewline
45 & 4750 & 4806.63633465672 & -56.6363346567223 \tabularnewline
46 & 5100 & 5150.50044944758 & -50.5004494475806 \tabularnewline
47 & 5200 & 5164.94818195637 & 35.0518180436347 \tabularnewline
48 & 4850 & 5099.85773603665 & -249.857736036649 \tabularnewline
49 & 4600 & 4661.71515475271 & -61.7151547527083 \tabularnewline
50 & 4650 & 4787.3561967312 & -137.356196731202 \tabularnewline
51 & 4850 & 4726.37388269888 & 123.626117301117 \tabularnewline
52 & 5000 & 4928.3612587715 & 71.6387412284957 \tabularnewline
53 & 5050 & 4998.29145149359 & 51.7085485064126 \tabularnewline
54 & 5150 & 5053.91131724679 & 96.0886827532086 \tabularnewline
55 & 4650 & 4725.81345379162 & -75.813453791623 \tabularnewline
56 & 4700 & 4745.08885260057 & -45.0888526005656 \tabularnewline
57 & 5100 & 5049.63606030069 & 50.3639396993085 \tabularnewline
58 & 5450 & 5439.35479073619 & 10.645209263811 \tabularnewline
59 & 5550 & 5529.74387133074 & 20.2561286692589 \tabularnewline
60 & 5300 & 5286.11024969169 & 13.8897503083072 \tabularnewline
61 & 5200 & 5065.88221251344 & 134.117787486555 \tabularnewline
62 & 5400 & 5222.78418347262 & 177.215816527383 \tabularnewline
63 & 5500 & 5443.8869218691 & 56.1130781309048 \tabularnewline
64 & 5500 & 5587.77317218379 & -87.7731721837881 \tabularnewline
65 & 5650 & 5582.8475744418 & 67.1524255581999 \tabularnewline
66 & 5500 & 5671.45295430816 & -171.452954308158 \tabularnewline
67 & 4850 & 5133.79169871408 & -283.791698714077 \tabularnewline
68 & 5050 & 5089.79446064861 & -39.7944606486053 \tabularnewline
69 & 5550 & 5454.29157176778 & 95.7084282322212 \tabularnewline
70 & 6050 & 5837.78806238016 & 212.211937619844 \tabularnewline
71 & 6050 & 6013.37708934717 & 36.6229106528253 \tabularnewline
72 & 5850 & 5772.3290323997 & 77.6709676002993 \tabularnewline
73 & 5600 & 5650.10120707933 & -50.1012070793277 \tabularnewline
74 & 5700 & 5760.58751785363 & -60.5875178536307 \tabularnewline
75 & 5700 & 5814.63275073735 & -114.632750737346 \tabularnewline
76 & 5750 & 5804.05589235152 & -54.0558923515173 \tabularnewline
77 & 5950 & 5906.32605879663 & 43.6739412033667 \tabularnewline
78 & 5850 & 5841.03947692683 & 8.96052307316768 \tabularnewline
79 & 5150 & 5306.32046638117 & -156.320466381168 \tabularnewline
80 & 5250 & 5460.43445002235 & -210.434450022345 \tabularnewline
81 & 5900 & 5839.88044122909 & 60.119558770908 \tabularnewline
82 & 6350 & 6279.98897459861 & 70.0110254013862 \tabularnewline
83 & 6400 & 6293.13666270404 & 106.863337295961 \tabularnewline
84 & 6200 & 6104.63213571014 & 95.3678642898567 \tabularnewline
85 & 5850 & 5911.91545325446 & -61.915453254459 \tabularnewline
86 & 5950 & 6011.39253422756 & -61.3925342275616 \tabularnewline
87 & 6150 & 6032.35765210281 & 117.642347897188 \tabularnewline
88 & 6250 & 6149.96958311601 & 100.030416883994 \tabularnewline
89 & 6250 & 6372.16183238045 & -122.16183238045 \tabularnewline
90 & 6200 & 6220.52801459422 & -20.5280145942215 \tabularnewline
91 & 5200 & 5574.00083917898 & -374.000839178984 \tabularnewline
92 & 5750 & 5609.59109680936 & 140.408903190635 \tabularnewline
93 & 6200 & 6291.20771447614 & -91.2077144761397 \tabularnewline
94 & 6650 & 6677.72243761573 & -27.7224376157346 \tabularnewline
95 & 6700 & 6674.72478245336 & 25.2752175466367 \tabularnewline
96 & 6550 & 6447.12345590936 & 102.876544090637 \tabularnewline
97 & 6100 & 6162.01582253982 & -62.01582253982 \tabularnewline
98 & 6250 & 6261.77038189751 & -11.7703818975115 \tabularnewline
99 & 6300 & 6410.80978645731 & -110.809786457312 \tabularnewline
100 & 6500 & 6427.78439689903 & 72.2156031009717 \tabularnewline
101 & 6250 & 6504.32702039508 & -254.327020395081 \tabularnewline
102 & 6500 & 6362.26083364638 & 137.739166353623 \tabularnewline
103 & 5400 & 5563.77559524583 & -163.775595245826 \tabularnewline
104 & 6100 & 5993.99276407773 & 106.007235922268 \tabularnewline
105 & 6550 & 6521.65275407992 & 28.3472459200793 \tabularnewline
106 & 6950 & 6993.73206933478 & -43.7320693347765 \tabularnewline
107 & 7150 & 7016.55813957711 & 133.441860422893 \tabularnewline
108 & 7150 & 6878.59425629129 & 271.405743708712 \tabularnewline
109 & 6700 & 6559.89016184543 & 140.109838154566 \tabularnewline
110 & 6950 & 6769.698083846 & 180.301916153995 \tabularnewline
111 & 7050 & 6934.33306394585 & 115.666936054146 \tabularnewline
112 & 7050 & 7151.44348116275 & -101.443481162745 \tabularnewline
113 & 7100 & 6961.64649368435 & 138.353506315653 \tabularnewline
114 & 7250 & 7211.88841061414 & 38.1115893858632 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=301585&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]4050[/C][C]3835.26976495727[/C][C]214.730235042734[/C][/ROW]
[ROW][C]14[/C][C]4100[/C][C]3975.66177495642[/C][C]124.338225043582[/C][/ROW]
[ROW][C]15[/C][C]4150[/C][C]4078.37557111936[/C][C]71.6244288806397[/C][/ROW]
[ROW][C]16[/C][C]4350[/C][C]4308.24821171125[/C][C]41.7517882887523[/C][/ROW]
[ROW][C]17[/C][C]4350[/C][C]4324.27416652102[/C][C]25.7258334789776[/C][/ROW]
[ROW][C]18[/C][C]4350[/C][C]4329.82269836605[/C][C]20.1773016339512[/C][/ROW]
[ROW][C]19[/C][C]4000[/C][C]4087.35297668411[/C][C]-87.3529766841089[/C][/ROW]
[ROW][C]20[/C][C]4050[/C][C]4052.53960751377[/C][C]-2.53960751376735[/C][/ROW]
[ROW][C]21[/C][C]4350[/C][C]4351.12434223217[/C][C]-1.12434223217406[/C][/ROW]
[ROW][C]22[/C][C]4750[/C][C]4696.0997183754[/C][C]53.9002816246002[/C][/ROW]
[ROW][C]23[/C][C]4750[/C][C]4712.74288253347[/C][C]37.2571174665272[/C][/ROW]
[ROW][C]24[/C][C]4700[/C][C]4574.91557688009[/C][C]125.08442311991[/C][/ROW]
[ROW][C]25[/C][C]4300[/C][C]4606.01289544033[/C][C]-306.012895440328[/C][/ROW]
[ROW][C]26[/C][C]4400[/C][C]4486.54773244587[/C][C]-86.5477324458661[/C][/ROW]
[ROW][C]27[/C][C]4450[/C][C]4474.2621478975[/C][C]-24.2621478975043[/C][/ROW]
[ROW][C]28[/C][C]4600[/C][C]4648.26695020142[/C][C]-48.2669502014214[/C][/ROW]
[ROW][C]29[/C][C]4500[/C][C]4619.12981415141[/C][C]-119.129814151413[/C][/ROW]
[ROW][C]30[/C][C]4500[/C][C]4564.27297293694[/C][C]-64.272972936943[/C][/ROW]
[ROW][C]31[/C][C]4200[/C][C]4223.3614971925[/C][C]-23.3614971925044[/C][/ROW]
[ROW][C]32[/C][C]4150[/C][C]4265.16218095907[/C][C]-115.162180959072[/C][/ROW]
[ROW][C]33[/C][C]4500[/C][C]4520.2559636692[/C][C]-20.2559636692013[/C][/ROW]
[ROW][C]34[/C][C]4850[/C][C]4891.05445913579[/C][C]-41.0544591357866[/C][/ROW]
[ROW][C]35[/C][C]4900[/C][C]4860.21665376806[/C][C]39.7833462319368[/C][/ROW]
[ROW][C]36[/C][C]4850[/C][C]4776.62649863574[/C][C]73.373501364259[/C][/ROW]
[ROW][C]37[/C][C]4500[/C][C]4526.02259524652[/C][C]-26.0225952465198[/C][/ROW]
[ROW][C]38[/C][C]4650[/C][C]4649.85639456187[/C][C]0.14360543813018[/C][/ROW]
[ROW][C]39[/C][C]4600[/C][C]4709.46697710753[/C][C]-109.466977107525[/C][/ROW]
[ROW][C]40[/C][C]4700[/C][C]4835.36741737303[/C][C]-135.367417373031[/C][/ROW]
[ROW][C]41[/C][C]4750[/C][C]4728.97331742623[/C][C]21.0266825737672[/C][/ROW]
[ROW][C]42[/C][C]4800[/C][C]4762.56291284367[/C][C]37.4370871563333[/C][/ROW]
[ROW][C]43[/C][C]4400[/C][C]4486.50439112987[/C][C]-86.504391129869[/C][/ROW]
[ROW][C]44[/C][C]4450[/C][C]4447.7893554144[/C][C]2.21064458560431[/C][/ROW]
[ROW][C]45[/C][C]4750[/C][C]4806.63633465672[/C][C]-56.6363346567223[/C][/ROW]
[ROW][C]46[/C][C]5100[/C][C]5150.50044944758[/C][C]-50.5004494475806[/C][/ROW]
[ROW][C]47[/C][C]5200[/C][C]5164.94818195637[/C][C]35.0518180436347[/C][/ROW]
[ROW][C]48[/C][C]4850[/C][C]5099.85773603665[/C][C]-249.857736036649[/C][/ROW]
[ROW][C]49[/C][C]4600[/C][C]4661.71515475271[/C][C]-61.7151547527083[/C][/ROW]
[ROW][C]50[/C][C]4650[/C][C]4787.3561967312[/C][C]-137.356196731202[/C][/ROW]
[ROW][C]51[/C][C]4850[/C][C]4726.37388269888[/C][C]123.626117301117[/C][/ROW]
[ROW][C]52[/C][C]5000[/C][C]4928.3612587715[/C][C]71.6387412284957[/C][/ROW]
[ROW][C]53[/C][C]5050[/C][C]4998.29145149359[/C][C]51.7085485064126[/C][/ROW]
[ROW][C]54[/C][C]5150[/C][C]5053.91131724679[/C][C]96.0886827532086[/C][/ROW]
[ROW][C]55[/C][C]4650[/C][C]4725.81345379162[/C][C]-75.813453791623[/C][/ROW]
[ROW][C]56[/C][C]4700[/C][C]4745.08885260057[/C][C]-45.0888526005656[/C][/ROW]
[ROW][C]57[/C][C]5100[/C][C]5049.63606030069[/C][C]50.3639396993085[/C][/ROW]
[ROW][C]58[/C][C]5450[/C][C]5439.35479073619[/C][C]10.645209263811[/C][/ROW]
[ROW][C]59[/C][C]5550[/C][C]5529.74387133074[/C][C]20.2561286692589[/C][/ROW]
[ROW][C]60[/C][C]5300[/C][C]5286.11024969169[/C][C]13.8897503083072[/C][/ROW]
[ROW][C]61[/C][C]5200[/C][C]5065.88221251344[/C][C]134.117787486555[/C][/ROW]
[ROW][C]62[/C][C]5400[/C][C]5222.78418347262[/C][C]177.215816527383[/C][/ROW]
[ROW][C]63[/C][C]5500[/C][C]5443.8869218691[/C][C]56.1130781309048[/C][/ROW]
[ROW][C]64[/C][C]5500[/C][C]5587.77317218379[/C][C]-87.7731721837881[/C][/ROW]
[ROW][C]65[/C][C]5650[/C][C]5582.8475744418[/C][C]67.1524255581999[/C][/ROW]
[ROW][C]66[/C][C]5500[/C][C]5671.45295430816[/C][C]-171.452954308158[/C][/ROW]
[ROW][C]67[/C][C]4850[/C][C]5133.79169871408[/C][C]-283.791698714077[/C][/ROW]
[ROW][C]68[/C][C]5050[/C][C]5089.79446064861[/C][C]-39.7944606486053[/C][/ROW]
[ROW][C]69[/C][C]5550[/C][C]5454.29157176778[/C][C]95.7084282322212[/C][/ROW]
[ROW][C]70[/C][C]6050[/C][C]5837.78806238016[/C][C]212.211937619844[/C][/ROW]
[ROW][C]71[/C][C]6050[/C][C]6013.37708934717[/C][C]36.6229106528253[/C][/ROW]
[ROW][C]72[/C][C]5850[/C][C]5772.3290323997[/C][C]77.6709676002993[/C][/ROW]
[ROW][C]73[/C][C]5600[/C][C]5650.10120707933[/C][C]-50.1012070793277[/C][/ROW]
[ROW][C]74[/C][C]5700[/C][C]5760.58751785363[/C][C]-60.5875178536307[/C][/ROW]
[ROW][C]75[/C][C]5700[/C][C]5814.63275073735[/C][C]-114.632750737346[/C][/ROW]
[ROW][C]76[/C][C]5750[/C][C]5804.05589235152[/C][C]-54.0558923515173[/C][/ROW]
[ROW][C]77[/C][C]5950[/C][C]5906.32605879663[/C][C]43.6739412033667[/C][/ROW]
[ROW][C]78[/C][C]5850[/C][C]5841.03947692683[/C][C]8.96052307316768[/C][/ROW]
[ROW][C]79[/C][C]5150[/C][C]5306.32046638117[/C][C]-156.320466381168[/C][/ROW]
[ROW][C]80[/C][C]5250[/C][C]5460.43445002235[/C][C]-210.434450022345[/C][/ROW]
[ROW][C]81[/C][C]5900[/C][C]5839.88044122909[/C][C]60.119558770908[/C][/ROW]
[ROW][C]82[/C][C]6350[/C][C]6279.98897459861[/C][C]70.0110254013862[/C][/ROW]
[ROW][C]83[/C][C]6400[/C][C]6293.13666270404[/C][C]106.863337295961[/C][/ROW]
[ROW][C]84[/C][C]6200[/C][C]6104.63213571014[/C][C]95.3678642898567[/C][/ROW]
[ROW][C]85[/C][C]5850[/C][C]5911.91545325446[/C][C]-61.915453254459[/C][/ROW]
[ROW][C]86[/C][C]5950[/C][C]6011.39253422756[/C][C]-61.3925342275616[/C][/ROW]
[ROW][C]87[/C][C]6150[/C][C]6032.35765210281[/C][C]117.642347897188[/C][/ROW]
[ROW][C]88[/C][C]6250[/C][C]6149.96958311601[/C][C]100.030416883994[/C][/ROW]
[ROW][C]89[/C][C]6250[/C][C]6372.16183238045[/C][C]-122.16183238045[/C][/ROW]
[ROW][C]90[/C][C]6200[/C][C]6220.52801459422[/C][C]-20.5280145942215[/C][/ROW]
[ROW][C]91[/C][C]5200[/C][C]5574.00083917898[/C][C]-374.000839178984[/C][/ROW]
[ROW][C]92[/C][C]5750[/C][C]5609.59109680936[/C][C]140.408903190635[/C][/ROW]
[ROW][C]93[/C][C]6200[/C][C]6291.20771447614[/C][C]-91.2077144761397[/C][/ROW]
[ROW][C]94[/C][C]6650[/C][C]6677.72243761573[/C][C]-27.7224376157346[/C][/ROW]
[ROW][C]95[/C][C]6700[/C][C]6674.72478245336[/C][C]25.2752175466367[/C][/ROW]
[ROW][C]96[/C][C]6550[/C][C]6447.12345590936[/C][C]102.876544090637[/C][/ROW]
[ROW][C]97[/C][C]6100[/C][C]6162.01582253982[/C][C]-62.01582253982[/C][/ROW]
[ROW][C]98[/C][C]6250[/C][C]6261.77038189751[/C][C]-11.7703818975115[/C][/ROW]
[ROW][C]99[/C][C]6300[/C][C]6410.80978645731[/C][C]-110.809786457312[/C][/ROW]
[ROW][C]100[/C][C]6500[/C][C]6427.78439689903[/C][C]72.2156031009717[/C][/ROW]
[ROW][C]101[/C][C]6250[/C][C]6504.32702039508[/C][C]-254.327020395081[/C][/ROW]
[ROW][C]102[/C][C]6500[/C][C]6362.26083364638[/C][C]137.739166353623[/C][/ROW]
[ROW][C]103[/C][C]5400[/C][C]5563.77559524583[/C][C]-163.775595245826[/C][/ROW]
[ROW][C]104[/C][C]6100[/C][C]5993.99276407773[/C][C]106.007235922268[/C][/ROW]
[ROW][C]105[/C][C]6550[/C][C]6521.65275407992[/C][C]28.3472459200793[/C][/ROW]
[ROW][C]106[/C][C]6950[/C][C]6993.73206933478[/C][C]-43.7320693347765[/C][/ROW]
[ROW][C]107[/C][C]7150[/C][C]7016.55813957711[/C][C]133.441860422893[/C][/ROW]
[ROW][C]108[/C][C]7150[/C][C]6878.59425629129[/C][C]271.405743708712[/C][/ROW]
[ROW][C]109[/C][C]6700[/C][C]6559.89016184543[/C][C]140.109838154566[/C][/ROW]
[ROW][C]110[/C][C]6950[/C][C]6769.698083846[/C][C]180.301916153995[/C][/ROW]
[ROW][C]111[/C][C]7050[/C][C]6934.33306394585[/C][C]115.666936054146[/C][/ROW]
[ROW][C]112[/C][C]7050[/C][C]7151.44348116275[/C][C]-101.443481162745[/C][/ROW]
[ROW][C]113[/C][C]7100[/C][C]6961.64649368435[/C][C]138.353506315653[/C][/ROW]
[ROW][C]114[/C][C]7250[/C][C]7211.88841061414[/C][C]38.1115893858632[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=301585&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=301585&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
1340503835.26976495727214.730235042734
1441003975.66177495642124.338225043582
1541504078.3755711193671.6244288806397
1643504308.2482117112541.7517882887523
1743504324.2741665210225.7258334789776
1843504329.8226983660520.1773016339512
1940004087.35297668411-87.3529766841089
2040504052.53960751377-2.53960751376735
2143504351.12434223217-1.12434223217406
2247504696.099718375453.9002816246002
2347504712.7428825334737.2571174665272
2447004574.91557688009125.08442311991
2543004606.01289544033-306.012895440328
2644004486.54773244587-86.5477324458661
2744504474.2621478975-24.2621478975043
2846004648.26695020142-48.2669502014214
2945004619.12981415141-119.129814151413
3045004564.27297293694-64.272972936943
3142004223.3614971925-23.3614971925044
3241504265.16218095907-115.162180959072
3345004520.2559636692-20.2559636692013
3448504891.05445913579-41.0544591357866
3549004860.2166537680639.7833462319368
3648504776.6264986357473.373501364259
3745004526.02259524652-26.0225952465198
3846504649.856394561870.14360543813018
3946004709.46697710753-109.466977107525
4047004835.36741737303-135.367417373031
4147504728.9733174262321.0266825737672
4248004762.5629128436737.4370871563333
4344004486.50439112987-86.504391129869
4444504447.78935541442.21064458560431
4547504806.63633465672-56.6363346567223
4651005150.50044944758-50.5004494475806
4752005164.9481819563735.0518180436347
4848505099.85773603665-249.857736036649
4946004661.71515475271-61.7151547527083
5046504787.3561967312-137.356196731202
5148504726.37388269888123.626117301117
5250004928.361258771571.6387412284957
5350504998.2914514935951.7085485064126
5451505053.9113172467996.0886827532086
5546504725.81345379162-75.813453791623
5647004745.08885260057-45.0888526005656
5751005049.6360603006950.3639396993085
5854505439.3547907361910.645209263811
5955505529.7438713307420.2561286692589
6053005286.1102496916913.8897503083072
6152005065.88221251344134.117787486555
6254005222.78418347262177.215816527383
6355005443.886921869156.1130781309048
6455005587.77317218379-87.7731721837881
6556505582.847574441867.1524255581999
6655005671.45295430816-171.452954308158
6748505133.79169871408-283.791698714077
6850505089.79446064861-39.7944606486053
6955505454.2915717677895.7084282322212
7060505837.78806238016212.211937619844
7160506013.3770893471736.6229106528253
7258505772.329032399777.6709676002993
7356005650.10120707933-50.1012070793277
7457005760.58751785363-60.5875178536307
7557005814.63275073735-114.632750737346
7657505804.05589235152-54.0558923515173
7759505906.3260587966343.6739412033667
7858505841.039476926838.96052307316768
7951505306.32046638117-156.320466381168
8052505460.43445002235-210.434450022345
8159005839.8804412290960.119558770908
8263506279.9889745986170.0110254013862
8364006293.13666270404106.863337295961
8462006104.6321357101495.3678642898567
8558505911.91545325446-61.915453254459
8659506011.39253422756-61.3925342275616
8761506032.35765210281117.642347897188
8862506149.96958311601100.030416883994
8962506372.16183238045-122.16183238045
9062006220.52801459422-20.5280145942215
9152005574.00083917898-374.000839178984
9257505609.59109680936140.408903190635
9362006291.20771447614-91.2077144761397
9466506677.72243761573-27.7224376157346
9567006674.7247824533625.2752175466367
9665506447.12345590936102.876544090637
9761006162.01582253982-62.01582253982
9862506261.77038189751-11.7703818975115
9963006410.80978645731-110.809786457312
10065006427.7843968990372.2156031009717
10162506504.32702039508-254.327020395081
10265006362.26083364638137.739166353623
10354005563.77559524583-163.775595245826
10461005993.99276407773106.007235922268
10565506521.6527540799228.3472459200793
10669506993.73206933478-43.7320693347765
10771507016.55813957711133.441860422893
10871506878.59425629129271.405743708712
10967006559.89016184543140.109838154566
11069506769.698083846180.301916153995
11170506934.33306394585115.666936054146
11270507151.44348116275-101.443481162745
11371006961.64649368435138.353506315653
11472507211.8884106141438.1115893858632







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
1156191.388249284555965.822261488366416.95423708074
1166849.644350735016607.219627792277092.06907367776
1177288.481673512547030.296705442627546.66664158247
1187705.702640079497432.665629436867978.73965072213
1197853.15543954847566.033617625958140.27726147084
1207746.280340574547445.733053001588046.82762814749
1217241.107400549916927.709245624167554.50555547565
1227420.107484074987094.365047548427745.84992060153
1237474.559755165977136.924054450467812.19545588149
1247514.506522472267165.382478841557863.63056610297
1257510.025196915887149.778990434187870.27140339758
1267645.017482517487273.982361905098016.05260312987

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
115 & 6191.38824928455 & 5965.82226148836 & 6416.95423708074 \tabularnewline
116 & 6849.64435073501 & 6607.21962779227 & 7092.06907367776 \tabularnewline
117 & 7288.48167351254 & 7030.29670544262 & 7546.66664158247 \tabularnewline
118 & 7705.70264007949 & 7432.66562943686 & 7978.73965072213 \tabularnewline
119 & 7853.1554395484 & 7566.03361762595 & 8140.27726147084 \tabularnewline
120 & 7746.28034057454 & 7445.73305300158 & 8046.82762814749 \tabularnewline
121 & 7241.10740054991 & 6927.70924562416 & 7554.50555547565 \tabularnewline
122 & 7420.10748407498 & 7094.36504754842 & 7745.84992060153 \tabularnewline
123 & 7474.55975516597 & 7136.92405445046 & 7812.19545588149 \tabularnewline
124 & 7514.50652247226 & 7165.38247884155 & 7863.63056610297 \tabularnewline
125 & 7510.02519691588 & 7149.77899043418 & 7870.27140339758 \tabularnewline
126 & 7645.01748251748 & 7273.98236190509 & 8016.05260312987 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=301585&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]115[/C][C]6191.38824928455[/C][C]5965.82226148836[/C][C]6416.95423708074[/C][/ROW]
[ROW][C]116[/C][C]6849.64435073501[/C][C]6607.21962779227[/C][C]7092.06907367776[/C][/ROW]
[ROW][C]117[/C][C]7288.48167351254[/C][C]7030.29670544262[/C][C]7546.66664158247[/C][/ROW]
[ROW][C]118[/C][C]7705.70264007949[/C][C]7432.66562943686[/C][C]7978.73965072213[/C][/ROW]
[ROW][C]119[/C][C]7853.1554395484[/C][C]7566.03361762595[/C][C]8140.27726147084[/C][/ROW]
[ROW][C]120[/C][C]7746.28034057454[/C][C]7445.73305300158[/C][C]8046.82762814749[/C][/ROW]
[ROW][C]121[/C][C]7241.10740054991[/C][C]6927.70924562416[/C][C]7554.50555547565[/C][/ROW]
[ROW][C]122[/C][C]7420.10748407498[/C][C]7094.36504754842[/C][C]7745.84992060153[/C][/ROW]
[ROW][C]123[/C][C]7474.55975516597[/C][C]7136.92405445046[/C][C]7812.19545588149[/C][/ROW]
[ROW][C]124[/C][C]7514.50652247226[/C][C]7165.38247884155[/C][C]7863.63056610297[/C][/ROW]
[ROW][C]125[/C][C]7510.02519691588[/C][C]7149.77899043418[/C][C]7870.27140339758[/C][/ROW]
[ROW][C]126[/C][C]7645.01748251748[/C][C]7273.98236190509[/C][C]8016.05260312987[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=301585&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=301585&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
1156191.388249284555965.822261488366416.95423708074
1166849.644350735016607.219627792277092.06907367776
1177288.481673512547030.296705442627546.66664158247
1187705.702640079497432.665629436867978.73965072213
1197853.15543954847566.033617625958140.27726147084
1207746.280340574547445.733053001588046.82762814749
1217241.107400549916927.709245624167554.50555547565
1227420.107484074987094.365047548427745.84992060153
1237474.559755165977136.924054450467812.19545588149
1247514.506522472267165.382478841557863.63056610297
1257510.025196915887149.778990434187870.27140339758
1267645.017482517487273.982361905098016.05260312987



Parameters (Session):
par1 = 12 ; par2 = Triple ; par3 = additive ; par4 = 12 ;
Parameters (R input):
par1 = 12 ; par2 = Triple ; 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')