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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 computationWed, 09 Aug 2017 14:09:12 +0200
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2017/Aug/09/t1502280664y1kbzfbhw025bit.htm/, Retrieved Tue, 14 May 2024 02:35:12 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=307017, Retrieved Tue, 14 May 2024 02:35:12 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact101
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [omzet nietjesmachine] [2017-08-09 12:09:12] [ff90ea2d7baa48124a9630d5b785d73f] [Current]
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Dataseries X:
133448
132951
132447
131404
141722
141176
133448
128310
128807
128807
129360
130354
131901
131901
130907
128310
141722
143766
140679
133448
136542
131901
133994
134995
136038
133448
133994
130354
141722
145313
142226
136542
142723
136038
142226
141722
143269
137585
143766
143269
152544
150451
142226
138082
143766
136038
141722
142723
144816
140182
142723
144270
149954
145313
139132
132447
138635
121625
129857
134491
139132
132447
132447
132447
136038
130907
124173
118538
122626
106666
116445
122129
123172
117488
117985
116445
121625
117985
110810
105623
114394
95347
107716
113351
113351
106666
100485
99988
105623
100485
90713
83979
91210
74207
89663
97888
100485
94801
87619
92757
94801
93254
77791
70616
75747
60291
76251
81935
86569
78841
71610
75747
77791
73703
58247
51513
57694
40691
59241
70616




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=307017&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=307017&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=307017&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
alpha0.405343002238495
beta0.0645195510983699
gamma1

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.405343002238495 \tabularnewline
beta & 0.0645195510983699 \tabularnewline
gamma & 1 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=307017&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]0.405343002238495[/C][/ROW]
[ROW][C]beta[/C][C]0.0645195510983699[/C][/ROW]
[ROW][C]gamma[/C][C]1[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=307017&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=307017&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
alpha0.405343002238495
beta0.0645195510983699
gamma1







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
13131901131895.2638888895.73611111106584
14131901131605.780661979295.219338021154
15130907130426.358173431480.641826568753
16128310127816.832068443493.167931557022
17141722141363.489264061358.510735938675
18143766143432.481743827333.518256172887
19140679135714.9410491964964.0589508035
20133448133101.972081074346.027918925742
21136542134260.8743953412281.1256046588
22131901135851.978929948-3950.97892994835
23133994135302.4486673-1308.44866730014
24134995135993.996954196-998.996954195929
25136038137039.972363133-1001.97236313342
26133448136574.103121349-3126.10312134936
27133994134088.596330985-94.5963309846993
28130354131208.76829149-854.768291490036
29141722144049.140251742-2327.14025174233
30145313144864.590450165448.409549835196
31142226139800.1377710072425.86222899298
32136542133198.7379475113343.26205248918
33142723136588.2067283436134.79327165656
34136038136001.12634745636.8736525437271
35142226138709.4582788363516.54172116393
36141722141737.001020871-15.0010208711901
37143269143401.997687922-132.9976879225
38137585142269.892672758-4684.89267275753
39143766141159.1424954372606.85750456271
40143269139196.8325138314072.16748616911
41152544153562.143277264-1018.14327726408
42150451156996.316111007-6545.31611100712
43142226150527.637758818-8301.63775881773
44138082140097.633654098-2015.63365409843
45143766142808.940899934957.059100065933
46136038136195.546453018-157.546453018382
47141722140587.8107619271134.18923807304
48142723140180.8526425852542.1473574148
49144816142510.3055647412305.69443525915
50140182139421.770742708760.229257292202
51142723144758.536332745-2035.53633274513
52144270141568.6943276112701.30567238925
53149954152098.36839901-2144.36839901013
54145313151506.82956759-6193.82956759029
55139132143862.97494716-4730.9749471597
56132447138438.472367043-5991.47236704326
57138635141022.097457783-2387.09745778321
58121625132019.070039912-10394.0700399124
59129857132391.165113593-2534.16511359307
60134491130599.5748610343891.42513896612
61139132132635.6842426396496.31575736083
62132447129736.7067306612710.29326933916
63132447133662.334658408-1215.33465840766
64132447133104.141380865-657.141380864748
65136038138785.535968644-2747.53596864367
66130907134920.250116724-4013.25011672385
67124173128465.985718307-4292.98571830735
68118538121916.720794371-3378.72079437133
69122626127218.368724973-4592.36872497344
70106666112017.969801136-5351.96980113561
71116445118697.578207704-2252.57820770402
72122129120438.2994789661690.70052103406
73123172122670.972447629501.02755237052
74117488114473.2654595063014.73454049394
75117985115578.6597337242406.34026627625
76116445116305.90193662139.09806338021
77121625120573.2838869851051.71611301515
78117985117100.997674746884.00232525407
79110810112199.194353065-1389.19435306535
80105623107180.317320652-1557.31732065155
81114394112355.8708584292038.1291415711
829534799422.1168576408-4075.11685764081
83107716108526.477635105-810.47763510533
84113351113298.4712429252.5287570798682
85113351114218.661698912-867.661698912023
86106666106984.15114344-318.151143439522
87100485106312.825753295-5827.82575329511
8899988102074.858650201-2086.85865020147
89105623105645.128602804-22.1286028035247
90100485101272.220265817-787.220265817203
919071393931.9050134829-3218.90501348287
928397987614.2192365884-3635.2192365884
939121093574.0519085118-2364.05190851176
947420774593.9765946707-386.976594670748
958966386604.45052777483058.54947222525
969788893028.91565841354859.08434158647
9710048595046.91143895675438.08856104329
989480190556.77370959434244.22629040571
998761988439.338108229-820.338108229014
1009275788567.60049537514189.39950462493
1019480196185.741236795-1384.74123679503
1029325491045.93179380262208.06820619738
1037779183792.4433401915-6001.44334019146
1047061676345.2664178553-5729.26641785525
1057574782403.3910546845-6656.39105468453
1066029162938.0629565151-2647.06295651509
1077625176101.1610480755149.838951924481
1088193582361.059353501-426.059353501041
1098656982386.60602514334182.39397485668
1107884176450.24110799432390.75889200569
1117161070294.06228970571315.9377102943
1127574774047.41919938141699.58080061861
1137779177056.6069895788734.393010421234
1147370374682.6632583546-979.663258354558
1155824760942.2395683878-2695.23956838783
1165151354770.5596701459-3257.55967014593
1175769461117.3921680892-3423.39216808921
1184069145269.4036955048-4578.40369550483
1195924159185.025283810355.9747161896594
1207061664934.14129014495681.85870985511

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 131901 & 131895.263888889 & 5.73611111106584 \tabularnewline
14 & 131901 & 131605.780661979 & 295.219338021154 \tabularnewline
15 & 130907 & 130426.358173431 & 480.641826568753 \tabularnewline
16 & 128310 & 127816.832068443 & 493.167931557022 \tabularnewline
17 & 141722 & 141363.489264061 & 358.510735938675 \tabularnewline
18 & 143766 & 143432.481743827 & 333.518256172887 \tabularnewline
19 & 140679 & 135714.941049196 & 4964.0589508035 \tabularnewline
20 & 133448 & 133101.972081074 & 346.027918925742 \tabularnewline
21 & 136542 & 134260.874395341 & 2281.1256046588 \tabularnewline
22 & 131901 & 135851.978929948 & -3950.97892994835 \tabularnewline
23 & 133994 & 135302.4486673 & -1308.44866730014 \tabularnewline
24 & 134995 & 135993.996954196 & -998.996954195929 \tabularnewline
25 & 136038 & 137039.972363133 & -1001.97236313342 \tabularnewline
26 & 133448 & 136574.103121349 & -3126.10312134936 \tabularnewline
27 & 133994 & 134088.596330985 & -94.5963309846993 \tabularnewline
28 & 130354 & 131208.76829149 & -854.768291490036 \tabularnewline
29 & 141722 & 144049.140251742 & -2327.14025174233 \tabularnewline
30 & 145313 & 144864.590450165 & 448.409549835196 \tabularnewline
31 & 142226 & 139800.137771007 & 2425.86222899298 \tabularnewline
32 & 136542 & 133198.737947511 & 3343.26205248918 \tabularnewline
33 & 142723 & 136588.206728343 & 6134.79327165656 \tabularnewline
34 & 136038 & 136001.126347456 & 36.8736525437271 \tabularnewline
35 & 142226 & 138709.458278836 & 3516.54172116393 \tabularnewline
36 & 141722 & 141737.001020871 & -15.0010208711901 \tabularnewline
37 & 143269 & 143401.997687922 & -132.9976879225 \tabularnewline
38 & 137585 & 142269.892672758 & -4684.89267275753 \tabularnewline
39 & 143766 & 141159.142495437 & 2606.85750456271 \tabularnewline
40 & 143269 & 139196.832513831 & 4072.16748616911 \tabularnewline
41 & 152544 & 153562.143277264 & -1018.14327726408 \tabularnewline
42 & 150451 & 156996.316111007 & -6545.31611100712 \tabularnewline
43 & 142226 & 150527.637758818 & -8301.63775881773 \tabularnewline
44 & 138082 & 140097.633654098 & -2015.63365409843 \tabularnewline
45 & 143766 & 142808.940899934 & 957.059100065933 \tabularnewline
46 & 136038 & 136195.546453018 & -157.546453018382 \tabularnewline
47 & 141722 & 140587.810761927 & 1134.18923807304 \tabularnewline
48 & 142723 & 140180.852642585 & 2542.1473574148 \tabularnewline
49 & 144816 & 142510.305564741 & 2305.69443525915 \tabularnewline
50 & 140182 & 139421.770742708 & 760.229257292202 \tabularnewline
51 & 142723 & 144758.536332745 & -2035.53633274513 \tabularnewline
52 & 144270 & 141568.694327611 & 2701.30567238925 \tabularnewline
53 & 149954 & 152098.36839901 & -2144.36839901013 \tabularnewline
54 & 145313 & 151506.82956759 & -6193.82956759029 \tabularnewline
55 & 139132 & 143862.97494716 & -4730.9749471597 \tabularnewline
56 & 132447 & 138438.472367043 & -5991.47236704326 \tabularnewline
57 & 138635 & 141022.097457783 & -2387.09745778321 \tabularnewline
58 & 121625 & 132019.070039912 & -10394.0700399124 \tabularnewline
59 & 129857 & 132391.165113593 & -2534.16511359307 \tabularnewline
60 & 134491 & 130599.574861034 & 3891.42513896612 \tabularnewline
61 & 139132 & 132635.684242639 & 6496.31575736083 \tabularnewline
62 & 132447 & 129736.706730661 & 2710.29326933916 \tabularnewline
63 & 132447 & 133662.334658408 & -1215.33465840766 \tabularnewline
64 & 132447 & 133104.141380865 & -657.141380864748 \tabularnewline
65 & 136038 & 138785.535968644 & -2747.53596864367 \tabularnewline
66 & 130907 & 134920.250116724 & -4013.25011672385 \tabularnewline
67 & 124173 & 128465.985718307 & -4292.98571830735 \tabularnewline
68 & 118538 & 121916.720794371 & -3378.72079437133 \tabularnewline
69 & 122626 & 127218.368724973 & -4592.36872497344 \tabularnewline
70 & 106666 & 112017.969801136 & -5351.96980113561 \tabularnewline
71 & 116445 & 118697.578207704 & -2252.57820770402 \tabularnewline
72 & 122129 & 120438.299478966 & 1690.70052103406 \tabularnewline
73 & 123172 & 122670.972447629 & 501.02755237052 \tabularnewline
74 & 117488 & 114473.265459506 & 3014.73454049394 \tabularnewline
75 & 117985 & 115578.659733724 & 2406.34026627625 \tabularnewline
76 & 116445 & 116305.90193662 & 139.09806338021 \tabularnewline
77 & 121625 & 120573.283886985 & 1051.71611301515 \tabularnewline
78 & 117985 & 117100.997674746 & 884.00232525407 \tabularnewline
79 & 110810 & 112199.194353065 & -1389.19435306535 \tabularnewline
80 & 105623 & 107180.317320652 & -1557.31732065155 \tabularnewline
81 & 114394 & 112355.870858429 & 2038.1291415711 \tabularnewline
82 & 95347 & 99422.1168576408 & -4075.11685764081 \tabularnewline
83 & 107716 & 108526.477635105 & -810.47763510533 \tabularnewline
84 & 113351 & 113298.47124292 & 52.5287570798682 \tabularnewline
85 & 113351 & 114218.661698912 & -867.661698912023 \tabularnewline
86 & 106666 & 106984.15114344 & -318.151143439522 \tabularnewline
87 & 100485 & 106312.825753295 & -5827.82575329511 \tabularnewline
88 & 99988 & 102074.858650201 & -2086.85865020147 \tabularnewline
89 & 105623 & 105645.128602804 & -22.1286028035247 \tabularnewline
90 & 100485 & 101272.220265817 & -787.220265817203 \tabularnewline
91 & 90713 & 93931.9050134829 & -3218.90501348287 \tabularnewline
92 & 83979 & 87614.2192365884 & -3635.2192365884 \tabularnewline
93 & 91210 & 93574.0519085118 & -2364.05190851176 \tabularnewline
94 & 74207 & 74593.9765946707 & -386.976594670748 \tabularnewline
95 & 89663 & 86604.4505277748 & 3058.54947222525 \tabularnewline
96 & 97888 & 93028.9156584135 & 4859.08434158647 \tabularnewline
97 & 100485 & 95046.9114389567 & 5438.08856104329 \tabularnewline
98 & 94801 & 90556.7737095943 & 4244.22629040571 \tabularnewline
99 & 87619 & 88439.338108229 & -820.338108229014 \tabularnewline
100 & 92757 & 88567.6004953751 & 4189.39950462493 \tabularnewline
101 & 94801 & 96185.741236795 & -1384.74123679503 \tabularnewline
102 & 93254 & 91045.9317938026 & 2208.06820619738 \tabularnewline
103 & 77791 & 83792.4433401915 & -6001.44334019146 \tabularnewline
104 & 70616 & 76345.2664178553 & -5729.26641785525 \tabularnewline
105 & 75747 & 82403.3910546845 & -6656.39105468453 \tabularnewline
106 & 60291 & 62938.0629565151 & -2647.06295651509 \tabularnewline
107 & 76251 & 76101.1610480755 & 149.838951924481 \tabularnewline
108 & 81935 & 82361.059353501 & -426.059353501041 \tabularnewline
109 & 86569 & 82386.6060251433 & 4182.39397485668 \tabularnewline
110 & 78841 & 76450.2411079943 & 2390.75889200569 \tabularnewline
111 & 71610 & 70294.0622897057 & 1315.9377102943 \tabularnewline
112 & 75747 & 74047.4191993814 & 1699.58080061861 \tabularnewline
113 & 77791 & 77056.6069895788 & 734.393010421234 \tabularnewline
114 & 73703 & 74682.6632583546 & -979.663258354558 \tabularnewline
115 & 58247 & 60942.2395683878 & -2695.23956838783 \tabularnewline
116 & 51513 & 54770.5596701459 & -3257.55967014593 \tabularnewline
117 & 57694 & 61117.3921680892 & -3423.39216808921 \tabularnewline
118 & 40691 & 45269.4036955048 & -4578.40369550483 \tabularnewline
119 & 59241 & 59185.0252838103 & 55.9747161896594 \tabularnewline
120 & 70616 & 64934.1412901449 & 5681.85870985511 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=307017&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]131901[/C][C]131895.263888889[/C][C]5.73611111106584[/C][/ROW]
[ROW][C]14[/C][C]131901[/C][C]131605.780661979[/C][C]295.219338021154[/C][/ROW]
[ROW][C]15[/C][C]130907[/C][C]130426.358173431[/C][C]480.641826568753[/C][/ROW]
[ROW][C]16[/C][C]128310[/C][C]127816.832068443[/C][C]493.167931557022[/C][/ROW]
[ROW][C]17[/C][C]141722[/C][C]141363.489264061[/C][C]358.510735938675[/C][/ROW]
[ROW][C]18[/C][C]143766[/C][C]143432.481743827[/C][C]333.518256172887[/C][/ROW]
[ROW][C]19[/C][C]140679[/C][C]135714.941049196[/C][C]4964.0589508035[/C][/ROW]
[ROW][C]20[/C][C]133448[/C][C]133101.972081074[/C][C]346.027918925742[/C][/ROW]
[ROW][C]21[/C][C]136542[/C][C]134260.874395341[/C][C]2281.1256046588[/C][/ROW]
[ROW][C]22[/C][C]131901[/C][C]135851.978929948[/C][C]-3950.97892994835[/C][/ROW]
[ROW][C]23[/C][C]133994[/C][C]135302.4486673[/C][C]-1308.44866730014[/C][/ROW]
[ROW][C]24[/C][C]134995[/C][C]135993.996954196[/C][C]-998.996954195929[/C][/ROW]
[ROW][C]25[/C][C]136038[/C][C]137039.972363133[/C][C]-1001.97236313342[/C][/ROW]
[ROW][C]26[/C][C]133448[/C][C]136574.103121349[/C][C]-3126.10312134936[/C][/ROW]
[ROW][C]27[/C][C]133994[/C][C]134088.596330985[/C][C]-94.5963309846993[/C][/ROW]
[ROW][C]28[/C][C]130354[/C][C]131208.76829149[/C][C]-854.768291490036[/C][/ROW]
[ROW][C]29[/C][C]141722[/C][C]144049.140251742[/C][C]-2327.14025174233[/C][/ROW]
[ROW][C]30[/C][C]145313[/C][C]144864.590450165[/C][C]448.409549835196[/C][/ROW]
[ROW][C]31[/C][C]142226[/C][C]139800.137771007[/C][C]2425.86222899298[/C][/ROW]
[ROW][C]32[/C][C]136542[/C][C]133198.737947511[/C][C]3343.26205248918[/C][/ROW]
[ROW][C]33[/C][C]142723[/C][C]136588.206728343[/C][C]6134.79327165656[/C][/ROW]
[ROW][C]34[/C][C]136038[/C][C]136001.126347456[/C][C]36.8736525437271[/C][/ROW]
[ROW][C]35[/C][C]142226[/C][C]138709.458278836[/C][C]3516.54172116393[/C][/ROW]
[ROW][C]36[/C][C]141722[/C][C]141737.001020871[/C][C]-15.0010208711901[/C][/ROW]
[ROW][C]37[/C][C]143269[/C][C]143401.997687922[/C][C]-132.9976879225[/C][/ROW]
[ROW][C]38[/C][C]137585[/C][C]142269.892672758[/C][C]-4684.89267275753[/C][/ROW]
[ROW][C]39[/C][C]143766[/C][C]141159.142495437[/C][C]2606.85750456271[/C][/ROW]
[ROW][C]40[/C][C]143269[/C][C]139196.832513831[/C][C]4072.16748616911[/C][/ROW]
[ROW][C]41[/C][C]152544[/C][C]153562.143277264[/C][C]-1018.14327726408[/C][/ROW]
[ROW][C]42[/C][C]150451[/C][C]156996.316111007[/C][C]-6545.31611100712[/C][/ROW]
[ROW][C]43[/C][C]142226[/C][C]150527.637758818[/C][C]-8301.63775881773[/C][/ROW]
[ROW][C]44[/C][C]138082[/C][C]140097.633654098[/C][C]-2015.63365409843[/C][/ROW]
[ROW][C]45[/C][C]143766[/C][C]142808.940899934[/C][C]957.059100065933[/C][/ROW]
[ROW][C]46[/C][C]136038[/C][C]136195.546453018[/C][C]-157.546453018382[/C][/ROW]
[ROW][C]47[/C][C]141722[/C][C]140587.810761927[/C][C]1134.18923807304[/C][/ROW]
[ROW][C]48[/C][C]142723[/C][C]140180.852642585[/C][C]2542.1473574148[/C][/ROW]
[ROW][C]49[/C][C]144816[/C][C]142510.305564741[/C][C]2305.69443525915[/C][/ROW]
[ROW][C]50[/C][C]140182[/C][C]139421.770742708[/C][C]760.229257292202[/C][/ROW]
[ROW][C]51[/C][C]142723[/C][C]144758.536332745[/C][C]-2035.53633274513[/C][/ROW]
[ROW][C]52[/C][C]144270[/C][C]141568.694327611[/C][C]2701.30567238925[/C][/ROW]
[ROW][C]53[/C][C]149954[/C][C]152098.36839901[/C][C]-2144.36839901013[/C][/ROW]
[ROW][C]54[/C][C]145313[/C][C]151506.82956759[/C][C]-6193.82956759029[/C][/ROW]
[ROW][C]55[/C][C]139132[/C][C]143862.97494716[/C][C]-4730.9749471597[/C][/ROW]
[ROW][C]56[/C][C]132447[/C][C]138438.472367043[/C][C]-5991.47236704326[/C][/ROW]
[ROW][C]57[/C][C]138635[/C][C]141022.097457783[/C][C]-2387.09745778321[/C][/ROW]
[ROW][C]58[/C][C]121625[/C][C]132019.070039912[/C][C]-10394.0700399124[/C][/ROW]
[ROW][C]59[/C][C]129857[/C][C]132391.165113593[/C][C]-2534.16511359307[/C][/ROW]
[ROW][C]60[/C][C]134491[/C][C]130599.574861034[/C][C]3891.42513896612[/C][/ROW]
[ROW][C]61[/C][C]139132[/C][C]132635.684242639[/C][C]6496.31575736083[/C][/ROW]
[ROW][C]62[/C][C]132447[/C][C]129736.706730661[/C][C]2710.29326933916[/C][/ROW]
[ROW][C]63[/C][C]132447[/C][C]133662.334658408[/C][C]-1215.33465840766[/C][/ROW]
[ROW][C]64[/C][C]132447[/C][C]133104.141380865[/C][C]-657.141380864748[/C][/ROW]
[ROW][C]65[/C][C]136038[/C][C]138785.535968644[/C][C]-2747.53596864367[/C][/ROW]
[ROW][C]66[/C][C]130907[/C][C]134920.250116724[/C][C]-4013.25011672385[/C][/ROW]
[ROW][C]67[/C][C]124173[/C][C]128465.985718307[/C][C]-4292.98571830735[/C][/ROW]
[ROW][C]68[/C][C]118538[/C][C]121916.720794371[/C][C]-3378.72079437133[/C][/ROW]
[ROW][C]69[/C][C]122626[/C][C]127218.368724973[/C][C]-4592.36872497344[/C][/ROW]
[ROW][C]70[/C][C]106666[/C][C]112017.969801136[/C][C]-5351.96980113561[/C][/ROW]
[ROW][C]71[/C][C]116445[/C][C]118697.578207704[/C][C]-2252.57820770402[/C][/ROW]
[ROW][C]72[/C][C]122129[/C][C]120438.299478966[/C][C]1690.70052103406[/C][/ROW]
[ROW][C]73[/C][C]123172[/C][C]122670.972447629[/C][C]501.02755237052[/C][/ROW]
[ROW][C]74[/C][C]117488[/C][C]114473.265459506[/C][C]3014.73454049394[/C][/ROW]
[ROW][C]75[/C][C]117985[/C][C]115578.659733724[/C][C]2406.34026627625[/C][/ROW]
[ROW][C]76[/C][C]116445[/C][C]116305.90193662[/C][C]139.09806338021[/C][/ROW]
[ROW][C]77[/C][C]121625[/C][C]120573.283886985[/C][C]1051.71611301515[/C][/ROW]
[ROW][C]78[/C][C]117985[/C][C]117100.997674746[/C][C]884.00232525407[/C][/ROW]
[ROW][C]79[/C][C]110810[/C][C]112199.194353065[/C][C]-1389.19435306535[/C][/ROW]
[ROW][C]80[/C][C]105623[/C][C]107180.317320652[/C][C]-1557.31732065155[/C][/ROW]
[ROW][C]81[/C][C]114394[/C][C]112355.870858429[/C][C]2038.1291415711[/C][/ROW]
[ROW][C]82[/C][C]95347[/C][C]99422.1168576408[/C][C]-4075.11685764081[/C][/ROW]
[ROW][C]83[/C][C]107716[/C][C]108526.477635105[/C][C]-810.47763510533[/C][/ROW]
[ROW][C]84[/C][C]113351[/C][C]113298.47124292[/C][C]52.5287570798682[/C][/ROW]
[ROW][C]85[/C][C]113351[/C][C]114218.661698912[/C][C]-867.661698912023[/C][/ROW]
[ROW][C]86[/C][C]106666[/C][C]106984.15114344[/C][C]-318.151143439522[/C][/ROW]
[ROW][C]87[/C][C]100485[/C][C]106312.825753295[/C][C]-5827.82575329511[/C][/ROW]
[ROW][C]88[/C][C]99988[/C][C]102074.858650201[/C][C]-2086.85865020147[/C][/ROW]
[ROW][C]89[/C][C]105623[/C][C]105645.128602804[/C][C]-22.1286028035247[/C][/ROW]
[ROW][C]90[/C][C]100485[/C][C]101272.220265817[/C][C]-787.220265817203[/C][/ROW]
[ROW][C]91[/C][C]90713[/C][C]93931.9050134829[/C][C]-3218.90501348287[/C][/ROW]
[ROW][C]92[/C][C]83979[/C][C]87614.2192365884[/C][C]-3635.2192365884[/C][/ROW]
[ROW][C]93[/C][C]91210[/C][C]93574.0519085118[/C][C]-2364.05190851176[/C][/ROW]
[ROW][C]94[/C][C]74207[/C][C]74593.9765946707[/C][C]-386.976594670748[/C][/ROW]
[ROW][C]95[/C][C]89663[/C][C]86604.4505277748[/C][C]3058.54947222525[/C][/ROW]
[ROW][C]96[/C][C]97888[/C][C]93028.9156584135[/C][C]4859.08434158647[/C][/ROW]
[ROW][C]97[/C][C]100485[/C][C]95046.9114389567[/C][C]5438.08856104329[/C][/ROW]
[ROW][C]98[/C][C]94801[/C][C]90556.7737095943[/C][C]4244.22629040571[/C][/ROW]
[ROW][C]99[/C][C]87619[/C][C]88439.338108229[/C][C]-820.338108229014[/C][/ROW]
[ROW][C]100[/C][C]92757[/C][C]88567.6004953751[/C][C]4189.39950462493[/C][/ROW]
[ROW][C]101[/C][C]94801[/C][C]96185.741236795[/C][C]-1384.74123679503[/C][/ROW]
[ROW][C]102[/C][C]93254[/C][C]91045.9317938026[/C][C]2208.06820619738[/C][/ROW]
[ROW][C]103[/C][C]77791[/C][C]83792.4433401915[/C][C]-6001.44334019146[/C][/ROW]
[ROW][C]104[/C][C]70616[/C][C]76345.2664178553[/C][C]-5729.26641785525[/C][/ROW]
[ROW][C]105[/C][C]75747[/C][C]82403.3910546845[/C][C]-6656.39105468453[/C][/ROW]
[ROW][C]106[/C][C]60291[/C][C]62938.0629565151[/C][C]-2647.06295651509[/C][/ROW]
[ROW][C]107[/C][C]76251[/C][C]76101.1610480755[/C][C]149.838951924481[/C][/ROW]
[ROW][C]108[/C][C]81935[/C][C]82361.059353501[/C][C]-426.059353501041[/C][/ROW]
[ROW][C]109[/C][C]86569[/C][C]82386.6060251433[/C][C]4182.39397485668[/C][/ROW]
[ROW][C]110[/C][C]78841[/C][C]76450.2411079943[/C][C]2390.75889200569[/C][/ROW]
[ROW][C]111[/C][C]71610[/C][C]70294.0622897057[/C][C]1315.9377102943[/C][/ROW]
[ROW][C]112[/C][C]75747[/C][C]74047.4191993814[/C][C]1699.58080061861[/C][/ROW]
[ROW][C]113[/C][C]77791[/C][C]77056.6069895788[/C][C]734.393010421234[/C][/ROW]
[ROW][C]114[/C][C]73703[/C][C]74682.6632583546[/C][C]-979.663258354558[/C][/ROW]
[ROW][C]115[/C][C]58247[/C][C]60942.2395683878[/C][C]-2695.23956838783[/C][/ROW]
[ROW][C]116[/C][C]51513[/C][C]54770.5596701459[/C][C]-3257.55967014593[/C][/ROW]
[ROW][C]117[/C][C]57694[/C][C]61117.3921680892[/C][C]-3423.39216808921[/C][/ROW]
[ROW][C]118[/C][C]40691[/C][C]45269.4036955048[/C][C]-4578.40369550483[/C][/ROW]
[ROW][C]119[/C][C]59241[/C][C]59185.0252838103[/C][C]55.9747161896594[/C][/ROW]
[ROW][C]120[/C][C]70616[/C][C]64934.1412901449[/C][C]5681.85870985511[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=307017&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=307017&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
13131901131895.2638888895.73611111106584
14131901131605.780661979295.219338021154
15130907130426.358173431480.641826568753
16128310127816.832068443493.167931557022
17141722141363.489264061358.510735938675
18143766143432.481743827333.518256172887
19140679135714.9410491964964.0589508035
20133448133101.972081074346.027918925742
21136542134260.8743953412281.1256046588
22131901135851.978929948-3950.97892994835
23133994135302.4486673-1308.44866730014
24134995135993.996954196-998.996954195929
25136038137039.972363133-1001.97236313342
26133448136574.103121349-3126.10312134936
27133994134088.596330985-94.5963309846993
28130354131208.76829149-854.768291490036
29141722144049.140251742-2327.14025174233
30145313144864.590450165448.409549835196
31142226139800.1377710072425.86222899298
32136542133198.7379475113343.26205248918
33142723136588.2067283436134.79327165656
34136038136001.12634745636.8736525437271
35142226138709.4582788363516.54172116393
36141722141737.001020871-15.0010208711901
37143269143401.997687922-132.9976879225
38137585142269.892672758-4684.89267275753
39143766141159.1424954372606.85750456271
40143269139196.8325138314072.16748616911
41152544153562.143277264-1018.14327726408
42150451156996.316111007-6545.31611100712
43142226150527.637758818-8301.63775881773
44138082140097.633654098-2015.63365409843
45143766142808.940899934957.059100065933
46136038136195.546453018-157.546453018382
47141722140587.8107619271134.18923807304
48142723140180.8526425852542.1473574148
49144816142510.3055647412305.69443525915
50140182139421.770742708760.229257292202
51142723144758.536332745-2035.53633274513
52144270141568.6943276112701.30567238925
53149954152098.36839901-2144.36839901013
54145313151506.82956759-6193.82956759029
55139132143862.97494716-4730.9749471597
56132447138438.472367043-5991.47236704326
57138635141022.097457783-2387.09745778321
58121625132019.070039912-10394.0700399124
59129857132391.165113593-2534.16511359307
60134491130599.5748610343891.42513896612
61139132132635.6842426396496.31575736083
62132447129736.7067306612710.29326933916
63132447133662.334658408-1215.33465840766
64132447133104.141380865-657.141380864748
65136038138785.535968644-2747.53596864367
66130907134920.250116724-4013.25011672385
67124173128465.985718307-4292.98571830735
68118538121916.720794371-3378.72079437133
69122626127218.368724973-4592.36872497344
70106666112017.969801136-5351.96980113561
71116445118697.578207704-2252.57820770402
72122129120438.2994789661690.70052103406
73123172122670.972447629501.02755237052
74117488114473.2654595063014.73454049394
75117985115578.6597337242406.34026627625
76116445116305.90193662139.09806338021
77121625120573.2838869851051.71611301515
78117985117100.997674746884.00232525407
79110810112199.194353065-1389.19435306535
80105623107180.317320652-1557.31732065155
81114394112355.8708584292038.1291415711
829534799422.1168576408-4075.11685764081
83107716108526.477635105-810.47763510533
84113351113298.4712429252.5287570798682
85113351114218.661698912-867.661698912023
86106666106984.15114344-318.151143439522
87100485106312.825753295-5827.82575329511
8899988102074.858650201-2086.85865020147
89105623105645.128602804-22.1286028035247
90100485101272.220265817-787.220265817203
919071393931.9050134829-3218.90501348287
928397987614.2192365884-3635.2192365884
939121093574.0519085118-2364.05190851176
947420774593.9765946707-386.976594670748
958966386604.45052777483058.54947222525
969788893028.91565841354859.08434158647
9710048595046.91143895675438.08856104329
989480190556.77370959434244.22629040571
998761988439.338108229-820.338108229014
1009275788567.60049537514189.39950462493
1019480196185.741236795-1384.74123679503
1029325491045.93179380262208.06820619738
1037779183792.4433401915-6001.44334019146
1047061676345.2664178553-5729.26641785525
1057574782403.3910546845-6656.39105468453
1066029162938.0629565151-2647.06295651509
1077625176101.1610480755149.838951924481
1088193582361.059353501-426.059353501041
1098656982386.60602514334182.39397485668
1107884176450.24110799432390.75889200569
1117161070294.06228970571315.9377102943
1127574774047.41919938141699.58080061861
1137779177056.6069895788734.393010421234
1147370374682.6632583546-979.663258354558
1155824760942.2395683878-2695.23956838783
1165151354770.5596701459-3257.55967014593
1175769461117.3921680892-3423.39216808921
1184069145269.4036955048-4578.40369550483
1195924159185.025283810355.9747161896594
1207061664934.14129014495681.85870985511







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
12170205.403320587463814.602916837276596.2037243376
12261428.410165217954468.043920473568388.7764099623
12353521.563816529645971.677153213961071.4504798453
12456792.795300970148634.335299186164951.2553027541
12558317.810532618349532.504056877367103.1170083594
12654386.400229401544956.65589876363816.14456004
12739808.00746918529716.835926565549899.1790118044
12834250.034610887523480.982960295445019.0862614796
12941759.474282587830296.571600928953222.3769642467
13026642.620224296414470.33181549338814.9086330998
13145319.990232006132423.178850770358216.8016132419
13254540.483649995540904.376336184768176.5909638062

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
121 & 70205.4033205874 & 63814.6029168372 & 76596.2037243376 \tabularnewline
122 & 61428.4101652179 & 54468.0439204735 & 68388.7764099623 \tabularnewline
123 & 53521.5638165296 & 45971.6771532139 & 61071.4504798453 \tabularnewline
124 & 56792.7953009701 & 48634.3352991861 & 64951.2553027541 \tabularnewline
125 & 58317.8105326183 & 49532.5040568773 & 67103.1170083594 \tabularnewline
126 & 54386.4002294015 & 44956.655898763 & 63816.14456004 \tabularnewline
127 & 39808.007469185 & 29716.8359265655 & 49899.1790118044 \tabularnewline
128 & 34250.0346108875 & 23480.9829602954 & 45019.0862614796 \tabularnewline
129 & 41759.4742825878 & 30296.5716009289 & 53222.3769642467 \tabularnewline
130 & 26642.6202242964 & 14470.331815493 & 38814.9086330998 \tabularnewline
131 & 45319.9902320061 & 32423.1788507703 & 58216.8016132419 \tabularnewline
132 & 54540.4836499955 & 40904.3763361847 & 68176.5909638062 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=307017&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]121[/C][C]70205.4033205874[/C][C]63814.6029168372[/C][C]76596.2037243376[/C][/ROW]
[ROW][C]122[/C][C]61428.4101652179[/C][C]54468.0439204735[/C][C]68388.7764099623[/C][/ROW]
[ROW][C]123[/C][C]53521.5638165296[/C][C]45971.6771532139[/C][C]61071.4504798453[/C][/ROW]
[ROW][C]124[/C][C]56792.7953009701[/C][C]48634.3352991861[/C][C]64951.2553027541[/C][/ROW]
[ROW][C]125[/C][C]58317.8105326183[/C][C]49532.5040568773[/C][C]67103.1170083594[/C][/ROW]
[ROW][C]126[/C][C]54386.4002294015[/C][C]44956.655898763[/C][C]63816.14456004[/C][/ROW]
[ROW][C]127[/C][C]39808.007469185[/C][C]29716.8359265655[/C][C]49899.1790118044[/C][/ROW]
[ROW][C]128[/C][C]34250.0346108875[/C][C]23480.9829602954[/C][C]45019.0862614796[/C][/ROW]
[ROW][C]129[/C][C]41759.4742825878[/C][C]30296.5716009289[/C][C]53222.3769642467[/C][/ROW]
[ROW][C]130[/C][C]26642.6202242964[/C][C]14470.331815493[/C][C]38814.9086330998[/C][/ROW]
[ROW][C]131[/C][C]45319.9902320061[/C][C]32423.1788507703[/C][C]58216.8016132419[/C][/ROW]
[ROW][C]132[/C][C]54540.4836499955[/C][C]40904.3763361847[/C][C]68176.5909638062[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=307017&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=307017&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
12170205.403320587463814.602916837276596.2037243376
12261428.410165217954468.043920473568388.7764099623
12353521.563816529645971.677153213961071.4504798453
12456792.795300970148634.335299186164951.2553027541
12558317.810532618349532.504056877367103.1170083594
12654386.400229401544956.65589876363816.14456004
12739808.00746918529716.835926565549899.1790118044
12834250.034610887523480.982960295445019.0862614796
12941759.474282587830296.571600928953222.3769642467
13026642.620224296414470.33181549338814.9086330998
13145319.990232006132423.178850770358216.8016132419
13254540.483649995540904.376336184768176.5909638062



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