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 computationWed, 07 Dec 2016 17:36:02 +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/07/t1481128580khwh5t7w0l2wcfh.htm/, Retrieved Tue, 07 May 2024 10:41:26 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=298251, Retrieved Tue, 07 May 2024 10:41:26 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact59
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [N2323] [2016-12-07 16:36:02] [8263efc94e08b372ab727a2b95bd56b1] [Current]
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Dataseries X:
5963
5957
5920
5923
5943
5953
5966
5995
6027
6035
6083
6124
6150
6220
6279
6346
6414
6439
6495
6568
6604
6646
6691
6717
6719
6746
6740
6748
6753
6782
6788
6794
6816
6842
6855
6860
6873
6908
6962
6998
6996
7002
7019
6999
6979
6994
6973
6938
6974
6986
7015
7031
7073
7086
7083
7072
7102
7163
7193
7242
7258
7287
7301
7315
7333
7365
7375
7419
7436
7438
7455
7511
7559
7593
7609
7623
7664
7692
7740
7767
7743
7798
7842
7837
7830
7818
7830
7860
7913
7900
7934
7943
7935
7930
7943
7906
7961
7949
7886
7877
7853
7833
7829
7825
7851
7862
7864
7893
7867
7869
7871
7891
7876
7904
7930




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=298251&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=298251&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=298251&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
alpha1
beta0.283070566134478
gammaFALSE

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 1 \tabularnewline
beta & 0.283070566134478 \tabularnewline
gamma & FALSE \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=298251&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]1[/C][/ROW]
[ROW][C]beta[/C][C]0.283070566134478[/C][/ROW]
[ROW][C]gamma[/C][C]FALSE[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=298251&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=298251&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
alpha1
beta0.283070566134478
gammaFALSE







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
359205951-31
459235905.2248124498317.775187550169
559435913.256444852829.7435551471963
659535941.6759698471711.3240301528276
759665954.8814694734611.1185305265426
859955971.0287982041923.9712017958109
960276006.8143398674520.1856601325471
1060356044.52830610897-9.52830610897126
1160836049.831123104433.1688768955974
1261246107.2202558652816.7797441347157
1361506152.97010753709-2.97010753708946
1462206178.1293575150941.8706424849142
1562796259.981703987719.0182960122957
1663466324.3652238068221.634776193182
1764146397.4893921520216.5106078479848
1864396470.16305926277-31.163059262768
1964956486.341714434778.65828556522592
2065686544.7926202314823.2073797685234
2166046624.36194636105-20.3619463610503
2266466654.59807867703-8.59807867702784
2366916694.16421567825-3.16421567825273
2467176738.26851935484-21.2685193548386
2567196758.24802754022-39.2480275402222
2667466749.13806616475-3.13806616474994
2767406775.24977199893-35.2497719989269
2867486759.27159908308-11.2715990830793
2967536764.08094114939-11.080941149391
3067826765.9442528649316.0557471350694
3167886799.48916229617-11.4891622961668
3267946802.23691862058-8.23691862057967
3368166805.9052894034510.0947105965515
3468426830.7628048469811.2371951530222
3568556859.94372404071-4.94372404070782
3668606871.54430127769-11.5443012776923
3768736873.27644937939-0.276449379388396
3869086886.1981946970621.8018053029427
3969626927.3696440669234.6303559330845
4069986991.172478526336.82752147366773
4169967029.10514889518-33.1051488951789
4270027017.73405565545-15.7340556554545
4370197019.28020761347-0.280207613473067
4469997036.20088908569-37.2008890856923
4569797005.6704123515-26.6704123514992
4669946978.1208036281215.8791963718795
4769736997.61573673487-24.6157367348687
4869386969.64774620151-31.6477462015127
4969746925.6892007673748.3107992326304
5069866975.3645660565610.6354339434401
5170156990.3751443640124.6248556359851
5270317026.345716189874.6542838101268
5370737043.6632069429629.3367930570439
5470867093.96758956218-7.967589562184
5570837104.71219947409-21.7121994740892
5670727095.56611487693-23.5661148769341
5771027077.8952413971324.1047586028699
5871637114.7185890613848.2814109386209
5971937189.385635389553.61436461045378
6072427220.4087556260421.5912443739562
6172587275.52060139453-17.5206013945271
6272877286.561034838760.438965161238229
6373017315.68529295547-14.685292955467
6473157325.52831876471-10.5283187647119
6573337336.54806161154-3.54806161154102
6673657353.5437098024811.4562901975178
6773757388.78664835449-13.786648354494
6874197394.8840539996924.1159460003091
6974367445.71056848687-9.71056848686658
7074387459.9617923678-21.9617923678015
7174557455.74505536892-0.745055368920475
7275117472.5341521238438.4658478761612
7375597539.4227014589919.577298541014
7475937592.964458440370.0355415596250168
7576097626.97451920978-17.9745192097789
7676237637.88646188107-14.8864618810721
7776647647.6725426886616.3274573113422
7876927693.29436527332-1.29436527331563
7977407720.9279685626119.0720314373866
8077677774.32669929893-7.32669929892927
8177437799.25272638048-56.2527263804841
8277987759.3292352773538.6707647226476
8378427825.2757905402516.7242094597541
8478377874.00992198017-37.0099219801696
8578307858.53350241265-28.5335024126507
8678187843.4565077309-25.4565077309016
8778307824.250519675715.74948032429165
8878607837.8780283260822.1219716739151
8979137874.1401073718338.8598926281693
9079007938.14019917801-38.1401991780122
9179347914.3438314042119.6561685957895
9279437953.90791417666-10.9079141766551
9379357959.82020473532-24.8202047353234
9479307944.79433532932-14.7943353293213
9579437935.606494452077.39350554793236
9679067950.69937825324-44.699378253239
9779617901.0462999452459.9537000547643
9879497973.01742776159-24.0174277615943
9978867954.21880088803-68.2188008880257
10078777871.908066299645.09193370036246
10178537864.34944285492-11.3494428549184
10278337837.13674964067-4.13674964066558
10378297815.9657575779313.0342424220744
10478257815.655367959489.34463204052372
10578517814.3005582415136.6994417584947
10678627850.689089996911.3109100030979
10778647864.89087569497-0.890875694974966
10878937866.6386950076426.361304992357
10978677903.10080453587-36.1008045358731
11078697866.881729357992.11827064200679
11178717869.481349427851.51865057214764
11278917871.9112347050719.0887652949295
11378767897.31470230391-21.3147023039146
11479047876.2811374557627.7188625442423
11579307912.1275315687617.8724684312401

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
3 & 5920 & 5951 & -31 \tabularnewline
4 & 5923 & 5905.22481244983 & 17.775187550169 \tabularnewline
5 & 5943 & 5913.2564448528 & 29.7435551471963 \tabularnewline
6 & 5953 & 5941.67596984717 & 11.3240301528276 \tabularnewline
7 & 5966 & 5954.88146947346 & 11.1185305265426 \tabularnewline
8 & 5995 & 5971.02879820419 & 23.9712017958109 \tabularnewline
9 & 6027 & 6006.81433986745 & 20.1856601325471 \tabularnewline
10 & 6035 & 6044.52830610897 & -9.52830610897126 \tabularnewline
11 & 6083 & 6049.8311231044 & 33.1688768955974 \tabularnewline
12 & 6124 & 6107.22025586528 & 16.7797441347157 \tabularnewline
13 & 6150 & 6152.97010753709 & -2.97010753708946 \tabularnewline
14 & 6220 & 6178.12935751509 & 41.8706424849142 \tabularnewline
15 & 6279 & 6259.9817039877 & 19.0182960122957 \tabularnewline
16 & 6346 & 6324.36522380682 & 21.634776193182 \tabularnewline
17 & 6414 & 6397.48939215202 & 16.5106078479848 \tabularnewline
18 & 6439 & 6470.16305926277 & -31.163059262768 \tabularnewline
19 & 6495 & 6486.34171443477 & 8.65828556522592 \tabularnewline
20 & 6568 & 6544.79262023148 & 23.2073797685234 \tabularnewline
21 & 6604 & 6624.36194636105 & -20.3619463610503 \tabularnewline
22 & 6646 & 6654.59807867703 & -8.59807867702784 \tabularnewline
23 & 6691 & 6694.16421567825 & -3.16421567825273 \tabularnewline
24 & 6717 & 6738.26851935484 & -21.2685193548386 \tabularnewline
25 & 6719 & 6758.24802754022 & -39.2480275402222 \tabularnewline
26 & 6746 & 6749.13806616475 & -3.13806616474994 \tabularnewline
27 & 6740 & 6775.24977199893 & -35.2497719989269 \tabularnewline
28 & 6748 & 6759.27159908308 & -11.2715990830793 \tabularnewline
29 & 6753 & 6764.08094114939 & -11.080941149391 \tabularnewline
30 & 6782 & 6765.94425286493 & 16.0557471350694 \tabularnewline
31 & 6788 & 6799.48916229617 & -11.4891622961668 \tabularnewline
32 & 6794 & 6802.23691862058 & -8.23691862057967 \tabularnewline
33 & 6816 & 6805.90528940345 & 10.0947105965515 \tabularnewline
34 & 6842 & 6830.76280484698 & 11.2371951530222 \tabularnewline
35 & 6855 & 6859.94372404071 & -4.94372404070782 \tabularnewline
36 & 6860 & 6871.54430127769 & -11.5443012776923 \tabularnewline
37 & 6873 & 6873.27644937939 & -0.276449379388396 \tabularnewline
38 & 6908 & 6886.19819469706 & 21.8018053029427 \tabularnewline
39 & 6962 & 6927.36964406692 & 34.6303559330845 \tabularnewline
40 & 6998 & 6991.17247852633 & 6.82752147366773 \tabularnewline
41 & 6996 & 7029.10514889518 & -33.1051488951789 \tabularnewline
42 & 7002 & 7017.73405565545 & -15.7340556554545 \tabularnewline
43 & 7019 & 7019.28020761347 & -0.280207613473067 \tabularnewline
44 & 6999 & 7036.20088908569 & -37.2008890856923 \tabularnewline
45 & 6979 & 7005.6704123515 & -26.6704123514992 \tabularnewline
46 & 6994 & 6978.12080362812 & 15.8791963718795 \tabularnewline
47 & 6973 & 6997.61573673487 & -24.6157367348687 \tabularnewline
48 & 6938 & 6969.64774620151 & -31.6477462015127 \tabularnewline
49 & 6974 & 6925.68920076737 & 48.3107992326304 \tabularnewline
50 & 6986 & 6975.36456605656 & 10.6354339434401 \tabularnewline
51 & 7015 & 6990.37514436401 & 24.6248556359851 \tabularnewline
52 & 7031 & 7026.34571618987 & 4.6542838101268 \tabularnewline
53 & 7073 & 7043.66320694296 & 29.3367930570439 \tabularnewline
54 & 7086 & 7093.96758956218 & -7.967589562184 \tabularnewline
55 & 7083 & 7104.71219947409 & -21.7121994740892 \tabularnewline
56 & 7072 & 7095.56611487693 & -23.5661148769341 \tabularnewline
57 & 7102 & 7077.89524139713 & 24.1047586028699 \tabularnewline
58 & 7163 & 7114.71858906138 & 48.2814109386209 \tabularnewline
59 & 7193 & 7189.38563538955 & 3.61436461045378 \tabularnewline
60 & 7242 & 7220.40875562604 & 21.5912443739562 \tabularnewline
61 & 7258 & 7275.52060139453 & -17.5206013945271 \tabularnewline
62 & 7287 & 7286.56103483876 & 0.438965161238229 \tabularnewline
63 & 7301 & 7315.68529295547 & -14.685292955467 \tabularnewline
64 & 7315 & 7325.52831876471 & -10.5283187647119 \tabularnewline
65 & 7333 & 7336.54806161154 & -3.54806161154102 \tabularnewline
66 & 7365 & 7353.54370980248 & 11.4562901975178 \tabularnewline
67 & 7375 & 7388.78664835449 & -13.786648354494 \tabularnewline
68 & 7419 & 7394.88405399969 & 24.1159460003091 \tabularnewline
69 & 7436 & 7445.71056848687 & -9.71056848686658 \tabularnewline
70 & 7438 & 7459.9617923678 & -21.9617923678015 \tabularnewline
71 & 7455 & 7455.74505536892 & -0.745055368920475 \tabularnewline
72 & 7511 & 7472.53415212384 & 38.4658478761612 \tabularnewline
73 & 7559 & 7539.42270145899 & 19.577298541014 \tabularnewline
74 & 7593 & 7592.96445844037 & 0.0355415596250168 \tabularnewline
75 & 7609 & 7626.97451920978 & -17.9745192097789 \tabularnewline
76 & 7623 & 7637.88646188107 & -14.8864618810721 \tabularnewline
77 & 7664 & 7647.67254268866 & 16.3274573113422 \tabularnewline
78 & 7692 & 7693.29436527332 & -1.29436527331563 \tabularnewline
79 & 7740 & 7720.92796856261 & 19.0720314373866 \tabularnewline
80 & 7767 & 7774.32669929893 & -7.32669929892927 \tabularnewline
81 & 7743 & 7799.25272638048 & -56.2527263804841 \tabularnewline
82 & 7798 & 7759.32923527735 & 38.6707647226476 \tabularnewline
83 & 7842 & 7825.27579054025 & 16.7242094597541 \tabularnewline
84 & 7837 & 7874.00992198017 & -37.0099219801696 \tabularnewline
85 & 7830 & 7858.53350241265 & -28.5335024126507 \tabularnewline
86 & 7818 & 7843.4565077309 & -25.4565077309016 \tabularnewline
87 & 7830 & 7824.25051967571 & 5.74948032429165 \tabularnewline
88 & 7860 & 7837.87802832608 & 22.1219716739151 \tabularnewline
89 & 7913 & 7874.14010737183 & 38.8598926281693 \tabularnewline
90 & 7900 & 7938.14019917801 & -38.1401991780122 \tabularnewline
91 & 7934 & 7914.34383140421 & 19.6561685957895 \tabularnewline
92 & 7943 & 7953.90791417666 & -10.9079141766551 \tabularnewline
93 & 7935 & 7959.82020473532 & -24.8202047353234 \tabularnewline
94 & 7930 & 7944.79433532932 & -14.7943353293213 \tabularnewline
95 & 7943 & 7935.60649445207 & 7.39350554793236 \tabularnewline
96 & 7906 & 7950.69937825324 & -44.699378253239 \tabularnewline
97 & 7961 & 7901.04629994524 & 59.9537000547643 \tabularnewline
98 & 7949 & 7973.01742776159 & -24.0174277615943 \tabularnewline
99 & 7886 & 7954.21880088803 & -68.2188008880257 \tabularnewline
100 & 7877 & 7871.90806629964 & 5.09193370036246 \tabularnewline
101 & 7853 & 7864.34944285492 & -11.3494428549184 \tabularnewline
102 & 7833 & 7837.13674964067 & -4.13674964066558 \tabularnewline
103 & 7829 & 7815.96575757793 & 13.0342424220744 \tabularnewline
104 & 7825 & 7815.65536795948 & 9.34463204052372 \tabularnewline
105 & 7851 & 7814.30055824151 & 36.6994417584947 \tabularnewline
106 & 7862 & 7850.6890899969 & 11.3109100030979 \tabularnewline
107 & 7864 & 7864.89087569497 & -0.890875694974966 \tabularnewline
108 & 7893 & 7866.63869500764 & 26.361304992357 \tabularnewline
109 & 7867 & 7903.10080453587 & -36.1008045358731 \tabularnewline
110 & 7869 & 7866.88172935799 & 2.11827064200679 \tabularnewline
111 & 7871 & 7869.48134942785 & 1.51865057214764 \tabularnewline
112 & 7891 & 7871.91123470507 & 19.0887652949295 \tabularnewline
113 & 7876 & 7897.31470230391 & -21.3147023039146 \tabularnewline
114 & 7904 & 7876.28113745576 & 27.7188625442423 \tabularnewline
115 & 7930 & 7912.12753156876 & 17.8724684312401 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=298251&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]3[/C][C]5920[/C][C]5951[/C][C]-31[/C][/ROW]
[ROW][C]4[/C][C]5923[/C][C]5905.22481244983[/C][C]17.775187550169[/C][/ROW]
[ROW][C]5[/C][C]5943[/C][C]5913.2564448528[/C][C]29.7435551471963[/C][/ROW]
[ROW][C]6[/C][C]5953[/C][C]5941.67596984717[/C][C]11.3240301528276[/C][/ROW]
[ROW][C]7[/C][C]5966[/C][C]5954.88146947346[/C][C]11.1185305265426[/C][/ROW]
[ROW][C]8[/C][C]5995[/C][C]5971.02879820419[/C][C]23.9712017958109[/C][/ROW]
[ROW][C]9[/C][C]6027[/C][C]6006.81433986745[/C][C]20.1856601325471[/C][/ROW]
[ROW][C]10[/C][C]6035[/C][C]6044.52830610897[/C][C]-9.52830610897126[/C][/ROW]
[ROW][C]11[/C][C]6083[/C][C]6049.8311231044[/C][C]33.1688768955974[/C][/ROW]
[ROW][C]12[/C][C]6124[/C][C]6107.22025586528[/C][C]16.7797441347157[/C][/ROW]
[ROW][C]13[/C][C]6150[/C][C]6152.97010753709[/C][C]-2.97010753708946[/C][/ROW]
[ROW][C]14[/C][C]6220[/C][C]6178.12935751509[/C][C]41.8706424849142[/C][/ROW]
[ROW][C]15[/C][C]6279[/C][C]6259.9817039877[/C][C]19.0182960122957[/C][/ROW]
[ROW][C]16[/C][C]6346[/C][C]6324.36522380682[/C][C]21.634776193182[/C][/ROW]
[ROW][C]17[/C][C]6414[/C][C]6397.48939215202[/C][C]16.5106078479848[/C][/ROW]
[ROW][C]18[/C][C]6439[/C][C]6470.16305926277[/C][C]-31.163059262768[/C][/ROW]
[ROW][C]19[/C][C]6495[/C][C]6486.34171443477[/C][C]8.65828556522592[/C][/ROW]
[ROW][C]20[/C][C]6568[/C][C]6544.79262023148[/C][C]23.2073797685234[/C][/ROW]
[ROW][C]21[/C][C]6604[/C][C]6624.36194636105[/C][C]-20.3619463610503[/C][/ROW]
[ROW][C]22[/C][C]6646[/C][C]6654.59807867703[/C][C]-8.59807867702784[/C][/ROW]
[ROW][C]23[/C][C]6691[/C][C]6694.16421567825[/C][C]-3.16421567825273[/C][/ROW]
[ROW][C]24[/C][C]6717[/C][C]6738.26851935484[/C][C]-21.2685193548386[/C][/ROW]
[ROW][C]25[/C][C]6719[/C][C]6758.24802754022[/C][C]-39.2480275402222[/C][/ROW]
[ROW][C]26[/C][C]6746[/C][C]6749.13806616475[/C][C]-3.13806616474994[/C][/ROW]
[ROW][C]27[/C][C]6740[/C][C]6775.24977199893[/C][C]-35.2497719989269[/C][/ROW]
[ROW][C]28[/C][C]6748[/C][C]6759.27159908308[/C][C]-11.2715990830793[/C][/ROW]
[ROW][C]29[/C][C]6753[/C][C]6764.08094114939[/C][C]-11.080941149391[/C][/ROW]
[ROW][C]30[/C][C]6782[/C][C]6765.94425286493[/C][C]16.0557471350694[/C][/ROW]
[ROW][C]31[/C][C]6788[/C][C]6799.48916229617[/C][C]-11.4891622961668[/C][/ROW]
[ROW][C]32[/C][C]6794[/C][C]6802.23691862058[/C][C]-8.23691862057967[/C][/ROW]
[ROW][C]33[/C][C]6816[/C][C]6805.90528940345[/C][C]10.0947105965515[/C][/ROW]
[ROW][C]34[/C][C]6842[/C][C]6830.76280484698[/C][C]11.2371951530222[/C][/ROW]
[ROW][C]35[/C][C]6855[/C][C]6859.94372404071[/C][C]-4.94372404070782[/C][/ROW]
[ROW][C]36[/C][C]6860[/C][C]6871.54430127769[/C][C]-11.5443012776923[/C][/ROW]
[ROW][C]37[/C][C]6873[/C][C]6873.27644937939[/C][C]-0.276449379388396[/C][/ROW]
[ROW][C]38[/C][C]6908[/C][C]6886.19819469706[/C][C]21.8018053029427[/C][/ROW]
[ROW][C]39[/C][C]6962[/C][C]6927.36964406692[/C][C]34.6303559330845[/C][/ROW]
[ROW][C]40[/C][C]6998[/C][C]6991.17247852633[/C][C]6.82752147366773[/C][/ROW]
[ROW][C]41[/C][C]6996[/C][C]7029.10514889518[/C][C]-33.1051488951789[/C][/ROW]
[ROW][C]42[/C][C]7002[/C][C]7017.73405565545[/C][C]-15.7340556554545[/C][/ROW]
[ROW][C]43[/C][C]7019[/C][C]7019.28020761347[/C][C]-0.280207613473067[/C][/ROW]
[ROW][C]44[/C][C]6999[/C][C]7036.20088908569[/C][C]-37.2008890856923[/C][/ROW]
[ROW][C]45[/C][C]6979[/C][C]7005.6704123515[/C][C]-26.6704123514992[/C][/ROW]
[ROW][C]46[/C][C]6994[/C][C]6978.12080362812[/C][C]15.8791963718795[/C][/ROW]
[ROW][C]47[/C][C]6973[/C][C]6997.61573673487[/C][C]-24.6157367348687[/C][/ROW]
[ROW][C]48[/C][C]6938[/C][C]6969.64774620151[/C][C]-31.6477462015127[/C][/ROW]
[ROW][C]49[/C][C]6974[/C][C]6925.68920076737[/C][C]48.3107992326304[/C][/ROW]
[ROW][C]50[/C][C]6986[/C][C]6975.36456605656[/C][C]10.6354339434401[/C][/ROW]
[ROW][C]51[/C][C]7015[/C][C]6990.37514436401[/C][C]24.6248556359851[/C][/ROW]
[ROW][C]52[/C][C]7031[/C][C]7026.34571618987[/C][C]4.6542838101268[/C][/ROW]
[ROW][C]53[/C][C]7073[/C][C]7043.66320694296[/C][C]29.3367930570439[/C][/ROW]
[ROW][C]54[/C][C]7086[/C][C]7093.96758956218[/C][C]-7.967589562184[/C][/ROW]
[ROW][C]55[/C][C]7083[/C][C]7104.71219947409[/C][C]-21.7121994740892[/C][/ROW]
[ROW][C]56[/C][C]7072[/C][C]7095.56611487693[/C][C]-23.5661148769341[/C][/ROW]
[ROW][C]57[/C][C]7102[/C][C]7077.89524139713[/C][C]24.1047586028699[/C][/ROW]
[ROW][C]58[/C][C]7163[/C][C]7114.71858906138[/C][C]48.2814109386209[/C][/ROW]
[ROW][C]59[/C][C]7193[/C][C]7189.38563538955[/C][C]3.61436461045378[/C][/ROW]
[ROW][C]60[/C][C]7242[/C][C]7220.40875562604[/C][C]21.5912443739562[/C][/ROW]
[ROW][C]61[/C][C]7258[/C][C]7275.52060139453[/C][C]-17.5206013945271[/C][/ROW]
[ROW][C]62[/C][C]7287[/C][C]7286.56103483876[/C][C]0.438965161238229[/C][/ROW]
[ROW][C]63[/C][C]7301[/C][C]7315.68529295547[/C][C]-14.685292955467[/C][/ROW]
[ROW][C]64[/C][C]7315[/C][C]7325.52831876471[/C][C]-10.5283187647119[/C][/ROW]
[ROW][C]65[/C][C]7333[/C][C]7336.54806161154[/C][C]-3.54806161154102[/C][/ROW]
[ROW][C]66[/C][C]7365[/C][C]7353.54370980248[/C][C]11.4562901975178[/C][/ROW]
[ROW][C]67[/C][C]7375[/C][C]7388.78664835449[/C][C]-13.786648354494[/C][/ROW]
[ROW][C]68[/C][C]7419[/C][C]7394.88405399969[/C][C]24.1159460003091[/C][/ROW]
[ROW][C]69[/C][C]7436[/C][C]7445.71056848687[/C][C]-9.71056848686658[/C][/ROW]
[ROW][C]70[/C][C]7438[/C][C]7459.9617923678[/C][C]-21.9617923678015[/C][/ROW]
[ROW][C]71[/C][C]7455[/C][C]7455.74505536892[/C][C]-0.745055368920475[/C][/ROW]
[ROW][C]72[/C][C]7511[/C][C]7472.53415212384[/C][C]38.4658478761612[/C][/ROW]
[ROW][C]73[/C][C]7559[/C][C]7539.42270145899[/C][C]19.577298541014[/C][/ROW]
[ROW][C]74[/C][C]7593[/C][C]7592.96445844037[/C][C]0.0355415596250168[/C][/ROW]
[ROW][C]75[/C][C]7609[/C][C]7626.97451920978[/C][C]-17.9745192097789[/C][/ROW]
[ROW][C]76[/C][C]7623[/C][C]7637.88646188107[/C][C]-14.8864618810721[/C][/ROW]
[ROW][C]77[/C][C]7664[/C][C]7647.67254268866[/C][C]16.3274573113422[/C][/ROW]
[ROW][C]78[/C][C]7692[/C][C]7693.29436527332[/C][C]-1.29436527331563[/C][/ROW]
[ROW][C]79[/C][C]7740[/C][C]7720.92796856261[/C][C]19.0720314373866[/C][/ROW]
[ROW][C]80[/C][C]7767[/C][C]7774.32669929893[/C][C]-7.32669929892927[/C][/ROW]
[ROW][C]81[/C][C]7743[/C][C]7799.25272638048[/C][C]-56.2527263804841[/C][/ROW]
[ROW][C]82[/C][C]7798[/C][C]7759.32923527735[/C][C]38.6707647226476[/C][/ROW]
[ROW][C]83[/C][C]7842[/C][C]7825.27579054025[/C][C]16.7242094597541[/C][/ROW]
[ROW][C]84[/C][C]7837[/C][C]7874.00992198017[/C][C]-37.0099219801696[/C][/ROW]
[ROW][C]85[/C][C]7830[/C][C]7858.53350241265[/C][C]-28.5335024126507[/C][/ROW]
[ROW][C]86[/C][C]7818[/C][C]7843.4565077309[/C][C]-25.4565077309016[/C][/ROW]
[ROW][C]87[/C][C]7830[/C][C]7824.25051967571[/C][C]5.74948032429165[/C][/ROW]
[ROW][C]88[/C][C]7860[/C][C]7837.87802832608[/C][C]22.1219716739151[/C][/ROW]
[ROW][C]89[/C][C]7913[/C][C]7874.14010737183[/C][C]38.8598926281693[/C][/ROW]
[ROW][C]90[/C][C]7900[/C][C]7938.14019917801[/C][C]-38.1401991780122[/C][/ROW]
[ROW][C]91[/C][C]7934[/C][C]7914.34383140421[/C][C]19.6561685957895[/C][/ROW]
[ROW][C]92[/C][C]7943[/C][C]7953.90791417666[/C][C]-10.9079141766551[/C][/ROW]
[ROW][C]93[/C][C]7935[/C][C]7959.82020473532[/C][C]-24.8202047353234[/C][/ROW]
[ROW][C]94[/C][C]7930[/C][C]7944.79433532932[/C][C]-14.7943353293213[/C][/ROW]
[ROW][C]95[/C][C]7943[/C][C]7935.60649445207[/C][C]7.39350554793236[/C][/ROW]
[ROW][C]96[/C][C]7906[/C][C]7950.69937825324[/C][C]-44.699378253239[/C][/ROW]
[ROW][C]97[/C][C]7961[/C][C]7901.04629994524[/C][C]59.9537000547643[/C][/ROW]
[ROW][C]98[/C][C]7949[/C][C]7973.01742776159[/C][C]-24.0174277615943[/C][/ROW]
[ROW][C]99[/C][C]7886[/C][C]7954.21880088803[/C][C]-68.2188008880257[/C][/ROW]
[ROW][C]100[/C][C]7877[/C][C]7871.90806629964[/C][C]5.09193370036246[/C][/ROW]
[ROW][C]101[/C][C]7853[/C][C]7864.34944285492[/C][C]-11.3494428549184[/C][/ROW]
[ROW][C]102[/C][C]7833[/C][C]7837.13674964067[/C][C]-4.13674964066558[/C][/ROW]
[ROW][C]103[/C][C]7829[/C][C]7815.96575757793[/C][C]13.0342424220744[/C][/ROW]
[ROW][C]104[/C][C]7825[/C][C]7815.65536795948[/C][C]9.34463204052372[/C][/ROW]
[ROW][C]105[/C][C]7851[/C][C]7814.30055824151[/C][C]36.6994417584947[/C][/ROW]
[ROW][C]106[/C][C]7862[/C][C]7850.6890899969[/C][C]11.3109100030979[/C][/ROW]
[ROW][C]107[/C][C]7864[/C][C]7864.89087569497[/C][C]-0.890875694974966[/C][/ROW]
[ROW][C]108[/C][C]7893[/C][C]7866.63869500764[/C][C]26.361304992357[/C][/ROW]
[ROW][C]109[/C][C]7867[/C][C]7903.10080453587[/C][C]-36.1008045358731[/C][/ROW]
[ROW][C]110[/C][C]7869[/C][C]7866.88172935799[/C][C]2.11827064200679[/C][/ROW]
[ROW][C]111[/C][C]7871[/C][C]7869.48134942785[/C][C]1.51865057214764[/C][/ROW]
[ROW][C]112[/C][C]7891[/C][C]7871.91123470507[/C][C]19.0887652949295[/C][/ROW]
[ROW][C]113[/C][C]7876[/C][C]7897.31470230391[/C][C]-21.3147023039146[/C][/ROW]
[ROW][C]114[/C][C]7904[/C][C]7876.28113745576[/C][C]27.7188625442423[/C][/ROW]
[ROW][C]115[/C][C]7930[/C][C]7912.12753156876[/C][C]17.8724684312401[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=298251&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=298251&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
359205951-31
459235905.2248124498317.775187550169
559435913.256444852829.7435551471963
659535941.6759698471711.3240301528276
759665954.8814694734611.1185305265426
859955971.0287982041923.9712017958109
960276006.8143398674520.1856601325471
1060356044.52830610897-9.52830610897126
1160836049.831123104433.1688768955974
1261246107.2202558652816.7797441347157
1361506152.97010753709-2.97010753708946
1462206178.1293575150941.8706424849142
1562796259.981703987719.0182960122957
1663466324.3652238068221.634776193182
1764146397.4893921520216.5106078479848
1864396470.16305926277-31.163059262768
1964956486.341714434778.65828556522592
2065686544.7926202314823.2073797685234
2166046624.36194636105-20.3619463610503
2266466654.59807867703-8.59807867702784
2366916694.16421567825-3.16421567825273
2467176738.26851935484-21.2685193548386
2567196758.24802754022-39.2480275402222
2667466749.13806616475-3.13806616474994
2767406775.24977199893-35.2497719989269
2867486759.27159908308-11.2715990830793
2967536764.08094114939-11.080941149391
3067826765.9442528649316.0557471350694
3167886799.48916229617-11.4891622961668
3267946802.23691862058-8.23691862057967
3368166805.9052894034510.0947105965515
3468426830.7628048469811.2371951530222
3568556859.94372404071-4.94372404070782
3668606871.54430127769-11.5443012776923
3768736873.27644937939-0.276449379388396
3869086886.1981946970621.8018053029427
3969626927.3696440669234.6303559330845
4069986991.172478526336.82752147366773
4169967029.10514889518-33.1051488951789
4270027017.73405565545-15.7340556554545
4370197019.28020761347-0.280207613473067
4469997036.20088908569-37.2008890856923
4569797005.6704123515-26.6704123514992
4669946978.1208036281215.8791963718795
4769736997.61573673487-24.6157367348687
4869386969.64774620151-31.6477462015127
4969746925.6892007673748.3107992326304
5069866975.3645660565610.6354339434401
5170156990.3751443640124.6248556359851
5270317026.345716189874.6542838101268
5370737043.6632069429629.3367930570439
5470867093.96758956218-7.967589562184
5570837104.71219947409-21.7121994740892
5670727095.56611487693-23.5661148769341
5771027077.8952413971324.1047586028699
5871637114.7185890613848.2814109386209
5971937189.385635389553.61436461045378
6072427220.4087556260421.5912443739562
6172587275.52060139453-17.5206013945271
6272877286.561034838760.438965161238229
6373017315.68529295547-14.685292955467
6473157325.52831876471-10.5283187647119
6573337336.54806161154-3.54806161154102
6673657353.5437098024811.4562901975178
6773757388.78664835449-13.786648354494
6874197394.8840539996924.1159460003091
6974367445.71056848687-9.71056848686658
7074387459.9617923678-21.9617923678015
7174557455.74505536892-0.745055368920475
7275117472.5341521238438.4658478761612
7375597539.4227014589919.577298541014
7475937592.964458440370.0355415596250168
7576097626.97451920978-17.9745192097789
7676237637.88646188107-14.8864618810721
7776647647.6725426886616.3274573113422
7876927693.29436527332-1.29436527331563
7977407720.9279685626119.0720314373866
8077677774.32669929893-7.32669929892927
8177437799.25272638048-56.2527263804841
8277987759.3292352773538.6707647226476
8378427825.2757905402516.7242094597541
8478377874.00992198017-37.0099219801696
8578307858.53350241265-28.5335024126507
8678187843.4565077309-25.4565077309016
8778307824.250519675715.74948032429165
8878607837.8780283260822.1219716739151
8979137874.1401073718338.8598926281693
9079007938.14019917801-38.1401991780122
9179347914.3438314042119.6561685957895
9279437953.90791417666-10.9079141766551
9379357959.82020473532-24.8202047353234
9479307944.79433532932-14.7943353293213
9579437935.606494452077.39350554793236
9679067950.69937825324-44.699378253239
9779617901.0462999452459.9537000547643
9879497973.01742776159-24.0174277615943
9978867954.21880088803-68.2188008880257
10078777871.908066299645.09193370036246
10178537864.34944285492-11.3494428549184
10278337837.13674964067-4.13674964066558
10378297815.9657575779313.0342424220744
10478257815.655367959489.34463204052372
10578517814.3005582415136.6994417584947
10678627850.689089996911.3109100030979
10778647864.89087569497-0.890875694974966
10878937866.6386950076426.361304992357
10978677903.10080453587-36.1008045358731
11078697866.881729357992.11827064200679
11178717869.481349427851.51865057214764
11278917871.9112347050719.0887652949295
11378767897.31470230391-21.3147023039146
11479047876.2811374557627.7188625442423
11579307912.1275315687617.8724684312401







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
1167943.186701325817896.31155083287990.06185181882
1177956.373402651627880.119906917358032.6268983859
1187969.560103977437863.710781591598075.40942636328
1197982.746805303257845.933569602328119.56004100417
1207995.933506629067826.498934396548165.36807886158
1218009.120207954877805.33883275298212.90158315684
1228022.306909280687782.460465251598262.15335330977
1238035.493610606497757.899285761998313.08793545099
1248048.68031193237731.70104177058365.65958209411
1258061.867013258127703.914231863158419.81979465308
1268075.053714583937674.586801356658475.52062781121
1278088.240415909747643.76470929338532.71612252618

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
116 & 7943.18670132581 & 7896.3115508328 & 7990.06185181882 \tabularnewline
117 & 7956.37340265162 & 7880.11990691735 & 8032.6268983859 \tabularnewline
118 & 7969.56010397743 & 7863.71078159159 & 8075.40942636328 \tabularnewline
119 & 7982.74680530325 & 7845.93356960232 & 8119.56004100417 \tabularnewline
120 & 7995.93350662906 & 7826.49893439654 & 8165.36807886158 \tabularnewline
121 & 8009.12020795487 & 7805.3388327529 & 8212.90158315684 \tabularnewline
122 & 8022.30690928068 & 7782.46046525159 & 8262.15335330977 \tabularnewline
123 & 8035.49361060649 & 7757.89928576199 & 8313.08793545099 \tabularnewline
124 & 8048.6803119323 & 7731.7010417705 & 8365.65958209411 \tabularnewline
125 & 8061.86701325812 & 7703.91423186315 & 8419.81979465308 \tabularnewline
126 & 8075.05371458393 & 7674.58680135665 & 8475.52062781121 \tabularnewline
127 & 8088.24041590974 & 7643.7647092933 & 8532.71612252618 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=298251&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]116[/C][C]7943.18670132581[/C][C]7896.3115508328[/C][C]7990.06185181882[/C][/ROW]
[ROW][C]117[/C][C]7956.37340265162[/C][C]7880.11990691735[/C][C]8032.6268983859[/C][/ROW]
[ROW][C]118[/C][C]7969.56010397743[/C][C]7863.71078159159[/C][C]8075.40942636328[/C][/ROW]
[ROW][C]119[/C][C]7982.74680530325[/C][C]7845.93356960232[/C][C]8119.56004100417[/C][/ROW]
[ROW][C]120[/C][C]7995.93350662906[/C][C]7826.49893439654[/C][C]8165.36807886158[/C][/ROW]
[ROW][C]121[/C][C]8009.12020795487[/C][C]7805.3388327529[/C][C]8212.90158315684[/C][/ROW]
[ROW][C]122[/C][C]8022.30690928068[/C][C]7782.46046525159[/C][C]8262.15335330977[/C][/ROW]
[ROW][C]123[/C][C]8035.49361060649[/C][C]7757.89928576199[/C][C]8313.08793545099[/C][/ROW]
[ROW][C]124[/C][C]8048.6803119323[/C][C]7731.7010417705[/C][C]8365.65958209411[/C][/ROW]
[ROW][C]125[/C][C]8061.86701325812[/C][C]7703.91423186315[/C][C]8419.81979465308[/C][/ROW]
[ROW][C]126[/C][C]8075.05371458393[/C][C]7674.58680135665[/C][C]8475.52062781121[/C][/ROW]
[ROW][C]127[/C][C]8088.24041590974[/C][C]7643.7647092933[/C][C]8532.71612252618[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=298251&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=298251&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
1167943.186701325817896.31155083287990.06185181882
1177956.373402651627880.119906917358032.6268983859
1187969.560103977437863.710781591598075.40942636328
1197982.746805303257845.933569602328119.56004100417
1207995.933506629067826.498934396548165.36807886158
1218009.120207954877805.33883275298212.90158315684
1228022.306909280687782.460465251598262.15335330977
1238035.493610606497757.899285761998313.08793545099
1248048.68031193237731.70104177058365.65958209411
1258061.867013258127703.914231863158419.81979465308
1268075.053714583937674.586801356658475.52062781121
1278088.240415909747643.76470929338532.71612252618



Parameters (Session):
par1 = 1 ; par2 = 0 ; par3 = 1 ; par4 = 1 ;
Parameters (R input):
par1 = 1 ; par2 = Double ; 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')