Free Statistics

of Irreproducible Research!

Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationWed, 16 Aug 2017 17:12:24 +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/16/t1502896382kowq2wqyksrmbkf.htm/, Retrieved Sat, 11 May 2024 22:31:58 +0200
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=, Retrieved Sat, 11 May 2024 22:31:58 +0200
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact0
Dataseries X:
1189593.60
1185163.20
1180670.40
1171372.80
1263350.40
1258483.20
1189593.60
1143792.00
1148222.40
1148222.40
1153152.00
1162012.80
1175803.20
1175803.20
1166942.40
1143792.00
1263350.40
1281571.20
1254052.80
1189593.60
1217174.40
1175803.20
1194460.80
1203384.00
1212681.60
1189593.60
1194460.80
1162012.80
1263350.40
1295361.60
1267843.20
1217174.40
1272273.60
1212681.60
1267843.20
1263350.40
1277140.80
1226472.00
1281571.20
1277140.80
1359820.80
1341163.20
1267843.20
1230902.40
1281571.20
1212681.60
1263350.40
1272273.60
1290931.20
1249622.40
1272273.60
1286064.00
1336732.80
1295361.60
1240262.40
1180670.40
1235832.00
1084200.00
1157582.40
1198891.20
1240262.40
1180670.40
1180670.40
1180670.40
1212681.60
1166942.40
1106913.60
1056681.60
1093123.20
950851.20
1038024.00
1088692.80
1097990.40
1047321.60
1051752.00
1038024.00
1084200.00
1051752.00
987792.00
941553.60
1019740.80
849950.40
960211.20
1010443.20
1010443.20
950851.20
895752.00
891321.60
941553.60
895752.00
808641.60
748612.80
813072.00
661502.40
799281.60
872601.60
895752.00
845083.20
781060.80
826862.40
845083.20
831292.80
693451.20
629491.20
675230.40
537451.20
679723.20
730392.00
771700.80
702811.20
638352.00
675230.40
693451.20
657009.60
519230.40
459201.60
514300.80
362731.20
528091.20
629491.20




Summary of computational transaction
Raw Input view raw input (R code)
Raw Outputview raw output of R engine
Computing time3 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 time3 seconds \tabularnewline
R ServerBig Analytics Cloud Computing Center \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=&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]3 seconds[/C][/ROW] [ROW]R Server[/C]Big Analytics Cloud Computing Center[/C][/ROW] [/TABLE] Source: https://freestatistics.org/blog/index.php?pk=&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=&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 time3 seconds
R ServerBig Analytics Cloud Computing Center







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.379244790290803
beta0.0506954647933953
gamma1

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.379244790290803 \tabularnewline
beta & 0.0506954647933953 \tabularnewline
gamma & 1 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=&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]0.379244790290803[/C][/ROW]
[ROW][C]beta[/C][C]0.0506954647933953[/C][/ROW]
[ROW][C]gamma[/C][C]1[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=&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
alpha0.379244790290803
beta0.0506954647933953
gamma1







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
131175803.21175892.6989163-89.4989163030405
141175803.21173289.630324572513.56967542972
151166942.41162725.155840114217.24415988731
1611437921139427.278919464364.72108053719
171263350.41259680.160677653670.2393223492
181281571.21278032.600395993538.59960400499
191254052.81209534.8839478144517.9160521922
201189593.61183262.205243036331.39475696813
211217174.41194463.529706722710.8702932955
221175803.21208512.96494906-32709.76494906
231194460.81205482.27367809-11021.4736780948
2412033841212419.36578255-9035.36578254658
251212681.61222231.97336807-9550.37336807116
261189593.61218096.66310663-28503.0631066265
271194460.81196441.5025798-1980.70257980167
281162012.81170055.93045306-8043.13045305642
291263350.41287077.51762078-23727.1176207832
301295361.61294143.316927991218.28307200852
311267843.21248355.7278995719487.4721004302
321217174.41187378.4192041429795.9807958601
331272273.61216697.5465414555576.0534585521
341212681.61207711.786349554969.81365044811
351267843.21233367.528553734475.6714463036
361263350.41260461.242153672889.1578463295
371277140.81276465.49109678675.308903219411
3812264721265184.8296619-38712.8296619023
391281571.21257796.7917230823774.4082769249
401277140.81237439.3699967639701.43000324
411359820.81374280.26904834-14459.4690483424
421341163.21406222.75086759-65059.5508675908
431267843.21346178.64344438-78335.443444384
441230902.41252018.59357913-21116.1935791308
451281571.21277262.053783344309.14621666353
461212681.61215289.96603856-2608.36603855737
471263350.41254219.722616239130.67738376581
481272273.61249696.2248046822577.3751953177
491290931.21269644.0961118421287.103888164
501249622.41239768.915749319853.48425069149
511272273.61289306.7716414-17033.1716414031
5212860641261512.1769326324551.8230673741
531336732.81356585.86242567-19853.0624256718
541295361.61352286.28602609-56924.6860260854
551240262.41284492.99478996-44230.594789963
561180670.41237464.96414093-56794.5641409343
5712358321262374.2557776-26542.2557775967
5810842001183534.10711644-99334.1071164366
591157582.41186055.99631355-28473.5963135478
601198891.21170424.4383143128466.761685692
611240262.41186000.2432658754262.1567341264
621180670.41160292.5011862220377.8988137823
631180670.41191144.37636519-10473.9763651872
641180670.41187310.91758001-6640.51758000953
651212681.61233676.17780275-20994.5778027512
661166942.41202417.25895537-35474.858955367
671106913.61149249.61301029-42336.0130102935
681056681.61093738.73343293-37057.1334329317
691093123.21135138.06966662-42014.8696666183
70950851.21010144.95643627-59293.7564362686
7110380241060407.07013004-22383.070130042
721088692.81075654.8967515513037.9032484514
731097990.41094621.79928773368.60071230237
741047321.61031474.3894798115847.2105201918
7510517521036013.801319215738.1986807956
7610380241039724.46927967-1700.46927967109
7710842001069631.2276478614568.7723521432
7810517521042502.035810419249.96418959415
799877921003357.87903736-15565.8790373626
80941553.6962185.903592774-20632.303592774
811019740.8999056.65157802820684.1484219721
82849950.4894836.275711086-44885.8757110862
83960211.2965141.999748623-4930.79974862281
841010443.21005089.426059685353.77394032315
851010443.21013795.45583778-3352.25583777775
86950851.2959359.1991987-8507.99919870007
87895752953320.408206258-57568.408206258
88891321.6917013.35482496-25691.7548249596
89941553.6939183.3659994582370.2340005415
90895752905175.975094029-9423.97509402886
91808641.6847885.51624927-39243.91624927
92748612.8796191.15068237-47578.3506823701
93813072830779.720659786-17707.7206597858
94661502.4694873.75200215-33371.3520021501
95799281.6766175.38445627733106.2155437225
96872601.6812241.78764259160359.8123574086
97895752831756.98343708763995.0165629133
98845083.2805415.42297566739667.7770243331
99781060.8789250.797626405-8189.99762640451
100826862.4789741.05506966537121.3449303347
101845083.2848765.323070885-3682.12307088461
102831292.8809661.50680793921631.2931920609
103693451.2752459.050970031-59007.8509700312
104629491.2691921.314224907-62430.1142249071
105675230.4731546.326139923-56315.9261399234
106537451.2587556.608032979-50105.4080329792
107679723.2674068.4304888965654.76951110444
108730392715389.57240263515002.4275973646
109771700.8715621.07293371656079.7270662837
110702811.2679067.16541844523744.0345815552
111638352635036.665338073315.33466192975
112675230.4658419.84858451916810.5514154807
113693451.2676697.19584475116754.004155249
114657009.6661769.410845689-4759.81084568857
115519230.4563995.714636258-44765.3146362579
116459201.6510877.858995061-51676.2589950606
117514300.8538962.479395858-24661.679395858
118362731.2432715.861123519-69984.6611235195
119528091.2507170.90924196120920.290758039
120629491.2544196.88902833385294.3109716665

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 1175803.2 & 1175892.6989163 & -89.4989163030405 \tabularnewline
14 & 1175803.2 & 1173289.63032457 & 2513.56967542972 \tabularnewline
15 & 1166942.4 & 1162725.15584011 & 4217.24415988731 \tabularnewline
16 & 1143792 & 1139427.27891946 & 4364.72108053719 \tabularnewline
17 & 1263350.4 & 1259680.16067765 & 3670.2393223492 \tabularnewline
18 & 1281571.2 & 1278032.60039599 & 3538.59960400499 \tabularnewline
19 & 1254052.8 & 1209534.88394781 & 44517.9160521922 \tabularnewline
20 & 1189593.6 & 1183262.20524303 & 6331.39475696813 \tabularnewline
21 & 1217174.4 & 1194463.5297067 & 22710.8702932955 \tabularnewline
22 & 1175803.2 & 1208512.96494906 & -32709.76494906 \tabularnewline
23 & 1194460.8 & 1205482.27367809 & -11021.4736780948 \tabularnewline
24 & 1203384 & 1212419.36578255 & -9035.36578254658 \tabularnewline
25 & 1212681.6 & 1222231.97336807 & -9550.37336807116 \tabularnewline
26 & 1189593.6 & 1218096.66310663 & -28503.0631066265 \tabularnewline
27 & 1194460.8 & 1196441.5025798 & -1980.70257980167 \tabularnewline
28 & 1162012.8 & 1170055.93045306 & -8043.13045305642 \tabularnewline
29 & 1263350.4 & 1287077.51762078 & -23727.1176207832 \tabularnewline
30 & 1295361.6 & 1294143.31692799 & 1218.28307200852 \tabularnewline
31 & 1267843.2 & 1248355.72789957 & 19487.4721004302 \tabularnewline
32 & 1217174.4 & 1187378.41920414 & 29795.9807958601 \tabularnewline
33 & 1272273.6 & 1216697.54654145 & 55576.0534585521 \tabularnewline
34 & 1212681.6 & 1207711.78634955 & 4969.81365044811 \tabularnewline
35 & 1267843.2 & 1233367.5285537 & 34475.6714463036 \tabularnewline
36 & 1263350.4 & 1260461.24215367 & 2889.1578463295 \tabularnewline
37 & 1277140.8 & 1276465.49109678 & 675.308903219411 \tabularnewline
38 & 1226472 & 1265184.8296619 & -38712.8296619023 \tabularnewline
39 & 1281571.2 & 1257796.79172308 & 23774.4082769249 \tabularnewline
40 & 1277140.8 & 1237439.36999676 & 39701.43000324 \tabularnewline
41 & 1359820.8 & 1374280.26904834 & -14459.4690483424 \tabularnewline
42 & 1341163.2 & 1406222.75086759 & -65059.5508675908 \tabularnewline
43 & 1267843.2 & 1346178.64344438 & -78335.443444384 \tabularnewline
44 & 1230902.4 & 1252018.59357913 & -21116.1935791308 \tabularnewline
45 & 1281571.2 & 1277262.05378334 & 4309.14621666353 \tabularnewline
46 & 1212681.6 & 1215289.96603856 & -2608.36603855737 \tabularnewline
47 & 1263350.4 & 1254219.72261623 & 9130.67738376581 \tabularnewline
48 & 1272273.6 & 1249696.22480468 & 22577.3751953177 \tabularnewline
49 & 1290931.2 & 1269644.09611184 & 21287.103888164 \tabularnewline
50 & 1249622.4 & 1239768.91574931 & 9853.48425069149 \tabularnewline
51 & 1272273.6 & 1289306.7716414 & -17033.1716414031 \tabularnewline
52 & 1286064 & 1261512.17693263 & 24551.8230673741 \tabularnewline
53 & 1336732.8 & 1356585.86242567 & -19853.0624256718 \tabularnewline
54 & 1295361.6 & 1352286.28602609 & -56924.6860260854 \tabularnewline
55 & 1240262.4 & 1284492.99478996 & -44230.594789963 \tabularnewline
56 & 1180670.4 & 1237464.96414093 & -56794.5641409343 \tabularnewline
57 & 1235832 & 1262374.2557776 & -26542.2557775967 \tabularnewline
58 & 1084200 & 1183534.10711644 & -99334.1071164366 \tabularnewline
59 & 1157582.4 & 1186055.99631355 & -28473.5963135478 \tabularnewline
60 & 1198891.2 & 1170424.43831431 & 28466.761685692 \tabularnewline
61 & 1240262.4 & 1186000.24326587 & 54262.1567341264 \tabularnewline
62 & 1180670.4 & 1160292.50118622 & 20377.8988137823 \tabularnewline
63 & 1180670.4 & 1191144.37636519 & -10473.9763651872 \tabularnewline
64 & 1180670.4 & 1187310.91758001 & -6640.51758000953 \tabularnewline
65 & 1212681.6 & 1233676.17780275 & -20994.5778027512 \tabularnewline
66 & 1166942.4 & 1202417.25895537 & -35474.858955367 \tabularnewline
67 & 1106913.6 & 1149249.61301029 & -42336.0130102935 \tabularnewline
68 & 1056681.6 & 1093738.73343293 & -37057.1334329317 \tabularnewline
69 & 1093123.2 & 1135138.06966662 & -42014.8696666183 \tabularnewline
70 & 950851.2 & 1010144.95643627 & -59293.7564362686 \tabularnewline
71 & 1038024 & 1060407.07013004 & -22383.070130042 \tabularnewline
72 & 1088692.8 & 1075654.89675155 & 13037.9032484514 \tabularnewline
73 & 1097990.4 & 1094621.7992877 & 3368.60071230237 \tabularnewline
74 & 1047321.6 & 1031474.38947981 & 15847.2105201918 \tabularnewline
75 & 1051752 & 1036013.8013192 & 15738.1986807956 \tabularnewline
76 & 1038024 & 1039724.46927967 & -1700.46927967109 \tabularnewline
77 & 1084200 & 1069631.22764786 & 14568.7723521432 \tabularnewline
78 & 1051752 & 1042502.03581041 & 9249.96418959415 \tabularnewline
79 & 987792 & 1003357.87903736 & -15565.8790373626 \tabularnewline
80 & 941553.6 & 962185.903592774 & -20632.303592774 \tabularnewline
81 & 1019740.8 & 999056.651578028 & 20684.1484219721 \tabularnewline
82 & 849950.4 & 894836.275711086 & -44885.8757110862 \tabularnewline
83 & 960211.2 & 965141.999748623 & -4930.79974862281 \tabularnewline
84 & 1010443.2 & 1005089.42605968 & 5353.77394032315 \tabularnewline
85 & 1010443.2 & 1013795.45583778 & -3352.25583777775 \tabularnewline
86 & 950851.2 & 959359.1991987 & -8507.99919870007 \tabularnewline
87 & 895752 & 953320.408206258 & -57568.408206258 \tabularnewline
88 & 891321.6 & 917013.35482496 & -25691.7548249596 \tabularnewline
89 & 941553.6 & 939183.365999458 & 2370.2340005415 \tabularnewline
90 & 895752 & 905175.975094029 & -9423.97509402886 \tabularnewline
91 & 808641.6 & 847885.51624927 & -39243.91624927 \tabularnewline
92 & 748612.8 & 796191.15068237 & -47578.3506823701 \tabularnewline
93 & 813072 & 830779.720659786 & -17707.7206597858 \tabularnewline
94 & 661502.4 & 694873.75200215 & -33371.3520021501 \tabularnewline
95 & 799281.6 & 766175.384456277 & 33106.2155437225 \tabularnewline
96 & 872601.6 & 812241.787642591 & 60359.8123574086 \tabularnewline
97 & 895752 & 831756.983437087 & 63995.0165629133 \tabularnewline
98 & 845083.2 & 805415.422975667 & 39667.7770243331 \tabularnewline
99 & 781060.8 & 789250.797626405 & -8189.99762640451 \tabularnewline
100 & 826862.4 & 789741.055069665 & 37121.3449303347 \tabularnewline
101 & 845083.2 & 848765.323070885 & -3682.12307088461 \tabularnewline
102 & 831292.8 & 809661.506807939 & 21631.2931920609 \tabularnewline
103 & 693451.2 & 752459.050970031 & -59007.8509700312 \tabularnewline
104 & 629491.2 & 691921.314224907 & -62430.1142249071 \tabularnewline
105 & 675230.4 & 731546.326139923 & -56315.9261399234 \tabularnewline
106 & 537451.2 & 587556.608032979 & -50105.4080329792 \tabularnewline
107 & 679723.2 & 674068.430488896 & 5654.76951110444 \tabularnewline
108 & 730392 & 715389.572402635 & 15002.4275973646 \tabularnewline
109 & 771700.8 & 715621.072933716 & 56079.7270662837 \tabularnewline
110 & 702811.2 & 679067.165418445 & 23744.0345815552 \tabularnewline
111 & 638352 & 635036.66533807 & 3315.33466192975 \tabularnewline
112 & 675230.4 & 658419.848584519 & 16810.5514154807 \tabularnewline
113 & 693451.2 & 676697.195844751 & 16754.004155249 \tabularnewline
114 & 657009.6 & 661769.410845689 & -4759.81084568857 \tabularnewline
115 & 519230.4 & 563995.714636258 & -44765.3146362579 \tabularnewline
116 & 459201.6 & 510877.858995061 & -51676.2589950606 \tabularnewline
117 & 514300.8 & 538962.479395858 & -24661.679395858 \tabularnewline
118 & 362731.2 & 432715.861123519 & -69984.6611235195 \tabularnewline
119 & 528091.2 & 507170.909241961 & 20920.290758039 \tabularnewline
120 & 629491.2 & 544196.889028333 & 85294.3109716665 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=&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]1175803.2[/C][C]1175892.6989163[/C][C]-89.4989163030405[/C][/ROW]
[ROW][C]14[/C][C]1175803.2[/C][C]1173289.63032457[/C][C]2513.56967542972[/C][/ROW]
[ROW][C]15[/C][C]1166942.4[/C][C]1162725.15584011[/C][C]4217.24415988731[/C][/ROW]
[ROW][C]16[/C][C]1143792[/C][C]1139427.27891946[/C][C]4364.72108053719[/C][/ROW]
[ROW][C]17[/C][C]1263350.4[/C][C]1259680.16067765[/C][C]3670.2393223492[/C][/ROW]
[ROW][C]18[/C][C]1281571.2[/C][C]1278032.60039599[/C][C]3538.59960400499[/C][/ROW]
[ROW][C]19[/C][C]1254052.8[/C][C]1209534.88394781[/C][C]44517.9160521922[/C][/ROW]
[ROW][C]20[/C][C]1189593.6[/C][C]1183262.20524303[/C][C]6331.39475696813[/C][/ROW]
[ROW][C]21[/C][C]1217174.4[/C][C]1194463.5297067[/C][C]22710.8702932955[/C][/ROW]
[ROW][C]22[/C][C]1175803.2[/C][C]1208512.96494906[/C][C]-32709.76494906[/C][/ROW]
[ROW][C]23[/C][C]1194460.8[/C][C]1205482.27367809[/C][C]-11021.4736780948[/C][/ROW]
[ROW][C]24[/C][C]1203384[/C][C]1212419.36578255[/C][C]-9035.36578254658[/C][/ROW]
[ROW][C]25[/C][C]1212681.6[/C][C]1222231.97336807[/C][C]-9550.37336807116[/C][/ROW]
[ROW][C]26[/C][C]1189593.6[/C][C]1218096.66310663[/C][C]-28503.0631066265[/C][/ROW]
[ROW][C]27[/C][C]1194460.8[/C][C]1196441.5025798[/C][C]-1980.70257980167[/C][/ROW]
[ROW][C]28[/C][C]1162012.8[/C][C]1170055.93045306[/C][C]-8043.13045305642[/C][/ROW]
[ROW][C]29[/C][C]1263350.4[/C][C]1287077.51762078[/C][C]-23727.1176207832[/C][/ROW]
[ROW][C]30[/C][C]1295361.6[/C][C]1294143.31692799[/C][C]1218.28307200852[/C][/ROW]
[ROW][C]31[/C][C]1267843.2[/C][C]1248355.72789957[/C][C]19487.4721004302[/C][/ROW]
[ROW][C]32[/C][C]1217174.4[/C][C]1187378.41920414[/C][C]29795.9807958601[/C][/ROW]
[ROW][C]33[/C][C]1272273.6[/C][C]1216697.54654145[/C][C]55576.0534585521[/C][/ROW]
[ROW][C]34[/C][C]1212681.6[/C][C]1207711.78634955[/C][C]4969.81365044811[/C][/ROW]
[ROW][C]35[/C][C]1267843.2[/C][C]1233367.5285537[/C][C]34475.6714463036[/C][/ROW]
[ROW][C]36[/C][C]1263350.4[/C][C]1260461.24215367[/C][C]2889.1578463295[/C][/ROW]
[ROW][C]37[/C][C]1277140.8[/C][C]1276465.49109678[/C][C]675.308903219411[/C][/ROW]
[ROW][C]38[/C][C]1226472[/C][C]1265184.8296619[/C][C]-38712.8296619023[/C][/ROW]
[ROW][C]39[/C][C]1281571.2[/C][C]1257796.79172308[/C][C]23774.4082769249[/C][/ROW]
[ROW][C]40[/C][C]1277140.8[/C][C]1237439.36999676[/C][C]39701.43000324[/C][/ROW]
[ROW][C]41[/C][C]1359820.8[/C][C]1374280.26904834[/C][C]-14459.4690483424[/C][/ROW]
[ROW][C]42[/C][C]1341163.2[/C][C]1406222.75086759[/C][C]-65059.5508675908[/C][/ROW]
[ROW][C]43[/C][C]1267843.2[/C][C]1346178.64344438[/C][C]-78335.443444384[/C][/ROW]
[ROW][C]44[/C][C]1230902.4[/C][C]1252018.59357913[/C][C]-21116.1935791308[/C][/ROW]
[ROW][C]45[/C][C]1281571.2[/C][C]1277262.05378334[/C][C]4309.14621666353[/C][/ROW]
[ROW][C]46[/C][C]1212681.6[/C][C]1215289.96603856[/C][C]-2608.36603855737[/C][/ROW]
[ROW][C]47[/C][C]1263350.4[/C][C]1254219.72261623[/C][C]9130.67738376581[/C][/ROW]
[ROW][C]48[/C][C]1272273.6[/C][C]1249696.22480468[/C][C]22577.3751953177[/C][/ROW]
[ROW][C]49[/C][C]1290931.2[/C][C]1269644.09611184[/C][C]21287.103888164[/C][/ROW]
[ROW][C]50[/C][C]1249622.4[/C][C]1239768.91574931[/C][C]9853.48425069149[/C][/ROW]
[ROW][C]51[/C][C]1272273.6[/C][C]1289306.7716414[/C][C]-17033.1716414031[/C][/ROW]
[ROW][C]52[/C][C]1286064[/C][C]1261512.17693263[/C][C]24551.8230673741[/C][/ROW]
[ROW][C]53[/C][C]1336732.8[/C][C]1356585.86242567[/C][C]-19853.0624256718[/C][/ROW]
[ROW][C]54[/C][C]1295361.6[/C][C]1352286.28602609[/C][C]-56924.6860260854[/C][/ROW]
[ROW][C]55[/C][C]1240262.4[/C][C]1284492.99478996[/C][C]-44230.594789963[/C][/ROW]
[ROW][C]56[/C][C]1180670.4[/C][C]1237464.96414093[/C][C]-56794.5641409343[/C][/ROW]
[ROW][C]57[/C][C]1235832[/C][C]1262374.2557776[/C][C]-26542.2557775967[/C][/ROW]
[ROW][C]58[/C][C]1084200[/C][C]1183534.10711644[/C][C]-99334.1071164366[/C][/ROW]
[ROW][C]59[/C][C]1157582.4[/C][C]1186055.99631355[/C][C]-28473.5963135478[/C][/ROW]
[ROW][C]60[/C][C]1198891.2[/C][C]1170424.43831431[/C][C]28466.761685692[/C][/ROW]
[ROW][C]61[/C][C]1240262.4[/C][C]1186000.24326587[/C][C]54262.1567341264[/C][/ROW]
[ROW][C]62[/C][C]1180670.4[/C][C]1160292.50118622[/C][C]20377.8988137823[/C][/ROW]
[ROW][C]63[/C][C]1180670.4[/C][C]1191144.37636519[/C][C]-10473.9763651872[/C][/ROW]
[ROW][C]64[/C][C]1180670.4[/C][C]1187310.91758001[/C][C]-6640.51758000953[/C][/ROW]
[ROW][C]65[/C][C]1212681.6[/C][C]1233676.17780275[/C][C]-20994.5778027512[/C][/ROW]
[ROW][C]66[/C][C]1166942.4[/C][C]1202417.25895537[/C][C]-35474.858955367[/C][/ROW]
[ROW][C]67[/C][C]1106913.6[/C][C]1149249.61301029[/C][C]-42336.0130102935[/C][/ROW]
[ROW][C]68[/C][C]1056681.6[/C][C]1093738.73343293[/C][C]-37057.1334329317[/C][/ROW]
[ROW][C]69[/C][C]1093123.2[/C][C]1135138.06966662[/C][C]-42014.8696666183[/C][/ROW]
[ROW][C]70[/C][C]950851.2[/C][C]1010144.95643627[/C][C]-59293.7564362686[/C][/ROW]
[ROW][C]71[/C][C]1038024[/C][C]1060407.07013004[/C][C]-22383.070130042[/C][/ROW]
[ROW][C]72[/C][C]1088692.8[/C][C]1075654.89675155[/C][C]13037.9032484514[/C][/ROW]
[ROW][C]73[/C][C]1097990.4[/C][C]1094621.7992877[/C][C]3368.60071230237[/C][/ROW]
[ROW][C]74[/C][C]1047321.6[/C][C]1031474.38947981[/C][C]15847.2105201918[/C][/ROW]
[ROW][C]75[/C][C]1051752[/C][C]1036013.8013192[/C][C]15738.1986807956[/C][/ROW]
[ROW][C]76[/C][C]1038024[/C][C]1039724.46927967[/C][C]-1700.46927967109[/C][/ROW]
[ROW][C]77[/C][C]1084200[/C][C]1069631.22764786[/C][C]14568.7723521432[/C][/ROW]
[ROW][C]78[/C][C]1051752[/C][C]1042502.03581041[/C][C]9249.96418959415[/C][/ROW]
[ROW][C]79[/C][C]987792[/C][C]1003357.87903736[/C][C]-15565.8790373626[/C][/ROW]
[ROW][C]80[/C][C]941553.6[/C][C]962185.903592774[/C][C]-20632.303592774[/C][/ROW]
[ROW][C]81[/C][C]1019740.8[/C][C]999056.651578028[/C][C]20684.1484219721[/C][/ROW]
[ROW][C]82[/C][C]849950.4[/C][C]894836.275711086[/C][C]-44885.8757110862[/C][/ROW]
[ROW][C]83[/C][C]960211.2[/C][C]965141.999748623[/C][C]-4930.79974862281[/C][/ROW]
[ROW][C]84[/C][C]1010443.2[/C][C]1005089.42605968[/C][C]5353.77394032315[/C][/ROW]
[ROW][C]85[/C][C]1010443.2[/C][C]1013795.45583778[/C][C]-3352.25583777775[/C][/ROW]
[ROW][C]86[/C][C]950851.2[/C][C]959359.1991987[/C][C]-8507.99919870007[/C][/ROW]
[ROW][C]87[/C][C]895752[/C][C]953320.408206258[/C][C]-57568.408206258[/C][/ROW]
[ROW][C]88[/C][C]891321.6[/C][C]917013.35482496[/C][C]-25691.7548249596[/C][/ROW]
[ROW][C]89[/C][C]941553.6[/C][C]939183.365999458[/C][C]2370.2340005415[/C][/ROW]
[ROW][C]90[/C][C]895752[/C][C]905175.975094029[/C][C]-9423.97509402886[/C][/ROW]
[ROW][C]91[/C][C]808641.6[/C][C]847885.51624927[/C][C]-39243.91624927[/C][/ROW]
[ROW][C]92[/C][C]748612.8[/C][C]796191.15068237[/C][C]-47578.3506823701[/C][/ROW]
[ROW][C]93[/C][C]813072[/C][C]830779.720659786[/C][C]-17707.7206597858[/C][/ROW]
[ROW][C]94[/C][C]661502.4[/C][C]694873.75200215[/C][C]-33371.3520021501[/C][/ROW]
[ROW][C]95[/C][C]799281.6[/C][C]766175.384456277[/C][C]33106.2155437225[/C][/ROW]
[ROW][C]96[/C][C]872601.6[/C][C]812241.787642591[/C][C]60359.8123574086[/C][/ROW]
[ROW][C]97[/C][C]895752[/C][C]831756.983437087[/C][C]63995.0165629133[/C][/ROW]
[ROW][C]98[/C][C]845083.2[/C][C]805415.422975667[/C][C]39667.7770243331[/C][/ROW]
[ROW][C]99[/C][C]781060.8[/C][C]789250.797626405[/C][C]-8189.99762640451[/C][/ROW]
[ROW][C]100[/C][C]826862.4[/C][C]789741.055069665[/C][C]37121.3449303347[/C][/ROW]
[ROW][C]101[/C][C]845083.2[/C][C]848765.323070885[/C][C]-3682.12307088461[/C][/ROW]
[ROW][C]102[/C][C]831292.8[/C][C]809661.506807939[/C][C]21631.2931920609[/C][/ROW]
[ROW][C]103[/C][C]693451.2[/C][C]752459.050970031[/C][C]-59007.8509700312[/C][/ROW]
[ROW][C]104[/C][C]629491.2[/C][C]691921.314224907[/C][C]-62430.1142249071[/C][/ROW]
[ROW][C]105[/C][C]675230.4[/C][C]731546.326139923[/C][C]-56315.9261399234[/C][/ROW]
[ROW][C]106[/C][C]537451.2[/C][C]587556.608032979[/C][C]-50105.4080329792[/C][/ROW]
[ROW][C]107[/C][C]679723.2[/C][C]674068.430488896[/C][C]5654.76951110444[/C][/ROW]
[ROW][C]108[/C][C]730392[/C][C]715389.572402635[/C][C]15002.4275973646[/C][/ROW]
[ROW][C]109[/C][C]771700.8[/C][C]715621.072933716[/C][C]56079.7270662837[/C][/ROW]
[ROW][C]110[/C][C]702811.2[/C][C]679067.165418445[/C][C]23744.0345815552[/C][/ROW]
[ROW][C]111[/C][C]638352[/C][C]635036.66533807[/C][C]3315.33466192975[/C][/ROW]
[ROW][C]112[/C][C]675230.4[/C][C]658419.848584519[/C][C]16810.5514154807[/C][/ROW]
[ROW][C]113[/C][C]693451.2[/C][C]676697.195844751[/C][C]16754.004155249[/C][/ROW]
[ROW][C]114[/C][C]657009.6[/C][C]661769.410845689[/C][C]-4759.81084568857[/C][/ROW]
[ROW][C]115[/C][C]519230.4[/C][C]563995.714636258[/C][C]-44765.3146362579[/C][/ROW]
[ROW][C]116[/C][C]459201.6[/C][C]510877.858995061[/C][C]-51676.2589950606[/C][/ROW]
[ROW][C]117[/C][C]514300.8[/C][C]538962.479395858[/C][C]-24661.679395858[/C][/ROW]
[ROW][C]118[/C][C]362731.2[/C][C]432715.861123519[/C][C]-69984.6611235195[/C][/ROW]
[ROW][C]119[/C][C]528091.2[/C][C]507170.909241961[/C][C]20920.290758039[/C][/ROW]
[ROW][C]120[/C][C]629491.2[/C][C]544196.889028333[/C][C]85294.3109716665[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=&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
131175803.21175892.6989163-89.4989163030405
141175803.21173289.630324572513.56967542972
151166942.41162725.155840114217.24415988731
1611437921139427.278919464364.72108053719
171263350.41259680.160677653670.2393223492
181281571.21278032.600395993538.59960400499
191254052.81209534.8839478144517.9160521922
201189593.61183262.205243036331.39475696813
211217174.41194463.529706722710.8702932955
221175803.21208512.96494906-32709.76494906
231194460.81205482.27367809-11021.4736780948
2412033841212419.36578255-9035.36578254658
251212681.61222231.97336807-9550.37336807116
261189593.61218096.66310663-28503.0631066265
271194460.81196441.5025798-1980.70257980167
281162012.81170055.93045306-8043.13045305642
291263350.41287077.51762078-23727.1176207832
301295361.61294143.316927991218.28307200852
311267843.21248355.7278995719487.4721004302
321217174.41187378.4192041429795.9807958601
331272273.61216697.5465414555576.0534585521
341212681.61207711.786349554969.81365044811
351267843.21233367.528553734475.6714463036
361263350.41260461.242153672889.1578463295
371277140.81276465.49109678675.308903219411
3812264721265184.8296619-38712.8296619023
391281571.21257796.7917230823774.4082769249
401277140.81237439.3699967639701.43000324
411359820.81374280.26904834-14459.4690483424
421341163.21406222.75086759-65059.5508675908
431267843.21346178.64344438-78335.443444384
441230902.41252018.59357913-21116.1935791308
451281571.21277262.053783344309.14621666353
461212681.61215289.96603856-2608.36603855737
471263350.41254219.722616239130.67738376581
481272273.61249696.2248046822577.3751953177
491290931.21269644.0961118421287.103888164
501249622.41239768.915749319853.48425069149
511272273.61289306.7716414-17033.1716414031
5212860641261512.1769326324551.8230673741
531336732.81356585.86242567-19853.0624256718
541295361.61352286.28602609-56924.6860260854
551240262.41284492.99478996-44230.594789963
561180670.41237464.96414093-56794.5641409343
5712358321262374.2557776-26542.2557775967
5810842001183534.10711644-99334.1071164366
591157582.41186055.99631355-28473.5963135478
601198891.21170424.4383143128466.761685692
611240262.41186000.2432658754262.1567341264
621180670.41160292.5011862220377.8988137823
631180670.41191144.37636519-10473.9763651872
641180670.41187310.91758001-6640.51758000953
651212681.61233676.17780275-20994.5778027512
661166942.41202417.25895537-35474.858955367
671106913.61149249.61301029-42336.0130102935
681056681.61093738.73343293-37057.1334329317
691093123.21135138.06966662-42014.8696666183
70950851.21010144.95643627-59293.7564362686
7110380241060407.07013004-22383.070130042
721088692.81075654.8967515513037.9032484514
731097990.41094621.79928773368.60071230237
741047321.61031474.3894798115847.2105201918
7510517521036013.801319215738.1986807956
7610380241039724.46927967-1700.46927967109
7710842001069631.2276478614568.7723521432
7810517521042502.035810419249.96418959415
799877921003357.87903736-15565.8790373626
80941553.6962185.903592774-20632.303592774
811019740.8999056.65157802820684.1484219721
82849950.4894836.275711086-44885.8757110862
83960211.2965141.999748623-4930.79974862281
841010443.21005089.426059685353.77394032315
851010443.21013795.45583778-3352.25583777775
86950851.2959359.1991987-8507.99919870007
87895752953320.408206258-57568.408206258
88891321.6917013.35482496-25691.7548249596
89941553.6939183.3659994582370.2340005415
90895752905175.975094029-9423.97509402886
91808641.6847885.51624927-39243.91624927
92748612.8796191.15068237-47578.3506823701
93813072830779.720659786-17707.7206597858
94661502.4694873.75200215-33371.3520021501
95799281.6766175.38445627733106.2155437225
96872601.6812241.78764259160359.8123574086
97895752831756.98343708763995.0165629133
98845083.2805415.42297566739667.7770243331
99781060.8789250.797626405-8189.99762640451
100826862.4789741.05506966537121.3449303347
101845083.2848765.323070885-3682.12307088461
102831292.8809661.50680793921631.2931920609
103693451.2752459.050970031-59007.8509700312
104629491.2691921.314224907-62430.1142249071
105675230.4731546.326139923-56315.9261399234
106537451.2587556.608032979-50105.4080329792
107679723.2674068.4304888965654.76951110444
108730392715389.57240263515002.4275973646
109771700.8715621.07293371656079.7270662837
110702811.2679067.16541844523744.0345815552
111638352635036.665338073315.33466192975
112675230.4658419.84858451916810.5514154807
113693451.2676697.19584475116754.004155249
114657009.6661769.410845689-4759.81084568857
115519230.4563995.714636258-44765.3146362579
116459201.6510877.858995061-51676.2589950606
117514300.8538962.479395858-24661.679395858
118362731.2432715.861123519-69984.6611235195
119528091.2507170.90924196120920.290758039
120629491.2544196.88902833385294.3109716665







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
121588310.894473417522536.01019103654085.778755805
122524693.866707399454701.073505512594686.659909285
123471388.472739691397625.525450454545151.420028928
124489195.042292724408657.247370062569732.837215387
125492533.779989125405473.682249586579593.877728664
126462562.371752256371651.133664695553473.609839817
127372473.179788684284544.808360676460401.551216691
128339053.012746306248670.737113168429435.288379445
129383370.702282584278962.709767496487778.694797673
130286018.771687315191474.080272835380563.463101795
131408929.270296932279874.182770998537984.357822865
132458266.834410172321399.118444867595134.550375478

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
121 & 588310.894473417 & 522536.01019103 & 654085.778755805 \tabularnewline
122 & 524693.866707399 & 454701.073505512 & 594686.659909285 \tabularnewline
123 & 471388.472739691 & 397625.525450454 & 545151.420028928 \tabularnewline
124 & 489195.042292724 & 408657.247370062 & 569732.837215387 \tabularnewline
125 & 492533.779989125 & 405473.682249586 & 579593.877728664 \tabularnewline
126 & 462562.371752256 & 371651.133664695 & 553473.609839817 \tabularnewline
127 & 372473.179788684 & 284544.808360676 & 460401.551216691 \tabularnewline
128 & 339053.012746306 & 248670.737113168 & 429435.288379445 \tabularnewline
129 & 383370.702282584 & 278962.709767496 & 487778.694797673 \tabularnewline
130 & 286018.771687315 & 191474.080272835 & 380563.463101795 \tabularnewline
131 & 408929.270296932 & 279874.182770998 & 537984.357822865 \tabularnewline
132 & 458266.834410172 & 321399.118444867 & 595134.550375478 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=&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]588310.894473417[/C][C]522536.01019103[/C][C]654085.778755805[/C][/ROW]
[ROW][C]122[/C][C]524693.866707399[/C][C]454701.073505512[/C][C]594686.659909285[/C][/ROW]
[ROW][C]123[/C][C]471388.472739691[/C][C]397625.525450454[/C][C]545151.420028928[/C][/ROW]
[ROW][C]124[/C][C]489195.042292724[/C][C]408657.247370062[/C][C]569732.837215387[/C][/ROW]
[ROW][C]125[/C][C]492533.779989125[/C][C]405473.682249586[/C][C]579593.877728664[/C][/ROW]
[ROW][C]126[/C][C]462562.371752256[/C][C]371651.133664695[/C][C]553473.609839817[/C][/ROW]
[ROW][C]127[/C][C]372473.179788684[/C][C]284544.808360676[/C][C]460401.551216691[/C][/ROW]
[ROW][C]128[/C][C]339053.012746306[/C][C]248670.737113168[/C][C]429435.288379445[/C][/ROW]
[ROW][C]129[/C][C]383370.702282584[/C][C]278962.709767496[/C][C]487778.694797673[/C][/ROW]
[ROW][C]130[/C][C]286018.771687315[/C][C]191474.080272835[/C][C]380563.463101795[/C][/ROW]
[ROW][C]131[/C][C]408929.270296932[/C][C]279874.182770998[/C][C]537984.357822865[/C][/ROW]
[ROW][C]132[/C][C]458266.834410172[/C][C]321399.118444867[/C][C]595134.550375478[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=&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
121588310.894473417522536.01019103654085.778755805
122524693.866707399454701.073505512594686.659909285
123471388.472739691397625.525450454545151.420028928
124489195.042292724408657.247370062569732.837215387
125492533.779989125405473.682249586579593.877728664
126462562.371752256371651.133664695553473.609839817
127372473.179788684284544.808360676460401.551216691
128339053.012746306248670.737113168429435.288379445
129383370.702282584278962.709767496487778.694797673
130286018.771687315191474.080272835380563.463101795
131408929.270296932279874.182770998537984.357822865
132458266.834410172321399.118444867595134.550375478



Parameters (Session):
par1 = 0.0112482002001212multiplicativeadditivemultiplicativeadditivemultiplicativemultiplicative12 ; par2 = 0.99155121212121212Triple ; par3 = 0.010012multiplicative ; par4 = 0P1 P5 Q1 Q3 P95 P99P1 P5 Q1 Q3 P95 P9912 ; par5 = 12 ; par6 = White Noise ; par7 = 0.95 ;
Parameters (R input):
par1 = 12 ; par2 = Triple ; par3 = multiplicative ; par4 = 12 ;
R code (references can be found in the software module):
par1 <- as.numeric(par1)
par4 <- as.numeric(par4)
if (par2 == 'Single') K <- 1
if (par2 == 'Double') K <- 2
if (par2 == 'Triple') K <- par1
nx <- length(x)
nxmK <- nx - K
x <- ts(x, frequency = par1)
if (par2 == 'Single') fit <- HoltWinters(x, gamma=F, beta=F)
if (par2 == 'Double') fit <- HoltWinters(x, gamma=F)
if (par2 == 'Triple') fit <- HoltWinters(x, seasonal=par3)
fit
myresid <- x - fit$fitted[,'xhat']
bitmap(file='test1.png')
op <- par(mfrow=c(2,1))
plot(fit,ylab='Observed (black) / Fitted (red)',main='Interpolation Fit of Exponential Smoothing')
plot(myresid,ylab='Residuals',main='Interpolation Prediction Errors')
par(op)
dev.off()
bitmap(file='test2.png')
p <- predict(fit, par4, prediction.interval=TRUE)
np <- length(p[,1])
plot(fit,p,ylab='Observed (black) / Fitted (red)',main='Extrapolation Fit of Exponential Smoothing')
dev.off()
bitmap(file='test3.png')
op <- par(mfrow = c(2,2))
acf(as.numeric(myresid),lag.max = nx/2,main='Residual ACF')
spectrum(myresid,main='Residals Periodogram')
cpgram(myresid,main='Residal Cumulative Periodogram')
qqnorm(myresid,main='Residual Normal QQ Plot')
qqline(myresid)
par(op)
dev.off()
load(file='createtable')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Estimated Parameters of Exponential Smoothing',2,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'Parameter',header=TRUE)
a<-table.element(a,'Value',header=TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'alpha',header=TRUE)
a<-table.element(a,fit$alpha)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'beta',header=TRUE)
a<-table.element(a,fit$beta)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'gamma',header=TRUE)
a<-table.element(a,fit$gamma)
a<-table.row.end(a)
a<-table.end(a)
table.save(a,file='mytable.tab')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Interpolation Forecasts of Exponential Smoothing',4,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'t',header=TRUE)
a<-table.element(a,'Observed',header=TRUE)
a<-table.element(a,'Fitted',header=TRUE)
a<-table.element(a,'Residuals',header=TRUE)
a<-table.row.end(a)
for (i in 1:nxmK) {
a<-table.row.start(a)
a<-table.element(a,i+K,header=TRUE)
a<-table.element(a,x[i+K])
a<-table.element(a,fit$fitted[i,'xhat'])
a<-table.element(a,myresid[i])
a<-table.row.end(a)
}
a<-table.end(a)
table.save(a,file='mytable1.tab')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Extrapolation Forecasts of Exponential Smoothing',4,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'t',header=TRUE)
a<-table.element(a,'Forecast',header=TRUE)
a<-table.element(a,'95% Lower Bound',header=TRUE)
a<-table.element(a,'95% Upper Bound',header=TRUE)
a<-table.row.end(a)
for (i in 1:np) {
a<-table.row.start(a)
a<-table.element(a,nx+i,header=TRUE)
a<-table.element(a,p[i,'fit'])
a<-table.element(a,p[i,'lwr'])
a<-table.element(a,p[i,'upr'])
a<-table.row.end(a)
}
a<-table.end(a)
table.save(a,file='mytable2.tab')