Free Statistics

of Irreproducible Research!

Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationMon, 19 Aug 2013 15:18:40 -0400
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2013/Aug/19/t1376940043hg2yl6rjkqoe4oa.htm/, Retrieved Thu, 02 May 2024 00:46:06 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=211226, Retrieved Thu, 02 May 2024 00:46:06 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact137
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [Exponential Smoothing] [single exponentia...] [2013-08-17 18:17:26] [251e6916fe5b161c77205c1c19032f50]
- R P     [Exponential Smoothing] [exponential smoot...] [2013-08-19 19:18:40] [d41d8cd98f00b204e9800998ecf8427e] [Current]
Feedback Forum

Post a new message
Dataseries X:
42364
42206
42046
41715
44991
44818
42364
40733
40891
40891
41067
41382
41873
41873
41558
40733
44991
45640
44660
42364
43346
41873
42538
42855
43186
42364
42538
41382
44991
46131
45151
43346
45309
43186
45151
44991
45482
43678
45640
45482
48426
47762
45151
43835
45640
43186
44991
45309
45973
44502
45309
45800
47604
46131
44169
42046
44011
38611
41224
42695
44169
42046
42046
42046
43186
41558
39420
37631
38929
33862
36967
38771
39102
37298
37455
36967
38611
37455
35178
33531
36315
30269
34195
35984
35984
33862
31900
31742
33531
31900
28798
26660
28956
23558
28464
31075
31900
30096
27816
29447
30096
29604
24696
22418
24047
19140
24207
26011
27482
25029
22733
24047
24696
23398
18491
16353
18316
12918
18807
22418




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time3 seconds
R Server'Sir Ronald Aylmer Fisher' @ fisher.wessa.net

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input & view raw input (R code)  \tabularnewline
Raw Output & view raw output of R engine  \tabularnewline
Computing time & 3 seconds \tabularnewline
R Server & 'Sir Ronald Aylmer Fisher' @ fisher.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=211226&T=0

[TABLE]
[ROW][C]Summary of computational transaction[/C][/ROW]
[ROW][C]Raw Input[/C][C]view raw input (R code) [/C][/ROW]
[ROW][C]Raw Output[/C][C]view raw output of R engine [/C][/ROW]
[ROW][C]Computing time[/C][C]3 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Sir Ronald Aylmer Fisher' @ fisher.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=211226&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=211226&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 Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time3 seconds
R Server'Sir Ronald Aylmer Fisher' @ fisher.wessa.net







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.405341516397662
beta0.0645237591066993
gamma1

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.405341516397662 \tabularnewline
beta & 0.0645237591066993 \tabularnewline
gamma & 1 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=211226&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]0.405341516397662[/C][/ROW]
[ROW][C]beta[/C][C]0.0645237591066993[/C][/ROW]
[ROW][C]gamma[/C][C]1[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=211226&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=211226&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
alpha0.405341516397662
beta0.0645237591066993
gamma1







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
134187341871.09615384621.90384615382209
144187341779.222142406493.7778575935663
154155841405.4161630194152.583836980608
164073340576.4790569926156.520943007432
174499144877.2314970229113.768502977058
184564045534.1717842916105.828215708381
194466043083.74472472411576.2552752759
204236442254.4850959858109.514904014184
214334642622.433971141723.566028858972
224187343127.2491875559-1254.24918755586
234253842953.2366197872-415.236619787174
244285543172.2838475371-317.283847537095
254318643504.2025801328-318.202580132849
264236443356.2197803188-992.219780318759
274253842567.7899674447-29.7899674446817
284138241653.1072084585-271.107208458525
294499145729.7536375459-738.753637545895
304613145988.7650829425142.234917057474
314515144380.8048175463770.195182453732
324334642284.83186129681061.16813870324
334530943360.79159967771948.20840032228
344318643175.025692302710.9743076973318
354515144035.02260936531115.97739063465
364499144995.2664401623-4.26644016233331
374548245523.9880451544-41.9880451543868
384367845164.8508302686-1486.85083026862
394564044813.0013244913826.998675508745
404548244189.2755683561292.72443164404
414842648749.7850095058-323.785009505817
424776249839.8079810691-2077.80798106913
434515147786.2509018059-2635.25090180586
444383544474.729068255-639.72906825503
454564045336.035301065303.964698934957
464318643236.0973910562-50.097391056217
474499144631.142512449359.857487550966
484530944501.6650194171807.334980582913
494597345241.0856166163731.914383383679
504450244260.8387535551241.161246444884
514530945954.9647039048-645.964703904792
524580044942.199574603857.800425396956
534760448284.8361999313-680.836199931262
544613148097.4394800768-1966.43948007676
554416945670.8018853701-1501.80188537011
564204643948.2777569299-1902.27775692991
574401144768.8849704824-757.884970482381
583861141910.1063714955-3299.10637149555
594122442029.1184087832-805.118408783157
604269541460.19713909641234.80286090356
614416942105.89181206842063.10818793155
624204641186.0718966139859.928103386097
634204642432.325445505-386.325445505048
644204642254.6728995362-208.672899536243
654318644057.8108966109-871.810896610856
664155842831.2651329706-1273.26513297061
673942040782.7857848316-1362.78578483158
683763138702.9853460851-1071.98534608512
693892940386.9040899344-1457.90408993438
703386235561.1480702292-1699.14807022921
713696737681.5345498269-714.534549826865
723877138234.5301306554536.469869344604
733910238943.598890824158.40110917596
743729836340.3035158453957.696484154701
753745536691.7110932468763.288906753194
763696736922.374451872244.6255481278276
773861138277.1558839606333.844116039429
783745537175.4285699953279.571430004689
793517835618.6018533232-440.601853323213
803353134025.104459689-494.104459689021
813631535668.4631155134646.536884486566
823026931561.9971467506-1292.99714675062
833419534452.8753108064-257.875310806434
843598435967.19083926716.8091607330425
853598436259.503064035-275.503064035023
863386233962.9930105513-100.993010551298
873190033749.3314562978-1849.33145629783
883174232404.968954124-662.968954124
893353133537.7495960244-6.74959602444142
903190032149.614218601-249.614218601018
912879829820.1114522608-1022.11145226081
922666027813.961419273-1153.96141927302
932895629705.7598251896-749.759825189616
942355823681.0526182465-123.052618246482
952846427493.396920736970.603079264027
963107529532.83408020231542.16591979766
973190030173.33009084831726.66990915172
983009628748.24220761951347.75779238051
992781628076.1305270965-260.130527096477
1002944728116.95719409831330.04280590171
1013009630535.4797267162-439.479726716152
1022960428903.8667346922700.133265307846
1032469626601.1512471624-1905.15124716245
1042241824236.7548876324-1818.75488763237
1052404726160.1517587612-2113.15175876118
1061914019980.5285375869-840.528537586881
1072420724158.683305026548.3166949735169
1082601126146.3241742285-135.324174228503
1092748226154.86730664291327.13269335707
1102502924270.3441758116758.655824188445
1112273322315.730192243417.269807757013
1122404723506.8918485954540.108151404598
1132469624462.4458560571233.554143942896
1142339823708.4109734179-310.410973417867
1151849119347.4844861228-856.484486122834
1161635317387.6186982753-1034.6186982753
1171831619402.3874149899-1086.3874149899
1181291814371.1792525412-1453.17925254116
1191880718788.9858922318.0141077700282
1202241820613.7730092321804.22699076802

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 41873 & 41871.0961538462 & 1.90384615382209 \tabularnewline
14 & 41873 & 41779.2221424064 & 93.7778575935663 \tabularnewline
15 & 41558 & 41405.4161630194 & 152.583836980608 \tabularnewline
16 & 40733 & 40576.4790569926 & 156.520943007432 \tabularnewline
17 & 44991 & 44877.2314970229 & 113.768502977058 \tabularnewline
18 & 45640 & 45534.1717842916 & 105.828215708381 \tabularnewline
19 & 44660 & 43083.7447247241 & 1576.2552752759 \tabularnewline
20 & 42364 & 42254.4850959858 & 109.514904014184 \tabularnewline
21 & 43346 & 42622.433971141 & 723.566028858972 \tabularnewline
22 & 41873 & 43127.2491875559 & -1254.24918755586 \tabularnewline
23 & 42538 & 42953.2366197872 & -415.236619787174 \tabularnewline
24 & 42855 & 43172.2838475371 & -317.283847537095 \tabularnewline
25 & 43186 & 43504.2025801328 & -318.202580132849 \tabularnewline
26 & 42364 & 43356.2197803188 & -992.219780318759 \tabularnewline
27 & 42538 & 42567.7899674447 & -29.7899674446817 \tabularnewline
28 & 41382 & 41653.1072084585 & -271.107208458525 \tabularnewline
29 & 44991 & 45729.7536375459 & -738.753637545895 \tabularnewline
30 & 46131 & 45988.7650829425 & 142.234917057474 \tabularnewline
31 & 45151 & 44380.8048175463 & 770.195182453732 \tabularnewline
32 & 43346 & 42284.8318612968 & 1061.16813870324 \tabularnewline
33 & 45309 & 43360.7915996777 & 1948.20840032228 \tabularnewline
34 & 43186 & 43175.0256923027 & 10.9743076973318 \tabularnewline
35 & 45151 & 44035.0226093653 & 1115.97739063465 \tabularnewline
36 & 44991 & 44995.2664401623 & -4.26644016233331 \tabularnewline
37 & 45482 & 45523.9880451544 & -41.9880451543868 \tabularnewline
38 & 43678 & 45164.8508302686 & -1486.85083026862 \tabularnewline
39 & 45640 & 44813.0013244913 & 826.998675508745 \tabularnewline
40 & 45482 & 44189.275568356 & 1292.72443164404 \tabularnewline
41 & 48426 & 48749.7850095058 & -323.785009505817 \tabularnewline
42 & 47762 & 49839.8079810691 & -2077.80798106913 \tabularnewline
43 & 45151 & 47786.2509018059 & -2635.25090180586 \tabularnewline
44 & 43835 & 44474.729068255 & -639.72906825503 \tabularnewline
45 & 45640 & 45336.035301065 & 303.964698934957 \tabularnewline
46 & 43186 & 43236.0973910562 & -50.097391056217 \tabularnewline
47 & 44991 & 44631.142512449 & 359.857487550966 \tabularnewline
48 & 45309 & 44501.6650194171 & 807.334980582913 \tabularnewline
49 & 45973 & 45241.0856166163 & 731.914383383679 \tabularnewline
50 & 44502 & 44260.8387535551 & 241.161246444884 \tabularnewline
51 & 45309 & 45954.9647039048 & -645.964703904792 \tabularnewline
52 & 45800 & 44942.199574603 & 857.800425396956 \tabularnewline
53 & 47604 & 48284.8361999313 & -680.836199931262 \tabularnewline
54 & 46131 & 48097.4394800768 & -1966.43948007676 \tabularnewline
55 & 44169 & 45670.8018853701 & -1501.80188537011 \tabularnewline
56 & 42046 & 43948.2777569299 & -1902.27775692991 \tabularnewline
57 & 44011 & 44768.8849704824 & -757.884970482381 \tabularnewline
58 & 38611 & 41910.1063714955 & -3299.10637149555 \tabularnewline
59 & 41224 & 42029.1184087832 & -805.118408783157 \tabularnewline
60 & 42695 & 41460.1971390964 & 1234.80286090356 \tabularnewline
61 & 44169 & 42105.8918120684 & 2063.10818793155 \tabularnewline
62 & 42046 & 41186.0718966139 & 859.928103386097 \tabularnewline
63 & 42046 & 42432.325445505 & -386.325445505048 \tabularnewline
64 & 42046 & 42254.6728995362 & -208.672899536243 \tabularnewline
65 & 43186 & 44057.8108966109 & -871.810896610856 \tabularnewline
66 & 41558 & 42831.2651329706 & -1273.26513297061 \tabularnewline
67 & 39420 & 40782.7857848316 & -1362.78578483158 \tabularnewline
68 & 37631 & 38702.9853460851 & -1071.98534608512 \tabularnewline
69 & 38929 & 40386.9040899344 & -1457.90408993438 \tabularnewline
70 & 33862 & 35561.1480702292 & -1699.14807022921 \tabularnewline
71 & 36967 & 37681.5345498269 & -714.534549826865 \tabularnewline
72 & 38771 & 38234.5301306554 & 536.469869344604 \tabularnewline
73 & 39102 & 38943.598890824 & 158.40110917596 \tabularnewline
74 & 37298 & 36340.3035158453 & 957.696484154701 \tabularnewline
75 & 37455 & 36691.7110932468 & 763.288906753194 \tabularnewline
76 & 36967 & 36922.3744518722 & 44.6255481278276 \tabularnewline
77 & 38611 & 38277.1558839606 & 333.844116039429 \tabularnewline
78 & 37455 & 37175.4285699953 & 279.571430004689 \tabularnewline
79 & 35178 & 35618.6018533232 & -440.601853323213 \tabularnewline
80 & 33531 & 34025.104459689 & -494.104459689021 \tabularnewline
81 & 36315 & 35668.4631155134 & 646.536884486566 \tabularnewline
82 & 30269 & 31561.9971467506 & -1292.99714675062 \tabularnewline
83 & 34195 & 34452.8753108064 & -257.875310806434 \tabularnewline
84 & 35984 & 35967.190839267 & 16.8091607330425 \tabularnewline
85 & 35984 & 36259.503064035 & -275.503064035023 \tabularnewline
86 & 33862 & 33962.9930105513 & -100.993010551298 \tabularnewline
87 & 31900 & 33749.3314562978 & -1849.33145629783 \tabularnewline
88 & 31742 & 32404.968954124 & -662.968954124 \tabularnewline
89 & 33531 & 33537.7495960244 & -6.74959602444142 \tabularnewline
90 & 31900 & 32149.614218601 & -249.614218601018 \tabularnewline
91 & 28798 & 29820.1114522608 & -1022.11145226081 \tabularnewline
92 & 26660 & 27813.961419273 & -1153.96141927302 \tabularnewline
93 & 28956 & 29705.7598251896 & -749.759825189616 \tabularnewline
94 & 23558 & 23681.0526182465 & -123.052618246482 \tabularnewline
95 & 28464 & 27493.396920736 & 970.603079264027 \tabularnewline
96 & 31075 & 29532.8340802023 & 1542.16591979766 \tabularnewline
97 & 31900 & 30173.3300908483 & 1726.66990915172 \tabularnewline
98 & 30096 & 28748.2422076195 & 1347.75779238051 \tabularnewline
99 & 27816 & 28076.1305270965 & -260.130527096477 \tabularnewline
100 & 29447 & 28116.9571940983 & 1330.04280590171 \tabularnewline
101 & 30096 & 30535.4797267162 & -439.479726716152 \tabularnewline
102 & 29604 & 28903.8667346922 & 700.133265307846 \tabularnewline
103 & 24696 & 26601.1512471624 & -1905.15124716245 \tabularnewline
104 & 22418 & 24236.7548876324 & -1818.75488763237 \tabularnewline
105 & 24047 & 26160.1517587612 & -2113.15175876118 \tabularnewline
106 & 19140 & 19980.5285375869 & -840.528537586881 \tabularnewline
107 & 24207 & 24158.6833050265 & 48.3166949735169 \tabularnewline
108 & 26011 & 26146.3241742285 & -135.324174228503 \tabularnewline
109 & 27482 & 26154.8673066429 & 1327.13269335707 \tabularnewline
110 & 25029 & 24270.3441758116 & 758.655824188445 \tabularnewline
111 & 22733 & 22315.730192243 & 417.269807757013 \tabularnewline
112 & 24047 & 23506.8918485954 & 540.108151404598 \tabularnewline
113 & 24696 & 24462.4458560571 & 233.554143942896 \tabularnewline
114 & 23398 & 23708.4109734179 & -310.410973417867 \tabularnewline
115 & 18491 & 19347.4844861228 & -856.484486122834 \tabularnewline
116 & 16353 & 17387.6186982753 & -1034.6186982753 \tabularnewline
117 & 18316 & 19402.3874149899 & -1086.3874149899 \tabularnewline
118 & 12918 & 14371.1792525412 & -1453.17925254116 \tabularnewline
119 & 18807 & 18788.98589223 & 18.0141077700282 \tabularnewline
120 & 22418 & 20613.773009232 & 1804.22699076802 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=211226&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]41873[/C][C]41871.0961538462[/C][C]1.90384615382209[/C][/ROW]
[ROW][C]14[/C][C]41873[/C][C]41779.2221424064[/C][C]93.7778575935663[/C][/ROW]
[ROW][C]15[/C][C]41558[/C][C]41405.4161630194[/C][C]152.583836980608[/C][/ROW]
[ROW][C]16[/C][C]40733[/C][C]40576.4790569926[/C][C]156.520943007432[/C][/ROW]
[ROW][C]17[/C][C]44991[/C][C]44877.2314970229[/C][C]113.768502977058[/C][/ROW]
[ROW][C]18[/C][C]45640[/C][C]45534.1717842916[/C][C]105.828215708381[/C][/ROW]
[ROW][C]19[/C][C]44660[/C][C]43083.7447247241[/C][C]1576.2552752759[/C][/ROW]
[ROW][C]20[/C][C]42364[/C][C]42254.4850959858[/C][C]109.514904014184[/C][/ROW]
[ROW][C]21[/C][C]43346[/C][C]42622.433971141[/C][C]723.566028858972[/C][/ROW]
[ROW][C]22[/C][C]41873[/C][C]43127.2491875559[/C][C]-1254.24918755586[/C][/ROW]
[ROW][C]23[/C][C]42538[/C][C]42953.2366197872[/C][C]-415.236619787174[/C][/ROW]
[ROW][C]24[/C][C]42855[/C][C]43172.2838475371[/C][C]-317.283847537095[/C][/ROW]
[ROW][C]25[/C][C]43186[/C][C]43504.2025801328[/C][C]-318.202580132849[/C][/ROW]
[ROW][C]26[/C][C]42364[/C][C]43356.2197803188[/C][C]-992.219780318759[/C][/ROW]
[ROW][C]27[/C][C]42538[/C][C]42567.7899674447[/C][C]-29.7899674446817[/C][/ROW]
[ROW][C]28[/C][C]41382[/C][C]41653.1072084585[/C][C]-271.107208458525[/C][/ROW]
[ROW][C]29[/C][C]44991[/C][C]45729.7536375459[/C][C]-738.753637545895[/C][/ROW]
[ROW][C]30[/C][C]46131[/C][C]45988.7650829425[/C][C]142.234917057474[/C][/ROW]
[ROW][C]31[/C][C]45151[/C][C]44380.8048175463[/C][C]770.195182453732[/C][/ROW]
[ROW][C]32[/C][C]43346[/C][C]42284.8318612968[/C][C]1061.16813870324[/C][/ROW]
[ROW][C]33[/C][C]45309[/C][C]43360.7915996777[/C][C]1948.20840032228[/C][/ROW]
[ROW][C]34[/C][C]43186[/C][C]43175.0256923027[/C][C]10.9743076973318[/C][/ROW]
[ROW][C]35[/C][C]45151[/C][C]44035.0226093653[/C][C]1115.97739063465[/C][/ROW]
[ROW][C]36[/C][C]44991[/C][C]44995.2664401623[/C][C]-4.26644016233331[/C][/ROW]
[ROW][C]37[/C][C]45482[/C][C]45523.9880451544[/C][C]-41.9880451543868[/C][/ROW]
[ROW][C]38[/C][C]43678[/C][C]45164.8508302686[/C][C]-1486.85083026862[/C][/ROW]
[ROW][C]39[/C][C]45640[/C][C]44813.0013244913[/C][C]826.998675508745[/C][/ROW]
[ROW][C]40[/C][C]45482[/C][C]44189.275568356[/C][C]1292.72443164404[/C][/ROW]
[ROW][C]41[/C][C]48426[/C][C]48749.7850095058[/C][C]-323.785009505817[/C][/ROW]
[ROW][C]42[/C][C]47762[/C][C]49839.8079810691[/C][C]-2077.80798106913[/C][/ROW]
[ROW][C]43[/C][C]45151[/C][C]47786.2509018059[/C][C]-2635.25090180586[/C][/ROW]
[ROW][C]44[/C][C]43835[/C][C]44474.729068255[/C][C]-639.72906825503[/C][/ROW]
[ROW][C]45[/C][C]45640[/C][C]45336.035301065[/C][C]303.964698934957[/C][/ROW]
[ROW][C]46[/C][C]43186[/C][C]43236.0973910562[/C][C]-50.097391056217[/C][/ROW]
[ROW][C]47[/C][C]44991[/C][C]44631.142512449[/C][C]359.857487550966[/C][/ROW]
[ROW][C]48[/C][C]45309[/C][C]44501.6650194171[/C][C]807.334980582913[/C][/ROW]
[ROW][C]49[/C][C]45973[/C][C]45241.0856166163[/C][C]731.914383383679[/C][/ROW]
[ROW][C]50[/C][C]44502[/C][C]44260.8387535551[/C][C]241.161246444884[/C][/ROW]
[ROW][C]51[/C][C]45309[/C][C]45954.9647039048[/C][C]-645.964703904792[/C][/ROW]
[ROW][C]52[/C][C]45800[/C][C]44942.199574603[/C][C]857.800425396956[/C][/ROW]
[ROW][C]53[/C][C]47604[/C][C]48284.8361999313[/C][C]-680.836199931262[/C][/ROW]
[ROW][C]54[/C][C]46131[/C][C]48097.4394800768[/C][C]-1966.43948007676[/C][/ROW]
[ROW][C]55[/C][C]44169[/C][C]45670.8018853701[/C][C]-1501.80188537011[/C][/ROW]
[ROW][C]56[/C][C]42046[/C][C]43948.2777569299[/C][C]-1902.27775692991[/C][/ROW]
[ROW][C]57[/C][C]44011[/C][C]44768.8849704824[/C][C]-757.884970482381[/C][/ROW]
[ROW][C]58[/C][C]38611[/C][C]41910.1063714955[/C][C]-3299.10637149555[/C][/ROW]
[ROW][C]59[/C][C]41224[/C][C]42029.1184087832[/C][C]-805.118408783157[/C][/ROW]
[ROW][C]60[/C][C]42695[/C][C]41460.1971390964[/C][C]1234.80286090356[/C][/ROW]
[ROW][C]61[/C][C]44169[/C][C]42105.8918120684[/C][C]2063.10818793155[/C][/ROW]
[ROW][C]62[/C][C]42046[/C][C]41186.0718966139[/C][C]859.928103386097[/C][/ROW]
[ROW][C]63[/C][C]42046[/C][C]42432.325445505[/C][C]-386.325445505048[/C][/ROW]
[ROW][C]64[/C][C]42046[/C][C]42254.6728995362[/C][C]-208.672899536243[/C][/ROW]
[ROW][C]65[/C][C]43186[/C][C]44057.8108966109[/C][C]-871.810896610856[/C][/ROW]
[ROW][C]66[/C][C]41558[/C][C]42831.2651329706[/C][C]-1273.26513297061[/C][/ROW]
[ROW][C]67[/C][C]39420[/C][C]40782.7857848316[/C][C]-1362.78578483158[/C][/ROW]
[ROW][C]68[/C][C]37631[/C][C]38702.9853460851[/C][C]-1071.98534608512[/C][/ROW]
[ROW][C]69[/C][C]38929[/C][C]40386.9040899344[/C][C]-1457.90408993438[/C][/ROW]
[ROW][C]70[/C][C]33862[/C][C]35561.1480702292[/C][C]-1699.14807022921[/C][/ROW]
[ROW][C]71[/C][C]36967[/C][C]37681.5345498269[/C][C]-714.534549826865[/C][/ROW]
[ROW][C]72[/C][C]38771[/C][C]38234.5301306554[/C][C]536.469869344604[/C][/ROW]
[ROW][C]73[/C][C]39102[/C][C]38943.598890824[/C][C]158.40110917596[/C][/ROW]
[ROW][C]74[/C][C]37298[/C][C]36340.3035158453[/C][C]957.696484154701[/C][/ROW]
[ROW][C]75[/C][C]37455[/C][C]36691.7110932468[/C][C]763.288906753194[/C][/ROW]
[ROW][C]76[/C][C]36967[/C][C]36922.3744518722[/C][C]44.6255481278276[/C][/ROW]
[ROW][C]77[/C][C]38611[/C][C]38277.1558839606[/C][C]333.844116039429[/C][/ROW]
[ROW][C]78[/C][C]37455[/C][C]37175.4285699953[/C][C]279.571430004689[/C][/ROW]
[ROW][C]79[/C][C]35178[/C][C]35618.6018533232[/C][C]-440.601853323213[/C][/ROW]
[ROW][C]80[/C][C]33531[/C][C]34025.104459689[/C][C]-494.104459689021[/C][/ROW]
[ROW][C]81[/C][C]36315[/C][C]35668.4631155134[/C][C]646.536884486566[/C][/ROW]
[ROW][C]82[/C][C]30269[/C][C]31561.9971467506[/C][C]-1292.99714675062[/C][/ROW]
[ROW][C]83[/C][C]34195[/C][C]34452.8753108064[/C][C]-257.875310806434[/C][/ROW]
[ROW][C]84[/C][C]35984[/C][C]35967.190839267[/C][C]16.8091607330425[/C][/ROW]
[ROW][C]85[/C][C]35984[/C][C]36259.503064035[/C][C]-275.503064035023[/C][/ROW]
[ROW][C]86[/C][C]33862[/C][C]33962.9930105513[/C][C]-100.993010551298[/C][/ROW]
[ROW][C]87[/C][C]31900[/C][C]33749.3314562978[/C][C]-1849.33145629783[/C][/ROW]
[ROW][C]88[/C][C]31742[/C][C]32404.968954124[/C][C]-662.968954124[/C][/ROW]
[ROW][C]89[/C][C]33531[/C][C]33537.7495960244[/C][C]-6.74959602444142[/C][/ROW]
[ROW][C]90[/C][C]31900[/C][C]32149.614218601[/C][C]-249.614218601018[/C][/ROW]
[ROW][C]91[/C][C]28798[/C][C]29820.1114522608[/C][C]-1022.11145226081[/C][/ROW]
[ROW][C]92[/C][C]26660[/C][C]27813.961419273[/C][C]-1153.96141927302[/C][/ROW]
[ROW][C]93[/C][C]28956[/C][C]29705.7598251896[/C][C]-749.759825189616[/C][/ROW]
[ROW][C]94[/C][C]23558[/C][C]23681.0526182465[/C][C]-123.052618246482[/C][/ROW]
[ROW][C]95[/C][C]28464[/C][C]27493.396920736[/C][C]970.603079264027[/C][/ROW]
[ROW][C]96[/C][C]31075[/C][C]29532.8340802023[/C][C]1542.16591979766[/C][/ROW]
[ROW][C]97[/C][C]31900[/C][C]30173.3300908483[/C][C]1726.66990915172[/C][/ROW]
[ROW][C]98[/C][C]30096[/C][C]28748.2422076195[/C][C]1347.75779238051[/C][/ROW]
[ROW][C]99[/C][C]27816[/C][C]28076.1305270965[/C][C]-260.130527096477[/C][/ROW]
[ROW][C]100[/C][C]29447[/C][C]28116.9571940983[/C][C]1330.04280590171[/C][/ROW]
[ROW][C]101[/C][C]30096[/C][C]30535.4797267162[/C][C]-439.479726716152[/C][/ROW]
[ROW][C]102[/C][C]29604[/C][C]28903.8667346922[/C][C]700.133265307846[/C][/ROW]
[ROW][C]103[/C][C]24696[/C][C]26601.1512471624[/C][C]-1905.15124716245[/C][/ROW]
[ROW][C]104[/C][C]22418[/C][C]24236.7548876324[/C][C]-1818.75488763237[/C][/ROW]
[ROW][C]105[/C][C]24047[/C][C]26160.1517587612[/C][C]-2113.15175876118[/C][/ROW]
[ROW][C]106[/C][C]19140[/C][C]19980.5285375869[/C][C]-840.528537586881[/C][/ROW]
[ROW][C]107[/C][C]24207[/C][C]24158.6833050265[/C][C]48.3166949735169[/C][/ROW]
[ROW][C]108[/C][C]26011[/C][C]26146.3241742285[/C][C]-135.324174228503[/C][/ROW]
[ROW][C]109[/C][C]27482[/C][C]26154.8673066429[/C][C]1327.13269335707[/C][/ROW]
[ROW][C]110[/C][C]25029[/C][C]24270.3441758116[/C][C]758.655824188445[/C][/ROW]
[ROW][C]111[/C][C]22733[/C][C]22315.730192243[/C][C]417.269807757013[/C][/ROW]
[ROW][C]112[/C][C]24047[/C][C]23506.8918485954[/C][C]540.108151404598[/C][/ROW]
[ROW][C]113[/C][C]24696[/C][C]24462.4458560571[/C][C]233.554143942896[/C][/ROW]
[ROW][C]114[/C][C]23398[/C][C]23708.4109734179[/C][C]-310.410973417867[/C][/ROW]
[ROW][C]115[/C][C]18491[/C][C]19347.4844861228[/C][C]-856.484486122834[/C][/ROW]
[ROW][C]116[/C][C]16353[/C][C]17387.6186982753[/C][C]-1034.6186982753[/C][/ROW]
[ROW][C]117[/C][C]18316[/C][C]19402.3874149899[/C][C]-1086.3874149899[/C][/ROW]
[ROW][C]118[/C][C]12918[/C][C]14371.1792525412[/C][C]-1453.17925254116[/C][/ROW]
[ROW][C]119[/C][C]18807[/C][C]18788.98589223[/C][C]18.0141077700282[/C][/ROW]
[ROW][C]120[/C][C]22418[/C][C]20613.773009232[/C][C]1804.22699076802[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=211226&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=211226&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
134187341871.09615384621.90384615382209
144187341779.222142406493.7778575935663
154155841405.4161630194152.583836980608
164073340576.4790569926156.520943007432
174499144877.2314970229113.768502977058
184564045534.1717842916105.828215708381
194466043083.74472472411576.2552752759
204236442254.4850959858109.514904014184
214334642622.433971141723.566028858972
224187343127.2491875559-1254.24918755586
234253842953.2366197872-415.236619787174
244285543172.2838475371-317.283847537095
254318643504.2025801328-318.202580132849
264236443356.2197803188-992.219780318759
274253842567.7899674447-29.7899674446817
284138241653.1072084585-271.107208458525
294499145729.7536375459-738.753637545895
304613145988.7650829425142.234917057474
314515144380.8048175463770.195182453732
324334642284.83186129681061.16813870324
334530943360.79159967771948.20840032228
344318643175.025692302710.9743076973318
354515144035.02260936531115.97739063465
364499144995.2664401623-4.26644016233331
374548245523.9880451544-41.9880451543868
384367845164.8508302686-1486.85083026862
394564044813.0013244913826.998675508745
404548244189.2755683561292.72443164404
414842648749.7850095058-323.785009505817
424776249839.8079810691-2077.80798106913
434515147786.2509018059-2635.25090180586
444383544474.729068255-639.72906825503
454564045336.035301065303.964698934957
464318643236.0973910562-50.097391056217
474499144631.142512449359.857487550966
484530944501.6650194171807.334980582913
494597345241.0856166163731.914383383679
504450244260.8387535551241.161246444884
514530945954.9647039048-645.964703904792
524580044942.199574603857.800425396956
534760448284.8361999313-680.836199931262
544613148097.4394800768-1966.43948007676
554416945670.8018853701-1501.80188537011
564204643948.2777569299-1902.27775692991
574401144768.8849704824-757.884970482381
583861141910.1063714955-3299.10637149555
594122442029.1184087832-805.118408783157
604269541460.19713909641234.80286090356
614416942105.89181206842063.10818793155
624204641186.0718966139859.928103386097
634204642432.325445505-386.325445505048
644204642254.6728995362-208.672899536243
654318644057.8108966109-871.810896610856
664155842831.2651329706-1273.26513297061
673942040782.7857848316-1362.78578483158
683763138702.9853460851-1071.98534608512
693892940386.9040899344-1457.90408993438
703386235561.1480702292-1699.14807022921
713696737681.5345498269-714.534549826865
723877138234.5301306554536.469869344604
733910238943.598890824158.40110917596
743729836340.3035158453957.696484154701
753745536691.7110932468763.288906753194
763696736922.374451872244.6255481278276
773861138277.1558839606333.844116039429
783745537175.4285699953279.571430004689
793517835618.6018533232-440.601853323213
803353134025.104459689-494.104459689021
813631535668.4631155134646.536884486566
823026931561.9971467506-1292.99714675062
833419534452.8753108064-257.875310806434
843598435967.19083926716.8091607330425
853598436259.503064035-275.503064035023
863386233962.9930105513-100.993010551298
873190033749.3314562978-1849.33145629783
883174232404.968954124-662.968954124
893353133537.7495960244-6.74959602444142
903190032149.614218601-249.614218601018
912879829820.1114522608-1022.11145226081
922666027813.961419273-1153.96141927302
932895629705.7598251896-749.759825189616
942355823681.0526182465-123.052618246482
952846427493.396920736970.603079264027
963107529532.83408020231542.16591979766
973190030173.33009084831726.66990915172
983009628748.24220761951347.75779238051
992781628076.1305270965-260.130527096477
1002944728116.95719409831330.04280590171
1013009630535.4797267162-439.479726716152
1022960428903.8667346922700.133265307846
1032469626601.1512471624-1905.15124716245
1042241824236.7548876324-1818.75488763237
1052404726160.1517587612-2113.15175876118
1061914019980.5285375869-840.528537586881
1072420724158.683305026548.3166949735169
1082601126146.3241742285-135.324174228503
1092748226154.86730664291327.13269335707
1102502924270.3441758116758.655824188445
1112273322315.730192243417.269807757013
1122404723506.8918485954540.108151404598
1132469624462.4458560571233.554143942896
1142339823708.4109734179-310.410973417867
1151849119347.4844861228-856.484486122834
1161635317387.6186982753-1034.6186982753
1171831619402.3874149899-1086.3874149899
1181291814371.1792525412-1453.17925254116
1191880718788.9858922318.0141077700282
1202241820613.7730092321804.22699076802







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
12122287.519208780720258.815565062224316.2228524993
12219501.65454152517292.147107864121711.1619751859
12316991.325795280114594.678910549519387.9726800106
12418030.292227918315440.456602096920620.1278537396
12518514.391652675415725.565652700221303.2176526506
12617265.874310904714272.472820816920259.2758009925
12712637.82177259399434.4508668727215841.192678315
12810873.37505684227454.8111745811814291.9389391031
12913257.97193250249619.1445697418116896.799295263
1308458.658316289874594.6354955850312322.6811369947
13114388.015632791110293.99158686318482.0396787191
13217314.875566861512986.160204564921643.5909291581

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
121 & 22287.5192087807 & 20258.8155650622 & 24316.2228524993 \tabularnewline
122 & 19501.654541525 & 17292.1471078641 & 21711.1619751859 \tabularnewline
123 & 16991.3257952801 & 14594.6789105495 & 19387.9726800106 \tabularnewline
124 & 18030.2922279183 & 15440.4566020969 & 20620.1278537396 \tabularnewline
125 & 18514.3916526754 & 15725.5656527002 & 21303.2176526506 \tabularnewline
126 & 17265.8743109047 & 14272.4728208169 & 20259.2758009925 \tabularnewline
127 & 12637.8217725939 & 9434.45086687272 & 15841.192678315 \tabularnewline
128 & 10873.3750568422 & 7454.81117458118 & 14291.9389391031 \tabularnewline
129 & 13257.9719325024 & 9619.14456974181 & 16896.799295263 \tabularnewline
130 & 8458.65831628987 & 4594.63549558503 & 12322.6811369947 \tabularnewline
131 & 14388.0156327911 & 10293.991586863 & 18482.0396787191 \tabularnewline
132 & 17314.8755668615 & 12986.1602045649 & 21643.5909291581 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=211226&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]22287.5192087807[/C][C]20258.8155650622[/C][C]24316.2228524993[/C][/ROW]
[ROW][C]122[/C][C]19501.654541525[/C][C]17292.1471078641[/C][C]21711.1619751859[/C][/ROW]
[ROW][C]123[/C][C]16991.3257952801[/C][C]14594.6789105495[/C][C]19387.9726800106[/C][/ROW]
[ROW][C]124[/C][C]18030.2922279183[/C][C]15440.4566020969[/C][C]20620.1278537396[/C][/ROW]
[ROW][C]125[/C][C]18514.3916526754[/C][C]15725.5656527002[/C][C]21303.2176526506[/C][/ROW]
[ROW][C]126[/C][C]17265.8743109047[/C][C]14272.4728208169[/C][C]20259.2758009925[/C][/ROW]
[ROW][C]127[/C][C]12637.8217725939[/C][C]9434.45086687272[/C][C]15841.192678315[/C][/ROW]
[ROW][C]128[/C][C]10873.3750568422[/C][C]7454.81117458118[/C][C]14291.9389391031[/C][/ROW]
[ROW][C]129[/C][C]13257.9719325024[/C][C]9619.14456974181[/C][C]16896.799295263[/C][/ROW]
[ROW][C]130[/C][C]8458.65831628987[/C][C]4594.63549558503[/C][C]12322.6811369947[/C][/ROW]
[ROW][C]131[/C][C]14388.0156327911[/C][C]10293.991586863[/C][C]18482.0396787191[/C][/ROW]
[ROW][C]132[/C][C]17314.8755668615[/C][C]12986.1602045649[/C][C]21643.5909291581[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=211226&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=211226&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
12122287.519208780720258.815565062224316.2228524993
12219501.65454152517292.147107864121711.1619751859
12316991.325795280114594.678910549519387.9726800106
12418030.292227918315440.456602096920620.1278537396
12518514.391652675415725.565652700221303.2176526506
12617265.874310904714272.472820816920259.2758009925
12712637.82177259399434.4508668727215841.192678315
12810873.37505684227454.8111745811814291.9389391031
12913257.97193250249619.1445697418116896.799295263
1308458.658316289874594.6354955850312322.6811369947
13114388.015632791110293.99158686318482.0396787191
13217314.875566861512986.160204564921643.5909291581



Parameters (Session):
par1 = 12 ; par2 = Triple ; par3 = multiplicative ;
Parameters (R input):
par1 = 12 ; par2 = Triple ; par3 = multiplicative ;
R code (references can be found in the software module):
par3 <- 'additive'
par2 <- 'Triple'
par1 <- '12'
par1 <- as.numeric(par1)
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$fitted[,'xhat']
bitmap(file='test1.png')
op <- par(mfrow=c(2,1))
plot(fit,ylab='Observed (black) / Fitted (red)',main='Interpolation Fit of Exponential Smoothing')
plot(myresid,ylab='Residuals',main='Interpolation Prediction Errors')
par(op)
dev.off()
bitmap(file='test2.png')
p <- predict(fit, par1, prediction.interval=TRUE)
np <- length(p[,1])
plot(fit,p,ylab='Observed (black) / Fitted (red)',main='Extrapolation Fit of Exponential Smoothing')
dev.off()
bitmap(file='test3.png')
op <- par(mfrow = c(2,2))
acf(as.numeric(myresid),lag.max = nx/2,main='Residual ACF')
spectrum(myresid,main='Residals Periodogram')
cpgram(myresid,main='Residal Cumulative Periodogram')
qqnorm(myresid,main='Residual Normal QQ Plot')
qqline(myresid)
par(op)
dev.off()
load(file='createtable')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Estimated Parameters of Exponential Smoothing',2,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'Parameter',header=TRUE)
a<-table.element(a,'Value',header=TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'alpha',header=TRUE)
a<-table.element(a,fit$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')