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 computationFri, 04 Dec 2009 12:32:15 -0700
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2009/Dec/04/t1259955185606htjzu5ua42i1.htm/, Retrieved Sun, 28 Apr 2024 08:13:11 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=64077, Retrieved Sun, 28 Apr 2024 08:13:11 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact131
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [Univariate Data Series] [data set] [2008-12-01 19:54:57] [b98453cac15ba1066b407e146608df68]
- RMP   [Exponential Smoothing] [] [2009-11-27 15:04:36] [b98453cac15ba1066b407e146608df68]
-   PD    [Exponential Smoothing] [BBWS9-exponential...] [2009-12-01 20:49:49] [408e92805dcb18620260f240a7fb9d53]
-   PD      [Exponential Smoothing] [shw-ws9] [2009-12-04 13:41:32] [2663058f2a5dda519058ac6b2228468f]
-   PD          [Exponential Smoothing] [ws 9 theorie 2] [2009-12-04 19:32:15] [4f297b039e1043ebee7ff7a83b1eaaaa] [Current]
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Dataseries X:
100.01
103.84
104.48
95.43
104.80
108.64
105.65
108.42
115.35
113.64
115.24
100.33
101.29
104.48
99.26
100.11
103.52
101.18
96.39
97.56
96.39
85.10
79.77
79.13
80.84
82.75
92.55
96.60
96.92
95.32
98.52
100.22
104.91
103.10
97.13
103.42
111.72
118.11
111.62
100.22
102.03
105.76
107.68
110.77
105.44
112.26
114.07
117.90
124.72
126.42
134.73
135.79
143.36
140.37
144.74
151.98
150.92
163.38
154.43
146.66
157.95
162.10
180.42
179.57
171.58
185.43
190.64
203.00
202.36
193.41
186.17
192.24
209.60
206.41
209.82
230.37
235.80
232.07
244.64
242.19
217.48
209.39
211.73
221.00
203.11
214.71
224.19
238.04
238.36
246.24
259.87
249.97
266.48
282.98
306.31
301.73
314.62
332.62
355.51
370.32
408.13
433.58
440.51
386.29
342.84
254.97
203.42
170.09
174.03
167.85
177.01
188.19
211.20
240.91
230.26
251.25
241.66




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'Gwilym Jenkins' @ 72.249.127.135

\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 & 2 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ 72.249.127.135 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=64077&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]2 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Gwilym Jenkins' @ 72.249.127.135[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=64077&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=64077&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 time2 seconds
R Server'Gwilym Jenkins' @ 72.249.127.135







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.920153543184328
beta0
gamma1

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.920153543184328 \tabularnewline
beta & 0 \tabularnewline
gamma & 1 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=64077&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]0.920153543184328[/C][/ROW]
[ROW][C]beta[/C][C]0[/C][/ROW]
[ROW][C]gamma[/C][C]1[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=64077&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=64077&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
alpha0.920153543184328
beta0
gamma1







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
13101.29102.550463407594-1.26046340759406
14104.48104.602730522094-0.122730522094429
1599.2699.6753984574467-0.415398457446727
16100.11101.289862238172-1.17986223817176
17103.52105.559180439175-2.0391804391746
18101.18102.963286964500-1.78328696450015
1996.3994.89787311406551.49212688593451
2097.5697.8852964365457-0.325296436545713
2196.39103.119535295576-6.72953529557613
2285.194.6332701866511-9.53327018665112
2379.7786.0655769472826-6.29557694728264
2479.1369.35063674480699.77936325519308
2580.8478.75493561197572.08506438802434
2682.7583.1372271531058-0.387227153105812
2792.5578.784053340280413.7659466597196
2896.693.16952744648663.43047255351337
2996.92101.377299851777-4.45729985177677
3095.3296.564852267570-1.24485226756993
3198.5289.55925308059198.96074691940808
32100.2299.30757644026210.912423559737888
33104.91105.290777026023-0.380777026023466
34103.1102.1915929707190.908407029281022
3597.13103.729976358562-6.59997635856163
36103.4285.923209636714817.4967903632852
37111.72101.9773835784089.74261642159215
38118.11114.3573944706273.7526055293734
39111.62113.850245539943-2.230245539943
40100.22113.035460127926-12.8154601279261
41102.03105.902646682722-3.87264668272198
42105.76101.9061009372493.85389906275057
43107.6899.89132804858637.78867195141372
44110.77108.0648696571102.70513034289016
45105.44116.205272156857-10.7652721568571
46112.26103.6295795184958.63042048150494
47114.07111.719037848182.35096215181997
48117.9102.25921975182215.6407802481777
49124.72115.9322353820068.78776461799356
50126.42127.359399204059-0.939399204058844
51134.73121.79517068882712.9348293111733
52135.79134.1832787295831.60672127041653
53143.36143.2228805716040.137119428395977
54140.37143.942195012112-3.57219501211239
55144.74133.89460311932310.8453968806771
56151.98144.9518474901977.02815250980285
57150.92157.886378739035-6.9663787390354
58163.38150.17718294092413.2028170590756
59154.43162.202177118590-7.7721771185904
60146.66140.7733395670045.88666043299571
61157.95144.75525091196313.1947490880372
62162.1160.3337042169741.76629578302607
63180.42157.46502637803822.9549736219623
64179.57178.2926864849711.27731351502882
65171.58189.580964914839-18.0009649148392
66185.43173.54580531557211.8841946844279
67190.64177.29122806907613.3487719309241
68203190.81558501792912.1844149820714
69202.36209.395850986913-7.03585098691346
70193.41203.538037353040-10.1280373530402
71186.17192.212178995332-6.04217899533177
72192.24170.86145790627721.3785420937233
73209.6189.56210205162520.0378979483749
74206.41211.583459744775-5.17345974477499
75209.82203.1950428966166.62495710338416
76230.37207.06972047595623.3002795240444
77235.8239.475619716213-3.67561971621279
78232.07240.352155936019-8.28215593601874
79244.64223.9807502912920.65924970871
80242.19244.617380800953-2.42738080095259
81217.48249.497595313175-32.0175953131751
82209.39220.472571918630-11.0825719186305
83211.73208.5086987830793.22130121692123
84221195.93294186297325.0670581370273
85203.11217.721859797283-14.6118597972831
86214.71205.7770935834818.93290641651939
87224.19211.22594558275312.9640544172466
88238.04222.07443789381015.9655621061904
89238.36245.841137318728-7.48113731872832
90246.24242.8899073646073.35009263539334
91259.87239.0606922603120.8093077396901
92249.97258.024929564917-8.05492956491722
93266.48255.20529142997911.2747085700207
94282.98268.29444972695214.6855502730481
95306.31281.26522737342125.0447726265787
96301.73284.53830592082417.1916940791764
97314.62294.50168828710620.1183117128938
98332.62318.62634926305213.9936507369484
99355.51328.08049558086627.4295044191337
100370.32352.34039572006317.979604279937
101408.13380.48515842140527.6448415785947
102433.58414.69419897462118.8858010253791
103440.51422.81328106255717.6967189374425
104386.29435.441061327431-49.1510613274305
105342.84400.222905935782-57.3829059357818
106254.97351.509404824083-96.5394048240827
107203.42262.739092371358-59.3190923713579
108170.09193.980810218526-23.8908102185262
109174.03168.3901056442535.63989435574683
110167.85176.012232952996-8.1622329529965
111177.01166.82679946962710.1832005303732
112188.19174.89221223549613.2977877645044
113211.2192.89056886466018.3094311353403
114240.91213.43372481363127.4762751863690
115230.26233.155433530494-2.89543353049393
116251.25225.15019624465826.0998037553421
117241.66254.445458589964-12.7854585899641

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 101.29 & 102.550463407594 & -1.26046340759406 \tabularnewline
14 & 104.48 & 104.602730522094 & -0.122730522094429 \tabularnewline
15 & 99.26 & 99.6753984574467 & -0.415398457446727 \tabularnewline
16 & 100.11 & 101.289862238172 & -1.17986223817176 \tabularnewline
17 & 103.52 & 105.559180439175 & -2.0391804391746 \tabularnewline
18 & 101.18 & 102.963286964500 & -1.78328696450015 \tabularnewline
19 & 96.39 & 94.8978731140655 & 1.49212688593451 \tabularnewline
20 & 97.56 & 97.8852964365457 & -0.325296436545713 \tabularnewline
21 & 96.39 & 103.119535295576 & -6.72953529557613 \tabularnewline
22 & 85.1 & 94.6332701866511 & -9.53327018665112 \tabularnewline
23 & 79.77 & 86.0655769472826 & -6.29557694728264 \tabularnewline
24 & 79.13 & 69.3506367448069 & 9.77936325519308 \tabularnewline
25 & 80.84 & 78.7549356119757 & 2.08506438802434 \tabularnewline
26 & 82.75 & 83.1372271531058 & -0.387227153105812 \tabularnewline
27 & 92.55 & 78.7840533402804 & 13.7659466597196 \tabularnewline
28 & 96.6 & 93.1695274464866 & 3.43047255351337 \tabularnewline
29 & 96.92 & 101.377299851777 & -4.45729985177677 \tabularnewline
30 & 95.32 & 96.564852267570 & -1.24485226756993 \tabularnewline
31 & 98.52 & 89.5592530805919 & 8.96074691940808 \tabularnewline
32 & 100.22 & 99.3075764402621 & 0.912423559737888 \tabularnewline
33 & 104.91 & 105.290777026023 & -0.380777026023466 \tabularnewline
34 & 103.1 & 102.191592970719 & 0.908407029281022 \tabularnewline
35 & 97.13 & 103.729976358562 & -6.59997635856163 \tabularnewline
36 & 103.42 & 85.9232096367148 & 17.4967903632852 \tabularnewline
37 & 111.72 & 101.977383578408 & 9.74261642159215 \tabularnewline
38 & 118.11 & 114.357394470627 & 3.7526055293734 \tabularnewline
39 & 111.62 & 113.850245539943 & -2.230245539943 \tabularnewline
40 & 100.22 & 113.035460127926 & -12.8154601279261 \tabularnewline
41 & 102.03 & 105.902646682722 & -3.87264668272198 \tabularnewline
42 & 105.76 & 101.906100937249 & 3.85389906275057 \tabularnewline
43 & 107.68 & 99.8913280485863 & 7.78867195141372 \tabularnewline
44 & 110.77 & 108.064869657110 & 2.70513034289016 \tabularnewline
45 & 105.44 & 116.205272156857 & -10.7652721568571 \tabularnewline
46 & 112.26 & 103.629579518495 & 8.63042048150494 \tabularnewline
47 & 114.07 & 111.71903784818 & 2.35096215181997 \tabularnewline
48 & 117.9 & 102.259219751822 & 15.6407802481777 \tabularnewline
49 & 124.72 & 115.932235382006 & 8.78776461799356 \tabularnewline
50 & 126.42 & 127.359399204059 & -0.939399204058844 \tabularnewline
51 & 134.73 & 121.795170688827 & 12.9348293111733 \tabularnewline
52 & 135.79 & 134.183278729583 & 1.60672127041653 \tabularnewline
53 & 143.36 & 143.222880571604 & 0.137119428395977 \tabularnewline
54 & 140.37 & 143.942195012112 & -3.57219501211239 \tabularnewline
55 & 144.74 & 133.894603119323 & 10.8453968806771 \tabularnewline
56 & 151.98 & 144.951847490197 & 7.02815250980285 \tabularnewline
57 & 150.92 & 157.886378739035 & -6.9663787390354 \tabularnewline
58 & 163.38 & 150.177182940924 & 13.2028170590756 \tabularnewline
59 & 154.43 & 162.202177118590 & -7.7721771185904 \tabularnewline
60 & 146.66 & 140.773339567004 & 5.88666043299571 \tabularnewline
61 & 157.95 & 144.755250911963 & 13.1947490880372 \tabularnewline
62 & 162.1 & 160.333704216974 & 1.76629578302607 \tabularnewline
63 & 180.42 & 157.465026378038 & 22.9549736219623 \tabularnewline
64 & 179.57 & 178.292686484971 & 1.27731351502882 \tabularnewline
65 & 171.58 & 189.580964914839 & -18.0009649148392 \tabularnewline
66 & 185.43 & 173.545805315572 & 11.8841946844279 \tabularnewline
67 & 190.64 & 177.291228069076 & 13.3487719309241 \tabularnewline
68 & 203 & 190.815585017929 & 12.1844149820714 \tabularnewline
69 & 202.36 & 209.395850986913 & -7.03585098691346 \tabularnewline
70 & 193.41 & 203.538037353040 & -10.1280373530402 \tabularnewline
71 & 186.17 & 192.212178995332 & -6.04217899533177 \tabularnewline
72 & 192.24 & 170.861457906277 & 21.3785420937233 \tabularnewline
73 & 209.6 & 189.562102051625 & 20.0378979483749 \tabularnewline
74 & 206.41 & 211.583459744775 & -5.17345974477499 \tabularnewline
75 & 209.82 & 203.195042896616 & 6.62495710338416 \tabularnewline
76 & 230.37 & 207.069720475956 & 23.3002795240444 \tabularnewline
77 & 235.8 & 239.475619716213 & -3.67561971621279 \tabularnewline
78 & 232.07 & 240.352155936019 & -8.28215593601874 \tabularnewline
79 & 244.64 & 223.98075029129 & 20.65924970871 \tabularnewline
80 & 242.19 & 244.617380800953 & -2.42738080095259 \tabularnewline
81 & 217.48 & 249.497595313175 & -32.0175953131751 \tabularnewline
82 & 209.39 & 220.472571918630 & -11.0825719186305 \tabularnewline
83 & 211.73 & 208.508698783079 & 3.22130121692123 \tabularnewline
84 & 221 & 195.932941862973 & 25.0670581370273 \tabularnewline
85 & 203.11 & 217.721859797283 & -14.6118597972831 \tabularnewline
86 & 214.71 & 205.777093583481 & 8.93290641651939 \tabularnewline
87 & 224.19 & 211.225945582753 & 12.9640544172466 \tabularnewline
88 & 238.04 & 222.074437893810 & 15.9655621061904 \tabularnewline
89 & 238.36 & 245.841137318728 & -7.48113731872832 \tabularnewline
90 & 246.24 & 242.889907364607 & 3.35009263539334 \tabularnewline
91 & 259.87 & 239.06069226031 & 20.8093077396901 \tabularnewline
92 & 249.97 & 258.024929564917 & -8.05492956491722 \tabularnewline
93 & 266.48 & 255.205291429979 & 11.2747085700207 \tabularnewline
94 & 282.98 & 268.294449726952 & 14.6855502730481 \tabularnewline
95 & 306.31 & 281.265227373421 & 25.0447726265787 \tabularnewline
96 & 301.73 & 284.538305920824 & 17.1916940791764 \tabularnewline
97 & 314.62 & 294.501688287106 & 20.1183117128938 \tabularnewline
98 & 332.62 & 318.626349263052 & 13.9936507369484 \tabularnewline
99 & 355.51 & 328.080495580866 & 27.4295044191337 \tabularnewline
100 & 370.32 & 352.340395720063 & 17.979604279937 \tabularnewline
101 & 408.13 & 380.485158421405 & 27.6448415785947 \tabularnewline
102 & 433.58 & 414.694198974621 & 18.8858010253791 \tabularnewline
103 & 440.51 & 422.813281062557 & 17.6967189374425 \tabularnewline
104 & 386.29 & 435.441061327431 & -49.1510613274305 \tabularnewline
105 & 342.84 & 400.222905935782 & -57.3829059357818 \tabularnewline
106 & 254.97 & 351.509404824083 & -96.5394048240827 \tabularnewline
107 & 203.42 & 262.739092371358 & -59.3190923713579 \tabularnewline
108 & 170.09 & 193.980810218526 & -23.8908102185262 \tabularnewline
109 & 174.03 & 168.390105644253 & 5.63989435574683 \tabularnewline
110 & 167.85 & 176.012232952996 & -8.1622329529965 \tabularnewline
111 & 177.01 & 166.826799469627 & 10.1832005303732 \tabularnewline
112 & 188.19 & 174.892212235496 & 13.2977877645044 \tabularnewline
113 & 211.2 & 192.890568864660 & 18.3094311353403 \tabularnewline
114 & 240.91 & 213.433724813631 & 27.4762751863690 \tabularnewline
115 & 230.26 & 233.155433530494 & -2.89543353049393 \tabularnewline
116 & 251.25 & 225.150196244658 & 26.0998037553421 \tabularnewline
117 & 241.66 & 254.445458589964 & -12.7854585899641 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=64077&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]101.29[/C][C]102.550463407594[/C][C]-1.26046340759406[/C][/ROW]
[ROW][C]14[/C][C]104.48[/C][C]104.602730522094[/C][C]-0.122730522094429[/C][/ROW]
[ROW][C]15[/C][C]99.26[/C][C]99.6753984574467[/C][C]-0.415398457446727[/C][/ROW]
[ROW][C]16[/C][C]100.11[/C][C]101.289862238172[/C][C]-1.17986223817176[/C][/ROW]
[ROW][C]17[/C][C]103.52[/C][C]105.559180439175[/C][C]-2.0391804391746[/C][/ROW]
[ROW][C]18[/C][C]101.18[/C][C]102.963286964500[/C][C]-1.78328696450015[/C][/ROW]
[ROW][C]19[/C][C]96.39[/C][C]94.8978731140655[/C][C]1.49212688593451[/C][/ROW]
[ROW][C]20[/C][C]97.56[/C][C]97.8852964365457[/C][C]-0.325296436545713[/C][/ROW]
[ROW][C]21[/C][C]96.39[/C][C]103.119535295576[/C][C]-6.72953529557613[/C][/ROW]
[ROW][C]22[/C][C]85.1[/C][C]94.6332701866511[/C][C]-9.53327018665112[/C][/ROW]
[ROW][C]23[/C][C]79.77[/C][C]86.0655769472826[/C][C]-6.29557694728264[/C][/ROW]
[ROW][C]24[/C][C]79.13[/C][C]69.3506367448069[/C][C]9.77936325519308[/C][/ROW]
[ROW][C]25[/C][C]80.84[/C][C]78.7549356119757[/C][C]2.08506438802434[/C][/ROW]
[ROW][C]26[/C][C]82.75[/C][C]83.1372271531058[/C][C]-0.387227153105812[/C][/ROW]
[ROW][C]27[/C][C]92.55[/C][C]78.7840533402804[/C][C]13.7659466597196[/C][/ROW]
[ROW][C]28[/C][C]96.6[/C][C]93.1695274464866[/C][C]3.43047255351337[/C][/ROW]
[ROW][C]29[/C][C]96.92[/C][C]101.377299851777[/C][C]-4.45729985177677[/C][/ROW]
[ROW][C]30[/C][C]95.32[/C][C]96.564852267570[/C][C]-1.24485226756993[/C][/ROW]
[ROW][C]31[/C][C]98.52[/C][C]89.5592530805919[/C][C]8.96074691940808[/C][/ROW]
[ROW][C]32[/C][C]100.22[/C][C]99.3075764402621[/C][C]0.912423559737888[/C][/ROW]
[ROW][C]33[/C][C]104.91[/C][C]105.290777026023[/C][C]-0.380777026023466[/C][/ROW]
[ROW][C]34[/C][C]103.1[/C][C]102.191592970719[/C][C]0.908407029281022[/C][/ROW]
[ROW][C]35[/C][C]97.13[/C][C]103.729976358562[/C][C]-6.59997635856163[/C][/ROW]
[ROW][C]36[/C][C]103.42[/C][C]85.9232096367148[/C][C]17.4967903632852[/C][/ROW]
[ROW][C]37[/C][C]111.72[/C][C]101.977383578408[/C][C]9.74261642159215[/C][/ROW]
[ROW][C]38[/C][C]118.11[/C][C]114.357394470627[/C][C]3.7526055293734[/C][/ROW]
[ROW][C]39[/C][C]111.62[/C][C]113.850245539943[/C][C]-2.230245539943[/C][/ROW]
[ROW][C]40[/C][C]100.22[/C][C]113.035460127926[/C][C]-12.8154601279261[/C][/ROW]
[ROW][C]41[/C][C]102.03[/C][C]105.902646682722[/C][C]-3.87264668272198[/C][/ROW]
[ROW][C]42[/C][C]105.76[/C][C]101.906100937249[/C][C]3.85389906275057[/C][/ROW]
[ROW][C]43[/C][C]107.68[/C][C]99.8913280485863[/C][C]7.78867195141372[/C][/ROW]
[ROW][C]44[/C][C]110.77[/C][C]108.064869657110[/C][C]2.70513034289016[/C][/ROW]
[ROW][C]45[/C][C]105.44[/C][C]116.205272156857[/C][C]-10.7652721568571[/C][/ROW]
[ROW][C]46[/C][C]112.26[/C][C]103.629579518495[/C][C]8.63042048150494[/C][/ROW]
[ROW][C]47[/C][C]114.07[/C][C]111.71903784818[/C][C]2.35096215181997[/C][/ROW]
[ROW][C]48[/C][C]117.9[/C][C]102.259219751822[/C][C]15.6407802481777[/C][/ROW]
[ROW][C]49[/C][C]124.72[/C][C]115.932235382006[/C][C]8.78776461799356[/C][/ROW]
[ROW][C]50[/C][C]126.42[/C][C]127.359399204059[/C][C]-0.939399204058844[/C][/ROW]
[ROW][C]51[/C][C]134.73[/C][C]121.795170688827[/C][C]12.9348293111733[/C][/ROW]
[ROW][C]52[/C][C]135.79[/C][C]134.183278729583[/C][C]1.60672127041653[/C][/ROW]
[ROW][C]53[/C][C]143.36[/C][C]143.222880571604[/C][C]0.137119428395977[/C][/ROW]
[ROW][C]54[/C][C]140.37[/C][C]143.942195012112[/C][C]-3.57219501211239[/C][/ROW]
[ROW][C]55[/C][C]144.74[/C][C]133.894603119323[/C][C]10.8453968806771[/C][/ROW]
[ROW][C]56[/C][C]151.98[/C][C]144.951847490197[/C][C]7.02815250980285[/C][/ROW]
[ROW][C]57[/C][C]150.92[/C][C]157.886378739035[/C][C]-6.9663787390354[/C][/ROW]
[ROW][C]58[/C][C]163.38[/C][C]150.177182940924[/C][C]13.2028170590756[/C][/ROW]
[ROW][C]59[/C][C]154.43[/C][C]162.202177118590[/C][C]-7.7721771185904[/C][/ROW]
[ROW][C]60[/C][C]146.66[/C][C]140.773339567004[/C][C]5.88666043299571[/C][/ROW]
[ROW][C]61[/C][C]157.95[/C][C]144.755250911963[/C][C]13.1947490880372[/C][/ROW]
[ROW][C]62[/C][C]162.1[/C][C]160.333704216974[/C][C]1.76629578302607[/C][/ROW]
[ROW][C]63[/C][C]180.42[/C][C]157.465026378038[/C][C]22.9549736219623[/C][/ROW]
[ROW][C]64[/C][C]179.57[/C][C]178.292686484971[/C][C]1.27731351502882[/C][/ROW]
[ROW][C]65[/C][C]171.58[/C][C]189.580964914839[/C][C]-18.0009649148392[/C][/ROW]
[ROW][C]66[/C][C]185.43[/C][C]173.545805315572[/C][C]11.8841946844279[/C][/ROW]
[ROW][C]67[/C][C]190.64[/C][C]177.291228069076[/C][C]13.3487719309241[/C][/ROW]
[ROW][C]68[/C][C]203[/C][C]190.815585017929[/C][C]12.1844149820714[/C][/ROW]
[ROW][C]69[/C][C]202.36[/C][C]209.395850986913[/C][C]-7.03585098691346[/C][/ROW]
[ROW][C]70[/C][C]193.41[/C][C]203.538037353040[/C][C]-10.1280373530402[/C][/ROW]
[ROW][C]71[/C][C]186.17[/C][C]192.212178995332[/C][C]-6.04217899533177[/C][/ROW]
[ROW][C]72[/C][C]192.24[/C][C]170.861457906277[/C][C]21.3785420937233[/C][/ROW]
[ROW][C]73[/C][C]209.6[/C][C]189.562102051625[/C][C]20.0378979483749[/C][/ROW]
[ROW][C]74[/C][C]206.41[/C][C]211.583459744775[/C][C]-5.17345974477499[/C][/ROW]
[ROW][C]75[/C][C]209.82[/C][C]203.195042896616[/C][C]6.62495710338416[/C][/ROW]
[ROW][C]76[/C][C]230.37[/C][C]207.069720475956[/C][C]23.3002795240444[/C][/ROW]
[ROW][C]77[/C][C]235.8[/C][C]239.475619716213[/C][C]-3.67561971621279[/C][/ROW]
[ROW][C]78[/C][C]232.07[/C][C]240.352155936019[/C][C]-8.28215593601874[/C][/ROW]
[ROW][C]79[/C][C]244.64[/C][C]223.98075029129[/C][C]20.65924970871[/C][/ROW]
[ROW][C]80[/C][C]242.19[/C][C]244.617380800953[/C][C]-2.42738080095259[/C][/ROW]
[ROW][C]81[/C][C]217.48[/C][C]249.497595313175[/C][C]-32.0175953131751[/C][/ROW]
[ROW][C]82[/C][C]209.39[/C][C]220.472571918630[/C][C]-11.0825719186305[/C][/ROW]
[ROW][C]83[/C][C]211.73[/C][C]208.508698783079[/C][C]3.22130121692123[/C][/ROW]
[ROW][C]84[/C][C]221[/C][C]195.932941862973[/C][C]25.0670581370273[/C][/ROW]
[ROW][C]85[/C][C]203.11[/C][C]217.721859797283[/C][C]-14.6118597972831[/C][/ROW]
[ROW][C]86[/C][C]214.71[/C][C]205.777093583481[/C][C]8.93290641651939[/C][/ROW]
[ROW][C]87[/C][C]224.19[/C][C]211.225945582753[/C][C]12.9640544172466[/C][/ROW]
[ROW][C]88[/C][C]238.04[/C][C]222.074437893810[/C][C]15.9655621061904[/C][/ROW]
[ROW][C]89[/C][C]238.36[/C][C]245.841137318728[/C][C]-7.48113731872832[/C][/ROW]
[ROW][C]90[/C][C]246.24[/C][C]242.889907364607[/C][C]3.35009263539334[/C][/ROW]
[ROW][C]91[/C][C]259.87[/C][C]239.06069226031[/C][C]20.8093077396901[/C][/ROW]
[ROW][C]92[/C][C]249.97[/C][C]258.024929564917[/C][C]-8.05492956491722[/C][/ROW]
[ROW][C]93[/C][C]266.48[/C][C]255.205291429979[/C][C]11.2747085700207[/C][/ROW]
[ROW][C]94[/C][C]282.98[/C][C]268.294449726952[/C][C]14.6855502730481[/C][/ROW]
[ROW][C]95[/C][C]306.31[/C][C]281.265227373421[/C][C]25.0447726265787[/C][/ROW]
[ROW][C]96[/C][C]301.73[/C][C]284.538305920824[/C][C]17.1916940791764[/C][/ROW]
[ROW][C]97[/C][C]314.62[/C][C]294.501688287106[/C][C]20.1183117128938[/C][/ROW]
[ROW][C]98[/C][C]332.62[/C][C]318.626349263052[/C][C]13.9936507369484[/C][/ROW]
[ROW][C]99[/C][C]355.51[/C][C]328.080495580866[/C][C]27.4295044191337[/C][/ROW]
[ROW][C]100[/C][C]370.32[/C][C]352.340395720063[/C][C]17.979604279937[/C][/ROW]
[ROW][C]101[/C][C]408.13[/C][C]380.485158421405[/C][C]27.6448415785947[/C][/ROW]
[ROW][C]102[/C][C]433.58[/C][C]414.694198974621[/C][C]18.8858010253791[/C][/ROW]
[ROW][C]103[/C][C]440.51[/C][C]422.813281062557[/C][C]17.6967189374425[/C][/ROW]
[ROW][C]104[/C][C]386.29[/C][C]435.441061327431[/C][C]-49.1510613274305[/C][/ROW]
[ROW][C]105[/C][C]342.84[/C][C]400.222905935782[/C][C]-57.3829059357818[/C][/ROW]
[ROW][C]106[/C][C]254.97[/C][C]351.509404824083[/C][C]-96.5394048240827[/C][/ROW]
[ROW][C]107[/C][C]203.42[/C][C]262.739092371358[/C][C]-59.3190923713579[/C][/ROW]
[ROW][C]108[/C][C]170.09[/C][C]193.980810218526[/C][C]-23.8908102185262[/C][/ROW]
[ROW][C]109[/C][C]174.03[/C][C]168.390105644253[/C][C]5.63989435574683[/C][/ROW]
[ROW][C]110[/C][C]167.85[/C][C]176.012232952996[/C][C]-8.1622329529965[/C][/ROW]
[ROW][C]111[/C][C]177.01[/C][C]166.826799469627[/C][C]10.1832005303732[/C][/ROW]
[ROW][C]112[/C][C]188.19[/C][C]174.892212235496[/C][C]13.2977877645044[/C][/ROW]
[ROW][C]113[/C][C]211.2[/C][C]192.890568864660[/C][C]18.3094311353403[/C][/ROW]
[ROW][C]114[/C][C]240.91[/C][C]213.433724813631[/C][C]27.4762751863690[/C][/ROW]
[ROW][C]115[/C][C]230.26[/C][C]233.155433530494[/C][C]-2.89543353049393[/C][/ROW]
[ROW][C]116[/C][C]251.25[/C][C]225.150196244658[/C][C]26.0998037553421[/C][/ROW]
[ROW][C]117[/C][C]241.66[/C][C]254.445458589964[/C][C]-12.7854585899641[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=64077&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=64077&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
13101.29102.550463407594-1.26046340759406
14104.48104.602730522094-0.122730522094429
1599.2699.6753984574467-0.415398457446727
16100.11101.289862238172-1.17986223817176
17103.52105.559180439175-2.0391804391746
18101.18102.963286964500-1.78328696450015
1996.3994.89787311406551.49212688593451
2097.5697.8852964365457-0.325296436545713
2196.39103.119535295576-6.72953529557613
2285.194.6332701866511-9.53327018665112
2379.7786.0655769472826-6.29557694728264
2479.1369.35063674480699.77936325519308
2580.8478.75493561197572.08506438802434
2682.7583.1372271531058-0.387227153105812
2792.5578.784053340280413.7659466597196
2896.693.16952744648663.43047255351337
2996.92101.377299851777-4.45729985177677
3095.3296.564852267570-1.24485226756993
3198.5289.55925308059198.96074691940808
32100.2299.30757644026210.912423559737888
33104.91105.290777026023-0.380777026023466
34103.1102.1915929707190.908407029281022
3597.13103.729976358562-6.59997635856163
36103.4285.923209636714817.4967903632852
37111.72101.9773835784089.74261642159215
38118.11114.3573944706273.7526055293734
39111.62113.850245539943-2.230245539943
40100.22113.035460127926-12.8154601279261
41102.03105.902646682722-3.87264668272198
42105.76101.9061009372493.85389906275057
43107.6899.89132804858637.78867195141372
44110.77108.0648696571102.70513034289016
45105.44116.205272156857-10.7652721568571
46112.26103.6295795184958.63042048150494
47114.07111.719037848182.35096215181997
48117.9102.25921975182215.6407802481777
49124.72115.9322353820068.78776461799356
50126.42127.359399204059-0.939399204058844
51134.73121.79517068882712.9348293111733
52135.79134.1832787295831.60672127041653
53143.36143.2228805716040.137119428395977
54140.37143.942195012112-3.57219501211239
55144.74133.89460311932310.8453968806771
56151.98144.9518474901977.02815250980285
57150.92157.886378739035-6.9663787390354
58163.38150.17718294092413.2028170590756
59154.43162.202177118590-7.7721771185904
60146.66140.7733395670045.88666043299571
61157.95144.75525091196313.1947490880372
62162.1160.3337042169741.76629578302607
63180.42157.46502637803822.9549736219623
64179.57178.2926864849711.27731351502882
65171.58189.580964914839-18.0009649148392
66185.43173.54580531557211.8841946844279
67190.64177.29122806907613.3487719309241
68203190.81558501792912.1844149820714
69202.36209.395850986913-7.03585098691346
70193.41203.538037353040-10.1280373530402
71186.17192.212178995332-6.04217899533177
72192.24170.86145790627721.3785420937233
73209.6189.56210205162520.0378979483749
74206.41211.583459744775-5.17345974477499
75209.82203.1950428966166.62495710338416
76230.37207.06972047595623.3002795240444
77235.8239.475619716213-3.67561971621279
78232.07240.352155936019-8.28215593601874
79244.64223.9807502912920.65924970871
80242.19244.617380800953-2.42738080095259
81217.48249.497595313175-32.0175953131751
82209.39220.472571918630-11.0825719186305
83211.73208.5086987830793.22130121692123
84221195.93294186297325.0670581370273
85203.11217.721859797283-14.6118597972831
86214.71205.7770935834818.93290641651939
87224.19211.22594558275312.9640544172466
88238.04222.07443789381015.9655621061904
89238.36245.841137318728-7.48113731872832
90246.24242.8899073646073.35009263539334
91259.87239.0606922603120.8093077396901
92249.97258.024929564917-8.05492956491722
93266.48255.20529142997911.2747085700207
94282.98268.29444972695214.6855502730481
95306.31281.26522737342125.0447726265787
96301.73284.53830592082417.1916940791764
97314.62294.50168828710620.1183117128938
98332.62318.62634926305213.9936507369484
99355.51328.08049558086627.4295044191337
100370.32352.34039572006317.979604279937
101408.13380.48515842140527.6448415785947
102433.58414.69419897462118.8858010253791
103440.51422.81328106255717.6967189374425
104386.29435.441061327431-49.1510613274305
105342.84400.222905935782-57.3829059357818
106254.97351.509404824083-96.5394048240827
107203.42262.739092371358-59.3190923713579
108170.09193.980810218526-23.8908102185262
109174.03168.3901056442535.63989435574683
110167.85176.012232952996-8.1622329529965
111177.01166.82679946962710.1832005303732
112188.19174.89221223549613.2977877645044
113211.2192.89056886466018.3094311353403
114240.91213.43372481363127.4762751863690
115230.26233.155433530494-2.89543353049393
116251.25225.15019624465826.0998037553421
117241.66254.445458589964-12.7854585899641







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
118241.267117570009205.495043998350277.039191141669
119242.915317003428194.071266861086291.759367145769
120229.23257997572172.282020809341286.183139142099
121227.813035915904162.157040952779293.469030879029
122229.770997095142155.641243594516303.900750595768
123229.728772663041148.396942294544311.060603031539
124228.513633017624140.898044244985316.129221790262
125236.037082278896139.504752943477332.569411614314
126240.828593914365136.688345597029344.968842231701
127232.842577490626126.509019616902339.176135364351
128229.589120588057119.311451647316339.866789528798
129231.457709368691112.476456961079350.438961776304

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
118 & 241.267117570009 & 205.495043998350 & 277.039191141669 \tabularnewline
119 & 242.915317003428 & 194.071266861086 & 291.759367145769 \tabularnewline
120 & 229.23257997572 & 172.282020809341 & 286.183139142099 \tabularnewline
121 & 227.813035915904 & 162.157040952779 & 293.469030879029 \tabularnewline
122 & 229.770997095142 & 155.641243594516 & 303.900750595768 \tabularnewline
123 & 229.728772663041 & 148.396942294544 & 311.060603031539 \tabularnewline
124 & 228.513633017624 & 140.898044244985 & 316.129221790262 \tabularnewline
125 & 236.037082278896 & 139.504752943477 & 332.569411614314 \tabularnewline
126 & 240.828593914365 & 136.688345597029 & 344.968842231701 \tabularnewline
127 & 232.842577490626 & 126.509019616902 & 339.176135364351 \tabularnewline
128 & 229.589120588057 & 119.311451647316 & 339.866789528798 \tabularnewline
129 & 231.457709368691 & 112.476456961079 & 350.438961776304 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=64077&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]118[/C][C]241.267117570009[/C][C]205.495043998350[/C][C]277.039191141669[/C][/ROW]
[ROW][C]119[/C][C]242.915317003428[/C][C]194.071266861086[/C][C]291.759367145769[/C][/ROW]
[ROW][C]120[/C][C]229.23257997572[/C][C]172.282020809341[/C][C]286.183139142099[/C][/ROW]
[ROW][C]121[/C][C]227.813035915904[/C][C]162.157040952779[/C][C]293.469030879029[/C][/ROW]
[ROW][C]122[/C][C]229.770997095142[/C][C]155.641243594516[/C][C]303.900750595768[/C][/ROW]
[ROW][C]123[/C][C]229.728772663041[/C][C]148.396942294544[/C][C]311.060603031539[/C][/ROW]
[ROW][C]124[/C][C]228.513633017624[/C][C]140.898044244985[/C][C]316.129221790262[/C][/ROW]
[ROW][C]125[/C][C]236.037082278896[/C][C]139.504752943477[/C][C]332.569411614314[/C][/ROW]
[ROW][C]126[/C][C]240.828593914365[/C][C]136.688345597029[/C][C]344.968842231701[/C][/ROW]
[ROW][C]127[/C][C]232.842577490626[/C][C]126.509019616902[/C][C]339.176135364351[/C][/ROW]
[ROW][C]128[/C][C]229.589120588057[/C][C]119.311451647316[/C][C]339.866789528798[/C][/ROW]
[ROW][C]129[/C][C]231.457709368691[/C][C]112.476456961079[/C][C]350.438961776304[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=64077&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=64077&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
118241.267117570009205.495043998350277.039191141669
119242.915317003428194.071266861086291.759367145769
120229.23257997572172.282020809341286.183139142099
121227.813035915904162.157040952779293.469030879029
122229.770997095142155.641243594516303.900750595768
123229.728772663041148.396942294544311.060603031539
124228.513633017624140.898044244985316.129221790262
125236.037082278896139.504752943477332.569411614314
126240.828593914365136.688345597029344.968842231701
127232.842577490626126.509019616902339.176135364351
128229.589120588057119.311451647316339.866789528798
129231.457709368691112.476456961079350.438961776304



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):
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=0, beta=0)
if (par2 == 'Double') fit <- HoltWinters(x, gamma=0)
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')