Free Statistics

of Irreproducible Research!

Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationTue, 17 Aug 2010 19:46:19 +0000
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2010/Aug/17/t1282074372axp61eec88rkzs4.htm/, Retrieved Sat, 27 Apr 2024 10:38:07 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=79156, Retrieved Sat, 27 Apr 2024 10:38:07 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywordsSchrauwen Nathalie
Estimated Impact121
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [TIJDREEKS B - STA...] [2010-08-17 19:46:19] [dd2ef098fd65ce7e9f689caa343b799f] [Current]
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Dataseries X:
162
161
160
158
156
155
156
158
159
159
160
162
168
177
174
169
169
160
168
172
173
175
170
177
187
201
188
179
176
170
179
183
174
177
170
166
171
178
165
162
159
149
153
156
149
150
139
131
141
150
128
124
120
113
120
121
115
119
106
98
106
116
93
94
90
93
100
99
90
91
83
83
92
104
71
69
67
75
86
81
88
87
77
70




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time3 seconds
R Server'George Udny Yule' @ 72.249.76.132

\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 & 'George Udny Yule' @ 72.249.76.132 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=79156&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]'George Udny Yule' @ 72.249.76.132[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=79156&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=79156&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'George Udny Yule' @ 72.249.76.132







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.807164232749437
beta0
gammaFALSE

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.807164232749437 \tabularnewline
beta & 0 \tabularnewline
gamma & FALSE \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=79156&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]0.807164232749437[/C][/ROW]
[ROW][C]beta[/C][C]0[/C][/ROW]
[ROW][C]gamma[/C][C]FALSE[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=79156&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=79156&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
alpha0.807164232749437
beta0
gammaFALSE







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
31601600
4158159-1
5156157.192835767251-1.19283576725056
6155155.230021400382-0.230021400381673
7156154.0443563532271.95564364677335
8158154.6228819569063.37711804309421
9159156.3487708510642.65122914893578
10159157.4887481929081.51125180709209
11160157.7085765982712.29142340172939
12162158.5581316102323.44186838976836
13168160.3362846682847.66371533171645
14177165.52216157401911.4778384259814
15174173.7866622207480.213337779252129
16169172.958860845654-3.95886084565439
17169168.763409968610.236590031390023
18160167.954376979773-7.95437697977309
19168160.5338883878957.46611161210524
20172165.5602666389016.43973336109866
21173169.7581890764233.24181092357651
22175171.3748629032713.62513709672913
23170173.300943906564-3.30094390656376
24177169.6365400508737.36345994912671
25187174.58006155109112.4199384489086
26201183.6049916417.3950083600001
27188196.645620216569-8.64562021656943
28179188.667184807819-9.66718480781915
29176179.864178999569-3.86417899956879
30170175.745151922175-5.74515192217535
31179170.1078707788848.89212922111628
32183176.2852794391556.71472056084508
33174180.705161708776-6.7051617087763
34177174.2929950026512.70700499734903
35170175.477992614385-5.47799261438507
36166170.056352908788-4.05635290878786
37171165.7822099254055.21779007459486
38178168.9938234476139.00617655238688
39165175.263287034526-10.2632870345265
40162165.979128829816-3.97912882981564
41159161.767318360886-2.76731836088632
42149158.533637959348-9.53363795934808
43153149.838426390583.16157360942003
44156151.3903355273084.60966447269163
45149154.111091814641-5.11109181464084
46150148.9856013115641.01439868843568
47139148.804387650618-9.80438765061754
48131139.890636615029-8.89063661502877
49141131.7144327330059.28556726699497
50150138.20941051171211.7905894882877
51128146.726352629690-18.7263526296896
52124130.611110577151-6.61111057715078
53120124.274858580523-4.27485858052319
54113119.824345634263-6.82434563426284
55120113.3159779263666.6840220736339
56121117.7110814751113.28891852488889
57115119.365778872828-4.36577887282846
58119114.8418783185884.15812168141183
59106117.198165415244-11.1981654152437
6098107.159406819647-9.15940681964724
6110698.76626124162677.2337387583733
62116103.60507643643912.3949235635611
6393112.609815404609-19.6098154046086
649495.7814737991896-1.78147379918960
659093.3435318669035-3.34353186690350
669389.6447525328813.35524746711897
6710091.35298828036268.6470117196374
689997.33254686061911.66745313938088
699097.6784553945131-7.67845539451314
709190.48068083730020.519319162699844
718389.8998566908129-6.89985669081285
728383.3305391588918-0.330539158891824
739282.06373977231139.93626022768875
7410489.083933635392414.9160663646076
7571100.123648898221-29.1236488982206
766975.6160811804244-6.61608118042437
776769.2758170906191-2.27581709061914
787566.43885893479158.56114106520852
798672.349105794150213.6508942058498
808182.3676193421587-1.36761934215869
818880.26372592515197.73627407484813
828785.5081696531161.49183034688397
837785.712321750451-8.71232175045097
847077.680047249282-7.68004724928198

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
3 & 160 & 160 & 0 \tabularnewline
4 & 158 & 159 & -1 \tabularnewline
5 & 156 & 157.192835767251 & -1.19283576725056 \tabularnewline
6 & 155 & 155.230021400382 & -0.230021400381673 \tabularnewline
7 & 156 & 154.044356353227 & 1.95564364677335 \tabularnewline
8 & 158 & 154.622881956906 & 3.37711804309421 \tabularnewline
9 & 159 & 156.348770851064 & 2.65122914893578 \tabularnewline
10 & 159 & 157.488748192908 & 1.51125180709209 \tabularnewline
11 & 160 & 157.708576598271 & 2.29142340172939 \tabularnewline
12 & 162 & 158.558131610232 & 3.44186838976836 \tabularnewline
13 & 168 & 160.336284668284 & 7.66371533171645 \tabularnewline
14 & 177 & 165.522161574019 & 11.4778384259814 \tabularnewline
15 & 174 & 173.786662220748 & 0.213337779252129 \tabularnewline
16 & 169 & 172.958860845654 & -3.95886084565439 \tabularnewline
17 & 169 & 168.76340996861 & 0.236590031390023 \tabularnewline
18 & 160 & 167.954376979773 & -7.95437697977309 \tabularnewline
19 & 168 & 160.533888387895 & 7.46611161210524 \tabularnewline
20 & 172 & 165.560266638901 & 6.43973336109866 \tabularnewline
21 & 173 & 169.758189076423 & 3.24181092357651 \tabularnewline
22 & 175 & 171.374862903271 & 3.62513709672913 \tabularnewline
23 & 170 & 173.300943906564 & -3.30094390656376 \tabularnewline
24 & 177 & 169.636540050873 & 7.36345994912671 \tabularnewline
25 & 187 & 174.580061551091 & 12.4199384489086 \tabularnewline
26 & 201 & 183.60499164 & 17.3950083600001 \tabularnewline
27 & 188 & 196.645620216569 & -8.64562021656943 \tabularnewline
28 & 179 & 188.667184807819 & -9.66718480781915 \tabularnewline
29 & 176 & 179.864178999569 & -3.86417899956879 \tabularnewline
30 & 170 & 175.745151922175 & -5.74515192217535 \tabularnewline
31 & 179 & 170.107870778884 & 8.89212922111628 \tabularnewline
32 & 183 & 176.285279439155 & 6.71472056084508 \tabularnewline
33 & 174 & 180.705161708776 & -6.7051617087763 \tabularnewline
34 & 177 & 174.292995002651 & 2.70700499734903 \tabularnewline
35 & 170 & 175.477992614385 & -5.47799261438507 \tabularnewline
36 & 166 & 170.056352908788 & -4.05635290878786 \tabularnewline
37 & 171 & 165.782209925405 & 5.21779007459486 \tabularnewline
38 & 178 & 168.993823447613 & 9.00617655238688 \tabularnewline
39 & 165 & 175.263287034526 & -10.2632870345265 \tabularnewline
40 & 162 & 165.979128829816 & -3.97912882981564 \tabularnewline
41 & 159 & 161.767318360886 & -2.76731836088632 \tabularnewline
42 & 149 & 158.533637959348 & -9.53363795934808 \tabularnewline
43 & 153 & 149.83842639058 & 3.16157360942003 \tabularnewline
44 & 156 & 151.390335527308 & 4.60966447269163 \tabularnewline
45 & 149 & 154.111091814641 & -5.11109181464084 \tabularnewline
46 & 150 & 148.985601311564 & 1.01439868843568 \tabularnewline
47 & 139 & 148.804387650618 & -9.80438765061754 \tabularnewline
48 & 131 & 139.890636615029 & -8.89063661502877 \tabularnewline
49 & 141 & 131.714432733005 & 9.28556726699497 \tabularnewline
50 & 150 & 138.209410511712 & 11.7905894882877 \tabularnewline
51 & 128 & 146.726352629690 & -18.7263526296896 \tabularnewline
52 & 124 & 130.611110577151 & -6.61111057715078 \tabularnewline
53 & 120 & 124.274858580523 & -4.27485858052319 \tabularnewline
54 & 113 & 119.824345634263 & -6.82434563426284 \tabularnewline
55 & 120 & 113.315977926366 & 6.6840220736339 \tabularnewline
56 & 121 & 117.711081475111 & 3.28891852488889 \tabularnewline
57 & 115 & 119.365778872828 & -4.36577887282846 \tabularnewline
58 & 119 & 114.841878318588 & 4.15812168141183 \tabularnewline
59 & 106 & 117.198165415244 & -11.1981654152437 \tabularnewline
60 & 98 & 107.159406819647 & -9.15940681964724 \tabularnewline
61 & 106 & 98.7662612416267 & 7.2337387583733 \tabularnewline
62 & 116 & 103.605076436439 & 12.3949235635611 \tabularnewline
63 & 93 & 112.609815404609 & -19.6098154046086 \tabularnewline
64 & 94 & 95.7814737991896 & -1.78147379918960 \tabularnewline
65 & 90 & 93.3435318669035 & -3.34353186690350 \tabularnewline
66 & 93 & 89.644752532881 & 3.35524746711897 \tabularnewline
67 & 100 & 91.3529882803626 & 8.6470117196374 \tabularnewline
68 & 99 & 97.3325468606191 & 1.66745313938088 \tabularnewline
69 & 90 & 97.6784553945131 & -7.67845539451314 \tabularnewline
70 & 91 & 90.4806808373002 & 0.519319162699844 \tabularnewline
71 & 83 & 89.8998566908129 & -6.89985669081285 \tabularnewline
72 & 83 & 83.3305391588918 & -0.330539158891824 \tabularnewline
73 & 92 & 82.0637397723113 & 9.93626022768875 \tabularnewline
74 & 104 & 89.0839336353924 & 14.9160663646076 \tabularnewline
75 & 71 & 100.123648898221 & -29.1236488982206 \tabularnewline
76 & 69 & 75.6160811804244 & -6.61608118042437 \tabularnewline
77 & 67 & 69.2758170906191 & -2.27581709061914 \tabularnewline
78 & 75 & 66.4388589347915 & 8.56114106520852 \tabularnewline
79 & 86 & 72.3491057941502 & 13.6508942058498 \tabularnewline
80 & 81 & 82.3676193421587 & -1.36761934215869 \tabularnewline
81 & 88 & 80.2637259251519 & 7.73627407484813 \tabularnewline
82 & 87 & 85.508169653116 & 1.49183034688397 \tabularnewline
83 & 77 & 85.712321750451 & -8.71232175045097 \tabularnewline
84 & 70 & 77.680047249282 & -7.68004724928198 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=79156&T=2

[TABLE]
[ROW][C]Interpolation Forecasts of Exponential Smoothing[/C][/ROW]
[ROW][C]t[/C][C]Observed[/C][C]Fitted[/C][C]Residuals[/C][/ROW]
[ROW][C]3[/C][C]160[/C][C]160[/C][C]0[/C][/ROW]
[ROW][C]4[/C][C]158[/C][C]159[/C][C]-1[/C][/ROW]
[ROW][C]5[/C][C]156[/C][C]157.192835767251[/C][C]-1.19283576725056[/C][/ROW]
[ROW][C]6[/C][C]155[/C][C]155.230021400382[/C][C]-0.230021400381673[/C][/ROW]
[ROW][C]7[/C][C]156[/C][C]154.044356353227[/C][C]1.95564364677335[/C][/ROW]
[ROW][C]8[/C][C]158[/C][C]154.622881956906[/C][C]3.37711804309421[/C][/ROW]
[ROW][C]9[/C][C]159[/C][C]156.348770851064[/C][C]2.65122914893578[/C][/ROW]
[ROW][C]10[/C][C]159[/C][C]157.488748192908[/C][C]1.51125180709209[/C][/ROW]
[ROW][C]11[/C][C]160[/C][C]157.708576598271[/C][C]2.29142340172939[/C][/ROW]
[ROW][C]12[/C][C]162[/C][C]158.558131610232[/C][C]3.44186838976836[/C][/ROW]
[ROW][C]13[/C][C]168[/C][C]160.336284668284[/C][C]7.66371533171645[/C][/ROW]
[ROW][C]14[/C][C]177[/C][C]165.522161574019[/C][C]11.4778384259814[/C][/ROW]
[ROW][C]15[/C][C]174[/C][C]173.786662220748[/C][C]0.213337779252129[/C][/ROW]
[ROW][C]16[/C][C]169[/C][C]172.958860845654[/C][C]-3.95886084565439[/C][/ROW]
[ROW][C]17[/C][C]169[/C][C]168.76340996861[/C][C]0.236590031390023[/C][/ROW]
[ROW][C]18[/C][C]160[/C][C]167.954376979773[/C][C]-7.95437697977309[/C][/ROW]
[ROW][C]19[/C][C]168[/C][C]160.533888387895[/C][C]7.46611161210524[/C][/ROW]
[ROW][C]20[/C][C]172[/C][C]165.560266638901[/C][C]6.43973336109866[/C][/ROW]
[ROW][C]21[/C][C]173[/C][C]169.758189076423[/C][C]3.24181092357651[/C][/ROW]
[ROW][C]22[/C][C]175[/C][C]171.374862903271[/C][C]3.62513709672913[/C][/ROW]
[ROW][C]23[/C][C]170[/C][C]173.300943906564[/C][C]-3.30094390656376[/C][/ROW]
[ROW][C]24[/C][C]177[/C][C]169.636540050873[/C][C]7.36345994912671[/C][/ROW]
[ROW][C]25[/C][C]187[/C][C]174.580061551091[/C][C]12.4199384489086[/C][/ROW]
[ROW][C]26[/C][C]201[/C][C]183.60499164[/C][C]17.3950083600001[/C][/ROW]
[ROW][C]27[/C][C]188[/C][C]196.645620216569[/C][C]-8.64562021656943[/C][/ROW]
[ROW][C]28[/C][C]179[/C][C]188.667184807819[/C][C]-9.66718480781915[/C][/ROW]
[ROW][C]29[/C][C]176[/C][C]179.864178999569[/C][C]-3.86417899956879[/C][/ROW]
[ROW][C]30[/C][C]170[/C][C]175.745151922175[/C][C]-5.74515192217535[/C][/ROW]
[ROW][C]31[/C][C]179[/C][C]170.107870778884[/C][C]8.89212922111628[/C][/ROW]
[ROW][C]32[/C][C]183[/C][C]176.285279439155[/C][C]6.71472056084508[/C][/ROW]
[ROW][C]33[/C][C]174[/C][C]180.705161708776[/C][C]-6.7051617087763[/C][/ROW]
[ROW][C]34[/C][C]177[/C][C]174.292995002651[/C][C]2.70700499734903[/C][/ROW]
[ROW][C]35[/C][C]170[/C][C]175.477992614385[/C][C]-5.47799261438507[/C][/ROW]
[ROW][C]36[/C][C]166[/C][C]170.056352908788[/C][C]-4.05635290878786[/C][/ROW]
[ROW][C]37[/C][C]171[/C][C]165.782209925405[/C][C]5.21779007459486[/C][/ROW]
[ROW][C]38[/C][C]178[/C][C]168.993823447613[/C][C]9.00617655238688[/C][/ROW]
[ROW][C]39[/C][C]165[/C][C]175.263287034526[/C][C]-10.2632870345265[/C][/ROW]
[ROW][C]40[/C][C]162[/C][C]165.979128829816[/C][C]-3.97912882981564[/C][/ROW]
[ROW][C]41[/C][C]159[/C][C]161.767318360886[/C][C]-2.76731836088632[/C][/ROW]
[ROW][C]42[/C][C]149[/C][C]158.533637959348[/C][C]-9.53363795934808[/C][/ROW]
[ROW][C]43[/C][C]153[/C][C]149.83842639058[/C][C]3.16157360942003[/C][/ROW]
[ROW][C]44[/C][C]156[/C][C]151.390335527308[/C][C]4.60966447269163[/C][/ROW]
[ROW][C]45[/C][C]149[/C][C]154.111091814641[/C][C]-5.11109181464084[/C][/ROW]
[ROW][C]46[/C][C]150[/C][C]148.985601311564[/C][C]1.01439868843568[/C][/ROW]
[ROW][C]47[/C][C]139[/C][C]148.804387650618[/C][C]-9.80438765061754[/C][/ROW]
[ROW][C]48[/C][C]131[/C][C]139.890636615029[/C][C]-8.89063661502877[/C][/ROW]
[ROW][C]49[/C][C]141[/C][C]131.714432733005[/C][C]9.28556726699497[/C][/ROW]
[ROW][C]50[/C][C]150[/C][C]138.209410511712[/C][C]11.7905894882877[/C][/ROW]
[ROW][C]51[/C][C]128[/C][C]146.726352629690[/C][C]-18.7263526296896[/C][/ROW]
[ROW][C]52[/C][C]124[/C][C]130.611110577151[/C][C]-6.61111057715078[/C][/ROW]
[ROW][C]53[/C][C]120[/C][C]124.274858580523[/C][C]-4.27485858052319[/C][/ROW]
[ROW][C]54[/C][C]113[/C][C]119.824345634263[/C][C]-6.82434563426284[/C][/ROW]
[ROW][C]55[/C][C]120[/C][C]113.315977926366[/C][C]6.6840220736339[/C][/ROW]
[ROW][C]56[/C][C]121[/C][C]117.711081475111[/C][C]3.28891852488889[/C][/ROW]
[ROW][C]57[/C][C]115[/C][C]119.365778872828[/C][C]-4.36577887282846[/C][/ROW]
[ROW][C]58[/C][C]119[/C][C]114.841878318588[/C][C]4.15812168141183[/C][/ROW]
[ROW][C]59[/C][C]106[/C][C]117.198165415244[/C][C]-11.1981654152437[/C][/ROW]
[ROW][C]60[/C][C]98[/C][C]107.159406819647[/C][C]-9.15940681964724[/C][/ROW]
[ROW][C]61[/C][C]106[/C][C]98.7662612416267[/C][C]7.2337387583733[/C][/ROW]
[ROW][C]62[/C][C]116[/C][C]103.605076436439[/C][C]12.3949235635611[/C][/ROW]
[ROW][C]63[/C][C]93[/C][C]112.609815404609[/C][C]-19.6098154046086[/C][/ROW]
[ROW][C]64[/C][C]94[/C][C]95.7814737991896[/C][C]-1.78147379918960[/C][/ROW]
[ROW][C]65[/C][C]90[/C][C]93.3435318669035[/C][C]-3.34353186690350[/C][/ROW]
[ROW][C]66[/C][C]93[/C][C]89.644752532881[/C][C]3.35524746711897[/C][/ROW]
[ROW][C]67[/C][C]100[/C][C]91.3529882803626[/C][C]8.6470117196374[/C][/ROW]
[ROW][C]68[/C][C]99[/C][C]97.3325468606191[/C][C]1.66745313938088[/C][/ROW]
[ROW][C]69[/C][C]90[/C][C]97.6784553945131[/C][C]-7.67845539451314[/C][/ROW]
[ROW][C]70[/C][C]91[/C][C]90.4806808373002[/C][C]0.519319162699844[/C][/ROW]
[ROW][C]71[/C][C]83[/C][C]89.8998566908129[/C][C]-6.89985669081285[/C][/ROW]
[ROW][C]72[/C][C]83[/C][C]83.3305391588918[/C][C]-0.330539158891824[/C][/ROW]
[ROW][C]73[/C][C]92[/C][C]82.0637397723113[/C][C]9.93626022768875[/C][/ROW]
[ROW][C]74[/C][C]104[/C][C]89.0839336353924[/C][C]14.9160663646076[/C][/ROW]
[ROW][C]75[/C][C]71[/C][C]100.123648898221[/C][C]-29.1236488982206[/C][/ROW]
[ROW][C]76[/C][C]69[/C][C]75.6160811804244[/C][C]-6.61608118042437[/C][/ROW]
[ROW][C]77[/C][C]67[/C][C]69.2758170906191[/C][C]-2.27581709061914[/C][/ROW]
[ROW][C]78[/C][C]75[/C][C]66.4388589347915[/C][C]8.56114106520852[/C][/ROW]
[ROW][C]79[/C][C]86[/C][C]72.3491057941502[/C][C]13.6508942058498[/C][/ROW]
[ROW][C]80[/C][C]81[/C][C]82.3676193421587[/C][C]-1.36761934215869[/C][/ROW]
[ROW][C]81[/C][C]88[/C][C]80.2637259251519[/C][C]7.73627407484813[/C][/ROW]
[ROW][C]82[/C][C]87[/C][C]85.508169653116[/C][C]1.49183034688397[/C][/ROW]
[ROW][C]83[/C][C]77[/C][C]85.712321750451[/C][C]-8.71232175045097[/C][/ROW]
[ROW][C]84[/C][C]70[/C][C]77.680047249282[/C][C]-7.68004724928198[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=79156&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=79156&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
31601600
4158159-1
5156157.192835767251-1.19283576725056
6155155.230021400382-0.230021400381673
7156154.0443563532271.95564364677335
8158154.6228819569063.37711804309421
9159156.3487708510642.65122914893578
10159157.4887481929081.51125180709209
11160157.7085765982712.29142340172939
12162158.5581316102323.44186838976836
13168160.3362846682847.66371533171645
14177165.52216157401911.4778384259814
15174173.7866622207480.213337779252129
16169172.958860845654-3.95886084565439
17169168.763409968610.236590031390023
18160167.954376979773-7.95437697977309
19168160.5338883878957.46611161210524
20172165.5602666389016.43973336109866
21173169.7581890764233.24181092357651
22175171.3748629032713.62513709672913
23170173.300943906564-3.30094390656376
24177169.6365400508737.36345994912671
25187174.58006155109112.4199384489086
26201183.6049916417.3950083600001
27188196.645620216569-8.64562021656943
28179188.667184807819-9.66718480781915
29176179.864178999569-3.86417899956879
30170175.745151922175-5.74515192217535
31179170.1078707788848.89212922111628
32183176.2852794391556.71472056084508
33174180.705161708776-6.7051617087763
34177174.2929950026512.70700499734903
35170175.477992614385-5.47799261438507
36166170.056352908788-4.05635290878786
37171165.7822099254055.21779007459486
38178168.9938234476139.00617655238688
39165175.263287034526-10.2632870345265
40162165.979128829816-3.97912882981564
41159161.767318360886-2.76731836088632
42149158.533637959348-9.53363795934808
43153149.838426390583.16157360942003
44156151.3903355273084.60966447269163
45149154.111091814641-5.11109181464084
46150148.9856013115641.01439868843568
47139148.804387650618-9.80438765061754
48131139.890636615029-8.89063661502877
49141131.7144327330059.28556726699497
50150138.20941051171211.7905894882877
51128146.726352629690-18.7263526296896
52124130.611110577151-6.61111057715078
53120124.274858580523-4.27485858052319
54113119.824345634263-6.82434563426284
55120113.3159779263666.6840220736339
56121117.7110814751113.28891852488889
57115119.365778872828-4.36577887282846
58119114.8418783185884.15812168141183
59106117.198165415244-11.1981654152437
6098107.159406819647-9.15940681964724
6110698.76626124162677.2337387583733
62116103.60507643643912.3949235635611
6393112.609815404609-19.6098154046086
649495.7814737991896-1.78147379918960
659093.3435318669035-3.34353186690350
669389.6447525328813.35524746711897
6710091.35298828036268.6470117196374
689997.33254686061911.66745313938088
699097.6784553945131-7.67845539451314
709190.48068083730020.519319162699844
718389.8998566908129-6.89985669081285
728383.3305391588918-0.330539158891824
739282.06373977231139.93626022768875
7410489.083933635392414.9160663646076
7571100.123648898221-29.1236488982206
766975.6160811804244-6.61608118042437
776769.2758170906191-2.27581709061914
787566.43885893479158.56114106520852
798672.349105794150213.6508942058498
808182.3676193421587-1.36761934215869
818880.26372592515197.73627407484813
828785.5081696531161.49183034688397
837785.712321750451-8.71232175045097
847077.680047249282-7.68004724928198







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
8570.480987803835954.449650667900786.512324939771
8669.480987803835948.87891630215190.0830593055207
8768.480987803835944.152261368712792.809714238959
8867.480987803835939.925071746669895.0369038610019
8966.480987803835936.038088967750996.9238866399208
9065.480987803835932.402117367579698.559858240092
9164.480987803835928.9612292301469100.000746377525
9263.480987803835925.6776172011016101.28435840657
9362.480987803835922.5243061507982102.437669456873
9461.480987803835919.481249846121103.480725761551
9560.480987803835916.5330689872271104.428906620445
9659.480987803835913.6676584322899105.294317175382

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
85 & 70.4809878038359 & 54.4496506679007 & 86.512324939771 \tabularnewline
86 & 69.4809878038359 & 48.878916302151 & 90.0830593055207 \tabularnewline
87 & 68.4809878038359 & 44.1522613687127 & 92.809714238959 \tabularnewline
88 & 67.4809878038359 & 39.9250717466698 & 95.0369038610019 \tabularnewline
89 & 66.4809878038359 & 36.0380889677509 & 96.9238866399208 \tabularnewline
90 & 65.4809878038359 & 32.4021173675796 & 98.559858240092 \tabularnewline
91 & 64.4809878038359 & 28.9612292301469 & 100.000746377525 \tabularnewline
92 & 63.4809878038359 & 25.6776172011016 & 101.28435840657 \tabularnewline
93 & 62.4809878038359 & 22.5243061507982 & 102.437669456873 \tabularnewline
94 & 61.4809878038359 & 19.481249846121 & 103.480725761551 \tabularnewline
95 & 60.4809878038359 & 16.5330689872271 & 104.428906620445 \tabularnewline
96 & 59.4809878038359 & 13.6676584322899 & 105.294317175382 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=79156&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]85[/C][C]70.4809878038359[/C][C]54.4496506679007[/C][C]86.512324939771[/C][/ROW]
[ROW][C]86[/C][C]69.4809878038359[/C][C]48.878916302151[/C][C]90.0830593055207[/C][/ROW]
[ROW][C]87[/C][C]68.4809878038359[/C][C]44.1522613687127[/C][C]92.809714238959[/C][/ROW]
[ROW][C]88[/C][C]67.4809878038359[/C][C]39.9250717466698[/C][C]95.0369038610019[/C][/ROW]
[ROW][C]89[/C][C]66.4809878038359[/C][C]36.0380889677509[/C][C]96.9238866399208[/C][/ROW]
[ROW][C]90[/C][C]65.4809878038359[/C][C]32.4021173675796[/C][C]98.559858240092[/C][/ROW]
[ROW][C]91[/C][C]64.4809878038359[/C][C]28.9612292301469[/C][C]100.000746377525[/C][/ROW]
[ROW][C]92[/C][C]63.4809878038359[/C][C]25.6776172011016[/C][C]101.28435840657[/C][/ROW]
[ROW][C]93[/C][C]62.4809878038359[/C][C]22.5243061507982[/C][C]102.437669456873[/C][/ROW]
[ROW][C]94[/C][C]61.4809878038359[/C][C]19.481249846121[/C][C]103.480725761551[/C][/ROW]
[ROW][C]95[/C][C]60.4809878038359[/C][C]16.5330689872271[/C][C]104.428906620445[/C][/ROW]
[ROW][C]96[/C][C]59.4809878038359[/C][C]13.6676584322899[/C][C]105.294317175382[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=79156&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=79156&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
8570.480987803835954.449650667900786.512324939771
8669.480987803835948.87891630215190.0830593055207
8768.480987803835944.152261368712792.809714238959
8867.480987803835939.925071746669895.0369038610019
8966.480987803835936.038088967750996.9238866399208
9065.480987803835932.402117367579698.559858240092
9164.480987803835928.9612292301469100.000746377525
9263.480987803835925.6776172011016101.28435840657
9362.480987803835922.5243061507982102.437669456873
9461.480987803835919.481249846121103.480725761551
9560.480987803835916.5330689872271104.428906620445
9659.480987803835913.6676584322899105.294317175382



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