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Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationSun, 07 Jun 2009 10:23:52 -0600
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/Jun/07/t1244391939qd77zln3lt3mqqj.htm/, Retrieved Sun, 12 May 2024 22:34:52 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=42181, Retrieved Sun, 12 May 2024 22:34:52 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact106
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [exposmoothPrijsin...] [2009-06-07 16:23:52] [f40d51a95968de218a79272805382c2a] [Current]
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Dataseries X:
159,7
191
239,4
321,9
362,7
413,6
407,1
383,2
347,7
333,8
312,3
295,4
283,3
287,6
265,7
250,2
234,7
244
231,2
223,8
223,5
210,5
201,6
190,7
207,5
198,8
196,6
204,2
227,4
229,7
217,9
221,4
216,3
197
193,8
196,8
180,5
174,8
181,6
190
190,6
179
174,1
161,1
168,6
169,4
152,2
148,3
137,7
145
153,4
141,7
142,7
135,9
131,8
134,6
127,5
126,5
118,7
117,1
110,7
107,1
105,4
99
104
101,1
99,3
95,8
94,1
104,8
110,9
166,7




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time1 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 & 1 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ 72.249.127.135 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=42181&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]1 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=42181&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=42181&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 time1 seconds
R Server'Gwilym Jenkins' @ 72.249.127.135







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.44783858329204
beta0.0652105176446376
gamma1

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.44783858329204 \tabularnewline
beta & 0.0652105176446376 \tabularnewline
gamma & 1 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=42181&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]0.44783858329204[/C][/ROW]
[ROW][C]beta[/C][C]0.0652105176446376[/C][/ROW]
[ROW][C]gamma[/C][C]1[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=42181&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=42181&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
alpha0.44783858329204
beta0.0652105176446376
gamma1







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
13283.3322.717895299146-39.4178952991455
14287.6313.424145549789-25.8241455497889
15265.7281.109871947066-15.4098719470659
16250.2257.905318613807-7.70531861380681
17234.7237.363637055603-2.66363705560340
18244243.0270267377140.972973262285905
19231.2317.634945335351-86.4349453353513
20223.8231.936497867248-8.13649786724835
21223.5173.51966631270949.9803336872907
22210.5171.20190922807939.2980907719215
23201.6164.07705130324837.5229486967517
24190.7165.93219509073824.767804909262
25207.5147.82919944630459.6708005536963
26198.8192.3457102360576.4542897639434
27196.6183.10855320180113.4914467981993
28204.2180.81653827756923.3834617224309
29227.4181.60459985936945.7954001406311
30229.7217.01616512263612.6838348773641
31217.9254.985733835673-37.0857338356731
32221.4242.442687421023-21.0426874210232
33216.3217.780467079882-1.48046707988220
34197192.4600341113234.53996588867687
35193.8173.71569159108320.0843084089165
36196.8165.13567661052331.664323389477
37180.5174.0121354600286.4878645399724
38174.8168.3928683723236.40713162767747
39181.6166.08455833881315.5154416611865
40190173.28438332983916.7156166701605
41190.6186.3900359276464.20996407235381
42179186.609359092086-7.60935909208612
43174.1189.131628367948-15.0316283679479
44161.1197.089287281392-35.9892872813923
45168.6177.864083572974-9.26408357297436
46169.4153.48396399097415.9160360090259
47152.2149.8513414727002.34865852729982
48148.3140.6387982197917.66120178020853
49137.7125.07942445150212.6205755484981
50145122.55630329758422.4436967024164
51153.4133.32163055516620.078369444834
52141.7144.223443094756-2.52344309475592
53142.7142.2419522882340.458047711765886
54135.9134.5792668801611.32073311983879
55131.8137.587696340848-5.78769634084847
56134.6138.968302910563-4.36830291056270
57127.5150.439443711805-22.9394437118045
58126.5135.217709757026-8.71770975702606
59118.7113.7216134631844.9783865368161
60117.1109.3567936997487.74320630025159
61110.797.311562822262313.3884371777377
62107.1101.3177359488025.78226405119752
63105.4103.5902791752411.80972082475905
649993.57221427680195.42778572319814
6510496.77143780139377.22856219860634
66101.192.78849935566478.31150064433533
6799.395.37812838599573.92187161400432
6895.8102.549809170383-6.74980917038266
6994.1103.289623938707-9.18962393870707
70104.8103.0693011233871.73069887661349
71110.995.11101293398715.7889870660130
72166.798.726086107556367.9739138924437

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 283.3 & 322.717895299146 & -39.4178952991455 \tabularnewline
14 & 287.6 & 313.424145549789 & -25.8241455497889 \tabularnewline
15 & 265.7 & 281.109871947066 & -15.4098719470659 \tabularnewline
16 & 250.2 & 257.905318613807 & -7.70531861380681 \tabularnewline
17 & 234.7 & 237.363637055603 & -2.66363705560340 \tabularnewline
18 & 244 & 243.027026737714 & 0.972973262285905 \tabularnewline
19 & 231.2 & 317.634945335351 & -86.4349453353513 \tabularnewline
20 & 223.8 & 231.936497867248 & -8.13649786724835 \tabularnewline
21 & 223.5 & 173.519666312709 & 49.9803336872907 \tabularnewline
22 & 210.5 & 171.201909228079 & 39.2980907719215 \tabularnewline
23 & 201.6 & 164.077051303248 & 37.5229486967517 \tabularnewline
24 & 190.7 & 165.932195090738 & 24.767804909262 \tabularnewline
25 & 207.5 & 147.829199446304 & 59.6708005536963 \tabularnewline
26 & 198.8 & 192.345710236057 & 6.4542897639434 \tabularnewline
27 & 196.6 & 183.108553201801 & 13.4914467981993 \tabularnewline
28 & 204.2 & 180.816538277569 & 23.3834617224309 \tabularnewline
29 & 227.4 & 181.604599859369 & 45.7954001406311 \tabularnewline
30 & 229.7 & 217.016165122636 & 12.6838348773641 \tabularnewline
31 & 217.9 & 254.985733835673 & -37.0857338356731 \tabularnewline
32 & 221.4 & 242.442687421023 & -21.0426874210232 \tabularnewline
33 & 216.3 & 217.780467079882 & -1.48046707988220 \tabularnewline
34 & 197 & 192.460034111323 & 4.53996588867687 \tabularnewline
35 & 193.8 & 173.715691591083 & 20.0843084089165 \tabularnewline
36 & 196.8 & 165.135676610523 & 31.664323389477 \tabularnewline
37 & 180.5 & 174.012135460028 & 6.4878645399724 \tabularnewline
38 & 174.8 & 168.392868372323 & 6.40713162767747 \tabularnewline
39 & 181.6 & 166.084558338813 & 15.5154416611865 \tabularnewline
40 & 190 & 173.284383329839 & 16.7156166701605 \tabularnewline
41 & 190.6 & 186.390035927646 & 4.20996407235381 \tabularnewline
42 & 179 & 186.609359092086 & -7.60935909208612 \tabularnewline
43 & 174.1 & 189.131628367948 & -15.0316283679479 \tabularnewline
44 & 161.1 & 197.089287281392 & -35.9892872813923 \tabularnewline
45 & 168.6 & 177.864083572974 & -9.26408357297436 \tabularnewline
46 & 169.4 & 153.483963990974 & 15.9160360090259 \tabularnewline
47 & 152.2 & 149.851341472700 & 2.34865852729982 \tabularnewline
48 & 148.3 & 140.638798219791 & 7.66120178020853 \tabularnewline
49 & 137.7 & 125.079424451502 & 12.6205755484981 \tabularnewline
50 & 145 & 122.556303297584 & 22.4436967024164 \tabularnewline
51 & 153.4 & 133.321630555166 & 20.078369444834 \tabularnewline
52 & 141.7 & 144.223443094756 & -2.52344309475592 \tabularnewline
53 & 142.7 & 142.241952288234 & 0.458047711765886 \tabularnewline
54 & 135.9 & 134.579266880161 & 1.32073311983879 \tabularnewline
55 & 131.8 & 137.587696340848 & -5.78769634084847 \tabularnewline
56 & 134.6 & 138.968302910563 & -4.36830291056270 \tabularnewline
57 & 127.5 & 150.439443711805 & -22.9394437118045 \tabularnewline
58 & 126.5 & 135.217709757026 & -8.71770975702606 \tabularnewline
59 & 118.7 & 113.721613463184 & 4.9783865368161 \tabularnewline
60 & 117.1 & 109.356793699748 & 7.74320630025159 \tabularnewline
61 & 110.7 & 97.3115628222623 & 13.3884371777377 \tabularnewline
62 & 107.1 & 101.317735948802 & 5.78226405119752 \tabularnewline
63 & 105.4 & 103.590279175241 & 1.80972082475905 \tabularnewline
64 & 99 & 93.5722142768019 & 5.42778572319814 \tabularnewline
65 & 104 & 96.7714378013937 & 7.22856219860634 \tabularnewline
66 & 101.1 & 92.7884993556647 & 8.31150064433533 \tabularnewline
67 & 99.3 & 95.3781283859957 & 3.92187161400432 \tabularnewline
68 & 95.8 & 102.549809170383 & -6.74980917038266 \tabularnewline
69 & 94.1 & 103.289623938707 & -9.18962393870707 \tabularnewline
70 & 104.8 & 103.069301123387 & 1.73069887661349 \tabularnewline
71 & 110.9 & 95.111012933987 & 15.7889870660130 \tabularnewline
72 & 166.7 & 98.7260861075563 & 67.9739138924437 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=42181&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]283.3[/C][C]322.717895299146[/C][C]-39.4178952991455[/C][/ROW]
[ROW][C]14[/C][C]287.6[/C][C]313.424145549789[/C][C]-25.8241455497889[/C][/ROW]
[ROW][C]15[/C][C]265.7[/C][C]281.109871947066[/C][C]-15.4098719470659[/C][/ROW]
[ROW][C]16[/C][C]250.2[/C][C]257.905318613807[/C][C]-7.70531861380681[/C][/ROW]
[ROW][C]17[/C][C]234.7[/C][C]237.363637055603[/C][C]-2.66363705560340[/C][/ROW]
[ROW][C]18[/C][C]244[/C][C]243.027026737714[/C][C]0.972973262285905[/C][/ROW]
[ROW][C]19[/C][C]231.2[/C][C]317.634945335351[/C][C]-86.4349453353513[/C][/ROW]
[ROW][C]20[/C][C]223.8[/C][C]231.936497867248[/C][C]-8.13649786724835[/C][/ROW]
[ROW][C]21[/C][C]223.5[/C][C]173.519666312709[/C][C]49.9803336872907[/C][/ROW]
[ROW][C]22[/C][C]210.5[/C][C]171.201909228079[/C][C]39.2980907719215[/C][/ROW]
[ROW][C]23[/C][C]201.6[/C][C]164.077051303248[/C][C]37.5229486967517[/C][/ROW]
[ROW][C]24[/C][C]190.7[/C][C]165.932195090738[/C][C]24.767804909262[/C][/ROW]
[ROW][C]25[/C][C]207.5[/C][C]147.829199446304[/C][C]59.6708005536963[/C][/ROW]
[ROW][C]26[/C][C]198.8[/C][C]192.345710236057[/C][C]6.4542897639434[/C][/ROW]
[ROW][C]27[/C][C]196.6[/C][C]183.108553201801[/C][C]13.4914467981993[/C][/ROW]
[ROW][C]28[/C][C]204.2[/C][C]180.816538277569[/C][C]23.3834617224309[/C][/ROW]
[ROW][C]29[/C][C]227.4[/C][C]181.604599859369[/C][C]45.7954001406311[/C][/ROW]
[ROW][C]30[/C][C]229.7[/C][C]217.016165122636[/C][C]12.6838348773641[/C][/ROW]
[ROW][C]31[/C][C]217.9[/C][C]254.985733835673[/C][C]-37.0857338356731[/C][/ROW]
[ROW][C]32[/C][C]221.4[/C][C]242.442687421023[/C][C]-21.0426874210232[/C][/ROW]
[ROW][C]33[/C][C]216.3[/C][C]217.780467079882[/C][C]-1.48046707988220[/C][/ROW]
[ROW][C]34[/C][C]197[/C][C]192.460034111323[/C][C]4.53996588867687[/C][/ROW]
[ROW][C]35[/C][C]193.8[/C][C]173.715691591083[/C][C]20.0843084089165[/C][/ROW]
[ROW][C]36[/C][C]196.8[/C][C]165.135676610523[/C][C]31.664323389477[/C][/ROW]
[ROW][C]37[/C][C]180.5[/C][C]174.012135460028[/C][C]6.4878645399724[/C][/ROW]
[ROW][C]38[/C][C]174.8[/C][C]168.392868372323[/C][C]6.40713162767747[/C][/ROW]
[ROW][C]39[/C][C]181.6[/C][C]166.084558338813[/C][C]15.5154416611865[/C][/ROW]
[ROW][C]40[/C][C]190[/C][C]173.284383329839[/C][C]16.7156166701605[/C][/ROW]
[ROW][C]41[/C][C]190.6[/C][C]186.390035927646[/C][C]4.20996407235381[/C][/ROW]
[ROW][C]42[/C][C]179[/C][C]186.609359092086[/C][C]-7.60935909208612[/C][/ROW]
[ROW][C]43[/C][C]174.1[/C][C]189.131628367948[/C][C]-15.0316283679479[/C][/ROW]
[ROW][C]44[/C][C]161.1[/C][C]197.089287281392[/C][C]-35.9892872813923[/C][/ROW]
[ROW][C]45[/C][C]168.6[/C][C]177.864083572974[/C][C]-9.26408357297436[/C][/ROW]
[ROW][C]46[/C][C]169.4[/C][C]153.483963990974[/C][C]15.9160360090259[/C][/ROW]
[ROW][C]47[/C][C]152.2[/C][C]149.851341472700[/C][C]2.34865852729982[/C][/ROW]
[ROW][C]48[/C][C]148.3[/C][C]140.638798219791[/C][C]7.66120178020853[/C][/ROW]
[ROW][C]49[/C][C]137.7[/C][C]125.079424451502[/C][C]12.6205755484981[/C][/ROW]
[ROW][C]50[/C][C]145[/C][C]122.556303297584[/C][C]22.4436967024164[/C][/ROW]
[ROW][C]51[/C][C]153.4[/C][C]133.321630555166[/C][C]20.078369444834[/C][/ROW]
[ROW][C]52[/C][C]141.7[/C][C]144.223443094756[/C][C]-2.52344309475592[/C][/ROW]
[ROW][C]53[/C][C]142.7[/C][C]142.241952288234[/C][C]0.458047711765886[/C][/ROW]
[ROW][C]54[/C][C]135.9[/C][C]134.579266880161[/C][C]1.32073311983879[/C][/ROW]
[ROW][C]55[/C][C]131.8[/C][C]137.587696340848[/C][C]-5.78769634084847[/C][/ROW]
[ROW][C]56[/C][C]134.6[/C][C]138.968302910563[/C][C]-4.36830291056270[/C][/ROW]
[ROW][C]57[/C][C]127.5[/C][C]150.439443711805[/C][C]-22.9394437118045[/C][/ROW]
[ROW][C]58[/C][C]126.5[/C][C]135.217709757026[/C][C]-8.71770975702606[/C][/ROW]
[ROW][C]59[/C][C]118.7[/C][C]113.721613463184[/C][C]4.9783865368161[/C][/ROW]
[ROW][C]60[/C][C]117.1[/C][C]109.356793699748[/C][C]7.74320630025159[/C][/ROW]
[ROW][C]61[/C][C]110.7[/C][C]97.3115628222623[/C][C]13.3884371777377[/C][/ROW]
[ROW][C]62[/C][C]107.1[/C][C]101.317735948802[/C][C]5.78226405119752[/C][/ROW]
[ROW][C]63[/C][C]105.4[/C][C]103.590279175241[/C][C]1.80972082475905[/C][/ROW]
[ROW][C]64[/C][C]99[/C][C]93.5722142768019[/C][C]5.42778572319814[/C][/ROW]
[ROW][C]65[/C][C]104[/C][C]96.7714378013937[/C][C]7.22856219860634[/C][/ROW]
[ROW][C]66[/C][C]101.1[/C][C]92.7884993556647[/C][C]8.31150064433533[/C][/ROW]
[ROW][C]67[/C][C]99.3[/C][C]95.3781283859957[/C][C]3.92187161400432[/C][/ROW]
[ROW][C]68[/C][C]95.8[/C][C]102.549809170383[/C][C]-6.74980917038266[/C][/ROW]
[ROW][C]69[/C][C]94.1[/C][C]103.289623938707[/C][C]-9.18962393870707[/C][/ROW]
[ROW][C]70[/C][C]104.8[/C][C]103.069301123387[/C][C]1.73069887661349[/C][/ROW]
[ROW][C]71[/C][C]110.9[/C][C]95.111012933987[/C][C]15.7889870660130[/C][/ROW]
[ROW][C]72[/C][C]166.7[/C][C]98.7260861075563[/C][C]67.9739138924437[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=42181&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=42181&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
13283.3322.717895299146-39.4178952991455
14287.6313.424145549789-25.8241455497889
15265.7281.109871947066-15.4098719470659
16250.2257.905318613807-7.70531861380681
17234.7237.363637055603-2.66363705560340
18244243.0270267377140.972973262285905
19231.2317.634945335351-86.4349453353513
20223.8231.936497867248-8.13649786724835
21223.5173.51966631270949.9803336872907
22210.5171.20190922807939.2980907719215
23201.6164.07705130324837.5229486967517
24190.7165.93219509073824.767804909262
25207.5147.82919944630459.6708005536963
26198.8192.3457102360576.4542897639434
27196.6183.10855320180113.4914467981993
28204.2180.81653827756923.3834617224309
29227.4181.60459985936945.7954001406311
30229.7217.01616512263612.6838348773641
31217.9254.985733835673-37.0857338356731
32221.4242.442687421023-21.0426874210232
33216.3217.780467079882-1.48046707988220
34197192.4600341113234.53996588867687
35193.8173.71569159108320.0843084089165
36196.8165.13567661052331.664323389477
37180.5174.0121354600286.4878645399724
38174.8168.3928683723236.40713162767747
39181.6166.08455833881315.5154416611865
40190173.28438332983916.7156166701605
41190.6186.3900359276464.20996407235381
42179186.609359092086-7.60935909208612
43174.1189.131628367948-15.0316283679479
44161.1197.089287281392-35.9892872813923
45168.6177.864083572974-9.26408357297436
46169.4153.48396399097415.9160360090259
47152.2149.8513414727002.34865852729982
48148.3140.6387982197917.66120178020853
49137.7125.07942445150212.6205755484981
50145122.55630329758422.4436967024164
51153.4133.32163055516620.078369444834
52141.7144.223443094756-2.52344309475592
53142.7142.2419522882340.458047711765886
54135.9134.5792668801611.32073311983879
55131.8137.587696340848-5.78769634084847
56134.6138.968302910563-4.36830291056270
57127.5150.439443711805-22.9394437118045
58126.5135.217709757026-8.71770975702606
59118.7113.7216134631844.9783865368161
60117.1109.3567936997487.74320630025159
61110.797.311562822262313.3884371777377
62107.1101.3177359488025.78226405119752
63105.4103.5902791752411.80972082475905
649993.57221427680195.42778572319814
6510496.77143780139377.22856219860634
66101.192.78849935566478.31150064433533
6799.395.37812838599573.92187161400432
6895.8102.549809170383-6.74980917038266
6994.1103.289623938707-9.18962393870707
70104.8103.0693011233871.73069887661349
71110.995.11101293398715.7889870660130
72166.798.726086107556367.9739138924437







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
73120.14239546712072.7331104629439167.551680471295
74116.93270827349964.4052439384798169.460172608519
75117.23321520946559.482272483595174.984157935336
76111.16056238766348.0766121040534174.244512671273
77115.52294048845646.9940520366559184.051828940255
78111.28923558755737.2022830055591185.376188169556
79109.87864864797330.1201218014538189.637175494492
80111.43271861351525.8892759194313196.976161307599
81116.07655174985624.6353994027191207.517704096993
82128.49821479692731.0473670911549225.949062502699
83129.97349101840426.401947793647233.545034243161
84157.31724534386347.5151108713384267.119379816387

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
73 & 120.142395467120 & 72.7331104629439 & 167.551680471295 \tabularnewline
74 & 116.932708273499 & 64.4052439384798 & 169.460172608519 \tabularnewline
75 & 117.233215209465 & 59.482272483595 & 174.984157935336 \tabularnewline
76 & 111.160562387663 & 48.0766121040534 & 174.244512671273 \tabularnewline
77 & 115.522940488456 & 46.9940520366559 & 184.051828940255 \tabularnewline
78 & 111.289235587557 & 37.2022830055591 & 185.376188169556 \tabularnewline
79 & 109.878648647973 & 30.1201218014538 & 189.637175494492 \tabularnewline
80 & 111.432718613515 & 25.8892759194313 & 196.976161307599 \tabularnewline
81 & 116.076551749856 & 24.6353994027191 & 207.517704096993 \tabularnewline
82 & 128.498214796927 & 31.0473670911549 & 225.949062502699 \tabularnewline
83 & 129.973491018404 & 26.401947793647 & 233.545034243161 \tabularnewline
84 & 157.317245343863 & 47.5151108713384 & 267.119379816387 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=42181&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]73[/C][C]120.142395467120[/C][C]72.7331104629439[/C][C]167.551680471295[/C][/ROW]
[ROW][C]74[/C][C]116.932708273499[/C][C]64.4052439384798[/C][C]169.460172608519[/C][/ROW]
[ROW][C]75[/C][C]117.233215209465[/C][C]59.482272483595[/C][C]174.984157935336[/C][/ROW]
[ROW][C]76[/C][C]111.160562387663[/C][C]48.0766121040534[/C][C]174.244512671273[/C][/ROW]
[ROW][C]77[/C][C]115.522940488456[/C][C]46.9940520366559[/C][C]184.051828940255[/C][/ROW]
[ROW][C]78[/C][C]111.289235587557[/C][C]37.2022830055591[/C][C]185.376188169556[/C][/ROW]
[ROW][C]79[/C][C]109.878648647973[/C][C]30.1201218014538[/C][C]189.637175494492[/C][/ROW]
[ROW][C]80[/C][C]111.432718613515[/C][C]25.8892759194313[/C][C]196.976161307599[/C][/ROW]
[ROW][C]81[/C][C]116.076551749856[/C][C]24.6353994027191[/C][C]207.517704096993[/C][/ROW]
[ROW][C]82[/C][C]128.498214796927[/C][C]31.0473670911549[/C][C]225.949062502699[/C][/ROW]
[ROW][C]83[/C][C]129.973491018404[/C][C]26.401947793647[/C][C]233.545034243161[/C][/ROW]
[ROW][C]84[/C][C]157.317245343863[/C][C]47.5151108713384[/C][C]267.119379816387[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=42181&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=42181&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
73120.14239546712072.7331104629439167.551680471295
74116.93270827349964.4052439384798169.460172608519
75117.23321520946559.482272483595174.984157935336
76111.16056238766348.0766121040534174.244512671273
77115.52294048845646.9940520366559184.051828940255
78111.28923558755737.2022830055591185.376188169556
79109.87864864797330.1201218014538189.637175494492
80111.43271861351525.8892759194313196.976161307599
81116.07655174985624.6353994027191207.517704096993
82128.49821479692731.0473670911549225.949062502699
83129.97349101840426.401947793647233.545034243161
84157.31724534386347.5151108713384267.119379816387



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