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Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationThu, 29 May 2008 12:48:37 -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/2008/May/29/t1212086952qhywcwr7x14ti9f.htm/, Retrieved Wed, 15 May 2024 23:25:53 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=13517, Retrieved Wed, 15 May 2024 23:25:53 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact219
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [exponential smoot...] [2008-05-29 18:48:37] [3e68c9212ad297cb41373898449ccda3] [Current]
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Dataseries X:
68.4
70.6
83.9
90.1
90.6
87.1
90.8
94.1
99.8
96.8
87
96.3
107.1
115.2
106.1
89.5
91.3
97.6
100.7
104.6
94.7
101.8
102.5
105.3
110.3
109.8
117.3
118.8
131.3
125.9
133.1
147
145.8
164.4
149.8
137.7
151.7
156.8
180
180.4
170.4
191.6
199.5
218.2
217.5
205
194
199.3
219.3
211.1
215.2
240.2
242.2
240.7
255.4
253
218.2
203.7
205.6
215.6
188.5
202.9
214
230.3
230
241
259.6
247.8
270.3
289.7
322.7
315
320.2




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time3 seconds
R Server'Herman Ole Andreas Wold' @ 193.190.124.10:1001

\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 & 'Herman Ole Andreas Wold' @ 193.190.124.10:1001 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=13517&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]'Herman Ole Andreas Wold' @ 193.190.124.10:1001[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=13517&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=13517&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'Herman Ole Andreas Wold' @ 193.190.124.10:1001







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.904548536281444
beta0.0104657928757387
gamma1

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.904548536281444 \tabularnewline
beta & 0.0104657928757387 \tabularnewline
gamma & 1 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=13517&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]0.904548536281444[/C][/ROW]
[ROW][C]beta[/C][C]0.0104657928757387[/C][/ROW]
[ROW][C]gamma[/C][C]1[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=13517&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=13517&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
alpha0.904548536281444
beta0.0104657928757387
gamma1







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
13107.197.7387638888899.36123611111108
14115.2114.9701335854250.229866414575199
15106.1107.368912292140-1.26891229213972
1689.591.1291270188985-1.6291270188985
1791.392.0897540601084-0.78975406010845
1897.698.1354915582625-0.535491558262478
19100.7101.718652429370-1.01865242936979
20104.6106.255127444955-1.6551274449546
2194.796.0668777938087-1.36687779380865
22101.8101.6805906265650.119409373435005
23102.5101.0398527677071.46014723229324
24105.3103.7673669908391.53263300916115
25110.3120.339334296878-10.0393342968784
26109.8119.008708675150-9.20870867515025
27117.3102.49578906009214.8042109399081
28118.8100.68171376484618.1182862351543
29131.3119.69307200565011.6069279943502
30125.9137.201955034841-11.3019550348411
31133.1131.1237597646651.9762402353349
32147138.4604112369818.53958876301857
33145.8137.7697057321898.03029426781109
34164.4152.36286106971112.0371389302891
35149.8163.080462386257-13.2804623862571
36137.7152.791950923431-15.0919509234309
37151.7153.374884340178-1.67488434017753
38156.8159.922049227953-3.12204922795291
39180151.49695324003128.5030467599689
40180.4162.81023396071017.5897660392897
41170.4181.136758741088-10.7367587410878
42191.6176.45123999789815.1487600021016
43199.5196.0200613440023.4799386559975
44218.2205.81123535625112.3887646437487
45217.5209.0579959119598.4420040880411
46205224.914232091180-19.9142320911795
47194204.519397750689-10.5193977506886
48199.3196.7873648616472.51263513835281
49219.3214.9737097137294.32629028627093
50211.1227.266436581910-16.1664365819098
51215.2210.3925742352944.80742576470561
52240.2199.33785835388240.862141646118
53242.2236.3394148126875.86058518731323
54240.7249.622780547128-8.92278054712844
55255.4246.5610088295418.83899117045928
56253262.357889386462-9.35788938646249
57218.2245.658973146754-27.4589731467545
58203.7226.096472012827-22.3964720128266
59205.6204.0916663055751.50833369442546
60215.6208.3356756764107.26432432358968
61188.5230.890702211273-42.3907022112734
62202.9198.4247520199924.47524798000759
63214201.87486305313112.1251369468687
64230.3200.60070491459229.6992950854079
65230223.7781558264456.22184417355459
66241235.5948046897045.40519531029636
67259.6246.94201074454012.6579892554604
68247.8264.245836377464-16.4458363774642
69270.3239.13004765290431.1699523470957
70289.7273.36080227771816.3391977222819
71322.7289.32006602315333.3799339768466
72315323.8886525337-8.88865253370011
73320.2327.885715270535-7.68571527053547

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 107.1 & 97.738763888889 & 9.36123611111108 \tabularnewline
14 & 115.2 & 114.970133585425 & 0.229866414575199 \tabularnewline
15 & 106.1 & 107.368912292140 & -1.26891229213972 \tabularnewline
16 & 89.5 & 91.1291270188985 & -1.6291270188985 \tabularnewline
17 & 91.3 & 92.0897540601084 & -0.78975406010845 \tabularnewline
18 & 97.6 & 98.1354915582625 & -0.535491558262478 \tabularnewline
19 & 100.7 & 101.718652429370 & -1.01865242936979 \tabularnewline
20 & 104.6 & 106.255127444955 & -1.6551274449546 \tabularnewline
21 & 94.7 & 96.0668777938087 & -1.36687779380865 \tabularnewline
22 & 101.8 & 101.680590626565 & 0.119409373435005 \tabularnewline
23 & 102.5 & 101.039852767707 & 1.46014723229324 \tabularnewline
24 & 105.3 & 103.767366990839 & 1.53263300916115 \tabularnewline
25 & 110.3 & 120.339334296878 & -10.0393342968784 \tabularnewline
26 & 109.8 & 119.008708675150 & -9.20870867515025 \tabularnewline
27 & 117.3 & 102.495789060092 & 14.8042109399081 \tabularnewline
28 & 118.8 & 100.681713764846 & 18.1182862351543 \tabularnewline
29 & 131.3 & 119.693072005650 & 11.6069279943502 \tabularnewline
30 & 125.9 & 137.201955034841 & -11.3019550348411 \tabularnewline
31 & 133.1 & 131.123759764665 & 1.9762402353349 \tabularnewline
32 & 147 & 138.460411236981 & 8.53958876301857 \tabularnewline
33 & 145.8 & 137.769705732189 & 8.03029426781109 \tabularnewline
34 & 164.4 & 152.362861069711 & 12.0371389302891 \tabularnewline
35 & 149.8 & 163.080462386257 & -13.2804623862571 \tabularnewline
36 & 137.7 & 152.791950923431 & -15.0919509234309 \tabularnewline
37 & 151.7 & 153.374884340178 & -1.67488434017753 \tabularnewline
38 & 156.8 & 159.922049227953 & -3.12204922795291 \tabularnewline
39 & 180 & 151.496953240031 & 28.5030467599689 \tabularnewline
40 & 180.4 & 162.810233960710 & 17.5897660392897 \tabularnewline
41 & 170.4 & 181.136758741088 & -10.7367587410878 \tabularnewline
42 & 191.6 & 176.451239997898 & 15.1487600021016 \tabularnewline
43 & 199.5 & 196.020061344002 & 3.4799386559975 \tabularnewline
44 & 218.2 & 205.811235356251 & 12.3887646437487 \tabularnewline
45 & 217.5 & 209.057995911959 & 8.4420040880411 \tabularnewline
46 & 205 & 224.914232091180 & -19.9142320911795 \tabularnewline
47 & 194 & 204.519397750689 & -10.5193977506886 \tabularnewline
48 & 199.3 & 196.787364861647 & 2.51263513835281 \tabularnewline
49 & 219.3 & 214.973709713729 & 4.32629028627093 \tabularnewline
50 & 211.1 & 227.266436581910 & -16.1664365819098 \tabularnewline
51 & 215.2 & 210.392574235294 & 4.80742576470561 \tabularnewline
52 & 240.2 & 199.337858353882 & 40.862141646118 \tabularnewline
53 & 242.2 & 236.339414812687 & 5.86058518731323 \tabularnewline
54 & 240.7 & 249.622780547128 & -8.92278054712844 \tabularnewline
55 & 255.4 & 246.561008829541 & 8.83899117045928 \tabularnewline
56 & 253 & 262.357889386462 & -9.35788938646249 \tabularnewline
57 & 218.2 & 245.658973146754 & -27.4589731467545 \tabularnewline
58 & 203.7 & 226.096472012827 & -22.3964720128266 \tabularnewline
59 & 205.6 & 204.091666305575 & 1.50833369442546 \tabularnewline
60 & 215.6 & 208.335675676410 & 7.26432432358968 \tabularnewline
61 & 188.5 & 230.890702211273 & -42.3907022112734 \tabularnewline
62 & 202.9 & 198.424752019992 & 4.47524798000759 \tabularnewline
63 & 214 & 201.874863053131 & 12.1251369468687 \tabularnewline
64 & 230.3 & 200.600704914592 & 29.6992950854079 \tabularnewline
65 & 230 & 223.778155826445 & 6.22184417355459 \tabularnewline
66 & 241 & 235.594804689704 & 5.40519531029636 \tabularnewline
67 & 259.6 & 246.942010744540 & 12.6579892554604 \tabularnewline
68 & 247.8 & 264.245836377464 & -16.4458363774642 \tabularnewline
69 & 270.3 & 239.130047652904 & 31.1699523470957 \tabularnewline
70 & 289.7 & 273.360802277718 & 16.3391977222819 \tabularnewline
71 & 322.7 & 289.320066023153 & 33.3799339768466 \tabularnewline
72 & 315 & 323.8886525337 & -8.88865253370011 \tabularnewline
73 & 320.2 & 327.885715270535 & -7.68571527053547 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=13517&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]107.1[/C][C]97.738763888889[/C][C]9.36123611111108[/C][/ROW]
[ROW][C]14[/C][C]115.2[/C][C]114.970133585425[/C][C]0.229866414575199[/C][/ROW]
[ROW][C]15[/C][C]106.1[/C][C]107.368912292140[/C][C]-1.26891229213972[/C][/ROW]
[ROW][C]16[/C][C]89.5[/C][C]91.1291270188985[/C][C]-1.6291270188985[/C][/ROW]
[ROW][C]17[/C][C]91.3[/C][C]92.0897540601084[/C][C]-0.78975406010845[/C][/ROW]
[ROW][C]18[/C][C]97.6[/C][C]98.1354915582625[/C][C]-0.535491558262478[/C][/ROW]
[ROW][C]19[/C][C]100.7[/C][C]101.718652429370[/C][C]-1.01865242936979[/C][/ROW]
[ROW][C]20[/C][C]104.6[/C][C]106.255127444955[/C][C]-1.6551274449546[/C][/ROW]
[ROW][C]21[/C][C]94.7[/C][C]96.0668777938087[/C][C]-1.36687779380865[/C][/ROW]
[ROW][C]22[/C][C]101.8[/C][C]101.680590626565[/C][C]0.119409373435005[/C][/ROW]
[ROW][C]23[/C][C]102.5[/C][C]101.039852767707[/C][C]1.46014723229324[/C][/ROW]
[ROW][C]24[/C][C]105.3[/C][C]103.767366990839[/C][C]1.53263300916115[/C][/ROW]
[ROW][C]25[/C][C]110.3[/C][C]120.339334296878[/C][C]-10.0393342968784[/C][/ROW]
[ROW][C]26[/C][C]109.8[/C][C]119.008708675150[/C][C]-9.20870867515025[/C][/ROW]
[ROW][C]27[/C][C]117.3[/C][C]102.495789060092[/C][C]14.8042109399081[/C][/ROW]
[ROW][C]28[/C][C]118.8[/C][C]100.681713764846[/C][C]18.1182862351543[/C][/ROW]
[ROW][C]29[/C][C]131.3[/C][C]119.693072005650[/C][C]11.6069279943502[/C][/ROW]
[ROW][C]30[/C][C]125.9[/C][C]137.201955034841[/C][C]-11.3019550348411[/C][/ROW]
[ROW][C]31[/C][C]133.1[/C][C]131.123759764665[/C][C]1.9762402353349[/C][/ROW]
[ROW][C]32[/C][C]147[/C][C]138.460411236981[/C][C]8.53958876301857[/C][/ROW]
[ROW][C]33[/C][C]145.8[/C][C]137.769705732189[/C][C]8.03029426781109[/C][/ROW]
[ROW][C]34[/C][C]164.4[/C][C]152.362861069711[/C][C]12.0371389302891[/C][/ROW]
[ROW][C]35[/C][C]149.8[/C][C]163.080462386257[/C][C]-13.2804623862571[/C][/ROW]
[ROW][C]36[/C][C]137.7[/C][C]152.791950923431[/C][C]-15.0919509234309[/C][/ROW]
[ROW][C]37[/C][C]151.7[/C][C]153.374884340178[/C][C]-1.67488434017753[/C][/ROW]
[ROW][C]38[/C][C]156.8[/C][C]159.922049227953[/C][C]-3.12204922795291[/C][/ROW]
[ROW][C]39[/C][C]180[/C][C]151.496953240031[/C][C]28.5030467599689[/C][/ROW]
[ROW][C]40[/C][C]180.4[/C][C]162.810233960710[/C][C]17.5897660392897[/C][/ROW]
[ROW][C]41[/C][C]170.4[/C][C]181.136758741088[/C][C]-10.7367587410878[/C][/ROW]
[ROW][C]42[/C][C]191.6[/C][C]176.451239997898[/C][C]15.1487600021016[/C][/ROW]
[ROW][C]43[/C][C]199.5[/C][C]196.020061344002[/C][C]3.4799386559975[/C][/ROW]
[ROW][C]44[/C][C]218.2[/C][C]205.811235356251[/C][C]12.3887646437487[/C][/ROW]
[ROW][C]45[/C][C]217.5[/C][C]209.057995911959[/C][C]8.4420040880411[/C][/ROW]
[ROW][C]46[/C][C]205[/C][C]224.914232091180[/C][C]-19.9142320911795[/C][/ROW]
[ROW][C]47[/C][C]194[/C][C]204.519397750689[/C][C]-10.5193977506886[/C][/ROW]
[ROW][C]48[/C][C]199.3[/C][C]196.787364861647[/C][C]2.51263513835281[/C][/ROW]
[ROW][C]49[/C][C]219.3[/C][C]214.973709713729[/C][C]4.32629028627093[/C][/ROW]
[ROW][C]50[/C][C]211.1[/C][C]227.266436581910[/C][C]-16.1664365819098[/C][/ROW]
[ROW][C]51[/C][C]215.2[/C][C]210.392574235294[/C][C]4.80742576470561[/C][/ROW]
[ROW][C]52[/C][C]240.2[/C][C]199.337858353882[/C][C]40.862141646118[/C][/ROW]
[ROW][C]53[/C][C]242.2[/C][C]236.339414812687[/C][C]5.86058518731323[/C][/ROW]
[ROW][C]54[/C][C]240.7[/C][C]249.622780547128[/C][C]-8.92278054712844[/C][/ROW]
[ROW][C]55[/C][C]255.4[/C][C]246.561008829541[/C][C]8.83899117045928[/C][/ROW]
[ROW][C]56[/C][C]253[/C][C]262.357889386462[/C][C]-9.35788938646249[/C][/ROW]
[ROW][C]57[/C][C]218.2[/C][C]245.658973146754[/C][C]-27.4589731467545[/C][/ROW]
[ROW][C]58[/C][C]203.7[/C][C]226.096472012827[/C][C]-22.3964720128266[/C][/ROW]
[ROW][C]59[/C][C]205.6[/C][C]204.091666305575[/C][C]1.50833369442546[/C][/ROW]
[ROW][C]60[/C][C]215.6[/C][C]208.335675676410[/C][C]7.26432432358968[/C][/ROW]
[ROW][C]61[/C][C]188.5[/C][C]230.890702211273[/C][C]-42.3907022112734[/C][/ROW]
[ROW][C]62[/C][C]202.9[/C][C]198.424752019992[/C][C]4.47524798000759[/C][/ROW]
[ROW][C]63[/C][C]214[/C][C]201.874863053131[/C][C]12.1251369468687[/C][/ROW]
[ROW][C]64[/C][C]230.3[/C][C]200.600704914592[/C][C]29.6992950854079[/C][/ROW]
[ROW][C]65[/C][C]230[/C][C]223.778155826445[/C][C]6.22184417355459[/C][/ROW]
[ROW][C]66[/C][C]241[/C][C]235.594804689704[/C][C]5.40519531029636[/C][/ROW]
[ROW][C]67[/C][C]259.6[/C][C]246.942010744540[/C][C]12.6579892554604[/C][/ROW]
[ROW][C]68[/C][C]247.8[/C][C]264.245836377464[/C][C]-16.4458363774642[/C][/ROW]
[ROW][C]69[/C][C]270.3[/C][C]239.130047652904[/C][C]31.1699523470957[/C][/ROW]
[ROW][C]70[/C][C]289.7[/C][C]273.360802277718[/C][C]16.3391977222819[/C][/ROW]
[ROW][C]71[/C][C]322.7[/C][C]289.320066023153[/C][C]33.3799339768466[/C][/ROW]
[ROW][C]72[/C][C]315[/C][C]323.8886525337[/C][C]-8.88865253370011[/C][/ROW]
[ROW][C]73[/C][C]320.2[/C][C]327.885715270535[/C][C]-7.68571527053547[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=13517&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=13517&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
13107.197.7387638888899.36123611111108
14115.2114.9701335854250.229866414575199
15106.1107.368912292140-1.26891229213972
1689.591.1291270188985-1.6291270188985
1791.392.0897540601084-0.78975406010845
1897.698.1354915582625-0.535491558262478
19100.7101.718652429370-1.01865242936979
20104.6106.255127444955-1.6551274449546
2194.796.0668777938087-1.36687779380865
22101.8101.6805906265650.119409373435005
23102.5101.0398527677071.46014723229324
24105.3103.7673669908391.53263300916115
25110.3120.339334296878-10.0393342968784
26109.8119.008708675150-9.20870867515025
27117.3102.49578906009214.8042109399081
28118.8100.68171376484618.1182862351543
29131.3119.69307200565011.6069279943502
30125.9137.201955034841-11.3019550348411
31133.1131.1237597646651.9762402353349
32147138.4604112369818.53958876301857
33145.8137.7697057321898.03029426781109
34164.4152.36286106971112.0371389302891
35149.8163.080462386257-13.2804623862571
36137.7152.791950923431-15.0919509234309
37151.7153.374884340178-1.67488434017753
38156.8159.922049227953-3.12204922795291
39180151.49695324003128.5030467599689
40180.4162.81023396071017.5897660392897
41170.4181.136758741088-10.7367587410878
42191.6176.45123999789815.1487600021016
43199.5196.0200613440023.4799386559975
44218.2205.81123535625112.3887646437487
45217.5209.0579959119598.4420040880411
46205224.914232091180-19.9142320911795
47194204.519397750689-10.5193977506886
48199.3196.7873648616472.51263513835281
49219.3214.9737097137294.32629028627093
50211.1227.266436581910-16.1664365819098
51215.2210.3925742352944.80742576470561
52240.2199.33785835388240.862141646118
53242.2236.3394148126875.86058518731323
54240.7249.622780547128-8.92278054712844
55255.4246.5610088295418.83899117045928
56253262.357889386462-9.35788938646249
57218.2245.658973146754-27.4589731467545
58203.7226.096472012827-22.3964720128266
59205.6204.0916663055751.50833369442546
60215.6208.3356756764107.26432432358968
61188.5230.890702211273-42.3907022112734
62202.9198.4247520199924.47524798000759
63214201.87486305313112.1251369468687
64230.3200.60070491459229.6992950854079
65230223.7781558264456.22184417355459
66241235.5948046897045.40519531029636
67259.6246.94201074454012.6579892554604
68247.8264.245836377464-16.4458363774642
69270.3239.13004765290431.1699523470957
70289.7273.36080227771816.3391977222819
71322.7289.32006602315333.3799339768466
72315323.8886525337-8.88865253370011
73320.2327.885715270535-7.68571527053547







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
74332.40691228315303.392508708162361.421315858138
75333.618149569852294.310067092635372.926232047070
76324.017921375785276.446301416255371.589541335314
77318.773029229436264.03924131819373.506817140682
78325.507934552910264.324098612851386.69177049297
79333.231165731096266.102687117761400.359644344431
80336.760388909931264.067534979149409.453242840713
81331.674509827784253.715111503978409.633908151589
82336.608687879156253.622942983719419.594432774593
83339.574012689299251.760004064190427.388021314408
84339.75732381089247.281286679227432.233360942553
85351.836667044331254.840085940485448.833248148177

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
74 & 332.40691228315 & 303.392508708162 & 361.421315858138 \tabularnewline
75 & 333.618149569852 & 294.310067092635 & 372.926232047070 \tabularnewline
76 & 324.017921375785 & 276.446301416255 & 371.589541335314 \tabularnewline
77 & 318.773029229436 & 264.03924131819 & 373.506817140682 \tabularnewline
78 & 325.507934552910 & 264.324098612851 & 386.69177049297 \tabularnewline
79 & 333.231165731096 & 266.102687117761 & 400.359644344431 \tabularnewline
80 & 336.760388909931 & 264.067534979149 & 409.453242840713 \tabularnewline
81 & 331.674509827784 & 253.715111503978 & 409.633908151589 \tabularnewline
82 & 336.608687879156 & 253.622942983719 & 419.594432774593 \tabularnewline
83 & 339.574012689299 & 251.760004064190 & 427.388021314408 \tabularnewline
84 & 339.75732381089 & 247.281286679227 & 432.233360942553 \tabularnewline
85 & 351.836667044331 & 254.840085940485 & 448.833248148177 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=13517&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]74[/C][C]332.40691228315[/C][C]303.392508708162[/C][C]361.421315858138[/C][/ROW]
[ROW][C]75[/C][C]333.618149569852[/C][C]294.310067092635[/C][C]372.926232047070[/C][/ROW]
[ROW][C]76[/C][C]324.017921375785[/C][C]276.446301416255[/C][C]371.589541335314[/C][/ROW]
[ROW][C]77[/C][C]318.773029229436[/C][C]264.03924131819[/C][C]373.506817140682[/C][/ROW]
[ROW][C]78[/C][C]325.507934552910[/C][C]264.324098612851[/C][C]386.69177049297[/C][/ROW]
[ROW][C]79[/C][C]333.231165731096[/C][C]266.102687117761[/C][C]400.359644344431[/C][/ROW]
[ROW][C]80[/C][C]336.760388909931[/C][C]264.067534979149[/C][C]409.453242840713[/C][/ROW]
[ROW][C]81[/C][C]331.674509827784[/C][C]253.715111503978[/C][C]409.633908151589[/C][/ROW]
[ROW][C]82[/C][C]336.608687879156[/C][C]253.622942983719[/C][C]419.594432774593[/C][/ROW]
[ROW][C]83[/C][C]339.574012689299[/C][C]251.760004064190[/C][C]427.388021314408[/C][/ROW]
[ROW][C]84[/C][C]339.75732381089[/C][C]247.281286679227[/C][C]432.233360942553[/C][/ROW]
[ROW][C]85[/C][C]351.836667044331[/C][C]254.840085940485[/C][C]448.833248148177[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=13517&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=13517&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
74332.40691228315303.392508708162361.421315858138
75333.618149569852294.310067092635372.926232047070
76324.017921375785276.446301416255371.589541335314
77318.773029229436264.03924131819373.506817140682
78325.507934552910264.324098612851386.69177049297
79333.231165731096266.102687117761400.359644344431
80336.760388909931264.067534979149409.453242840713
81331.674509827784253.715111503978409.633908151589
82336.608687879156253.622942983719419.594432774593
83339.574012689299251.760004064190427.388021314408
84339.75732381089247.281286679227432.233360942553
85351.836667044331254.840085940485448.833248148177



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')