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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 14:29:09 -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/t1244406612i0qap93fb4pc5ov.htm/, Retrieved Mon, 13 May 2024 01:44:47 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=42260, Retrieved Mon, 13 May 2024 01:44:47 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact102
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [exponantial smoot...] [2009-06-07 20:29:09] [d19dedf3d9cbe742e7fe81d57ca6286d] [Current]
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Dataseries X:
233084
233898
231355
232662
230037
231814
246796
247891
248291
245766
238776
242541
246861
246843
246947
241679
240085
241514
250525
250567
252145
251877
245817
248269
246310
246733
245028
240022
238614
238096
248530
248381
247567
241783
235000
237384
238020
236412
232279
230408
230254
229217
239658
239906
236558
223566
216054
214685
216086
211692
204681
203075
198401
191246
206750
209611
199573
195635
190062
193134
194795
190835
185045
184425
177293
180549
195344
196597
189102
185749
185145
192243
197356




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time1 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 & 1 seconds \tabularnewline
R Server & 'George Udny Yule' @ 72.249.76.132 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=42260&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]'George Udny Yule' @ 72.249.76.132[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=42260&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=42260&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'George Udny Yule' @ 72.249.76.132







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.773667308423978
beta0.166998649303154
gamma1

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.773667308423978 \tabularnewline
beta & 0.166998649303154 \tabularnewline
gamma & 1 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=42260&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]0.773667308423978[/C][/ROW]
[ROW][C]beta[/C][C]0.166998649303154[/C][/ROW]
[ROW][C]gamma[/C][C]1[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=42260&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=42260&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
alpha0.773667308423978
beta0.166998649303154
gamma1







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
13246861241488.4001068385372.59989316217
14246843246698.146581664144.85341833625
15246947247998.863442649-1051.86344264919
16241679242722.692366167-1043.69236616709
17240085240859.204807568-774.204807568109
18241514242143.140954864-629.140954863891
19250525255381.855706619-4856.85570661904
20250567251883.004897147-1316.00489714718
21252145250182.9399337521962.06006624809
22251877248511.1742327393365.82576726069
23245817244126.3255494841690.67445051644
24248269249390.446220837-1121.44622083745
25246310254368.315305939-8058.31530593935
26246733246493.671715601239.328284399002
27245028246098.710705382-1070.71070538196
28240022239309.458568613712.541431387013
29238614237592.2644561221021.73554387782
30238096239257.090559623-1161.09055962315
31248530250017.251528366-1487.25152836612
32248381249251.989465183-870.989465183375
33247567248020.874131474-453.874131474324
34241783243868.277593915-2085.27759391547
35235000233253.2371796741746.76282032573
36237384236297.8136849121086.18631508760
37238020240072.381781725-2052.38178172495
38236412238157.101756682-1745.1017566823
39232279235108.697450088-2829.69745008802
40230408226313.2694896414094.73051035873
41230254226670.8152438433583.18475615731
42229217229542.318780281-325.318780280533
43239658240702.263864742-1044.26386474186
44239906240303.437453434-397.437453433929
45236558239478.514574015-2920.51457401496
46223566232675.039548096-9109.03954809584
47216054216212.500823049-158.500823049166
48214685216106.605027618-1421.60502761812
49216086215379.684192603706.315807397041
50211692214173.761210970-2481.76121096950
51204681208720.266064819-4039.26606481895
52203075198810.2988350024264.70116499774
53198401197459.566253684941.433746316208
54191246195337.293807303-4091.29380730292
55206750200869.0196599095880.98034009055
56209611204317.2907779015293.70922209925
57199573206402.535808116-6829.53580811643
58195635193747.2309477021887.76905229830
59190062187812.2836884062249.71631159392
60193134189588.7306357123545.26936428761
61194795194132.928944042662.071055957844
62190835193112.285459732-2277.28545973162
63185045188431.967071973-3386.9670719734
64184425181957.8942623012467.10573769888
65177293179283.777727809-1990.77772780877
66180549174194.5534573226354.44654267828
67195344191855.1381183213488.86188167922
68196597194801.0010296871795.99897031314
69189102192465.600555133-3363.60055513267
70185749185941.896486569-192.896486569283
71185145179687.4108474245457.58915257579
72192243185861.6558285026381.34417149783
73197356193936.6409664523419.35903354763

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 246861 & 241488.400106838 & 5372.59989316217 \tabularnewline
14 & 246843 & 246698.146581664 & 144.85341833625 \tabularnewline
15 & 246947 & 247998.863442649 & -1051.86344264919 \tabularnewline
16 & 241679 & 242722.692366167 & -1043.69236616709 \tabularnewline
17 & 240085 & 240859.204807568 & -774.204807568109 \tabularnewline
18 & 241514 & 242143.140954864 & -629.140954863891 \tabularnewline
19 & 250525 & 255381.855706619 & -4856.85570661904 \tabularnewline
20 & 250567 & 251883.004897147 & -1316.00489714718 \tabularnewline
21 & 252145 & 250182.939933752 & 1962.06006624809 \tabularnewline
22 & 251877 & 248511.174232739 & 3365.82576726069 \tabularnewline
23 & 245817 & 244126.325549484 & 1690.67445051644 \tabularnewline
24 & 248269 & 249390.446220837 & -1121.44622083745 \tabularnewline
25 & 246310 & 254368.315305939 & -8058.31530593935 \tabularnewline
26 & 246733 & 246493.671715601 & 239.328284399002 \tabularnewline
27 & 245028 & 246098.710705382 & -1070.71070538196 \tabularnewline
28 & 240022 & 239309.458568613 & 712.541431387013 \tabularnewline
29 & 238614 & 237592.264456122 & 1021.73554387782 \tabularnewline
30 & 238096 & 239257.090559623 & -1161.09055962315 \tabularnewline
31 & 248530 & 250017.251528366 & -1487.25152836612 \tabularnewline
32 & 248381 & 249251.989465183 & -870.989465183375 \tabularnewline
33 & 247567 & 248020.874131474 & -453.874131474324 \tabularnewline
34 & 241783 & 243868.277593915 & -2085.27759391547 \tabularnewline
35 & 235000 & 233253.237179674 & 1746.76282032573 \tabularnewline
36 & 237384 & 236297.813684912 & 1086.18631508760 \tabularnewline
37 & 238020 & 240072.381781725 & -2052.38178172495 \tabularnewline
38 & 236412 & 238157.101756682 & -1745.1017566823 \tabularnewline
39 & 232279 & 235108.697450088 & -2829.69745008802 \tabularnewline
40 & 230408 & 226313.269489641 & 4094.73051035873 \tabularnewline
41 & 230254 & 226670.815243843 & 3583.18475615731 \tabularnewline
42 & 229217 & 229542.318780281 & -325.318780280533 \tabularnewline
43 & 239658 & 240702.263864742 & -1044.26386474186 \tabularnewline
44 & 239906 & 240303.437453434 & -397.437453433929 \tabularnewline
45 & 236558 & 239478.514574015 & -2920.51457401496 \tabularnewline
46 & 223566 & 232675.039548096 & -9109.03954809584 \tabularnewline
47 & 216054 & 216212.500823049 & -158.500823049166 \tabularnewline
48 & 214685 & 216106.605027618 & -1421.60502761812 \tabularnewline
49 & 216086 & 215379.684192603 & 706.315807397041 \tabularnewline
50 & 211692 & 214173.761210970 & -2481.76121096950 \tabularnewline
51 & 204681 & 208720.266064819 & -4039.26606481895 \tabularnewline
52 & 203075 & 198810.298835002 & 4264.70116499774 \tabularnewline
53 & 198401 & 197459.566253684 & 941.433746316208 \tabularnewline
54 & 191246 & 195337.293807303 & -4091.29380730292 \tabularnewline
55 & 206750 & 200869.019659909 & 5880.98034009055 \tabularnewline
56 & 209611 & 204317.290777901 & 5293.70922209925 \tabularnewline
57 & 199573 & 206402.535808116 & -6829.53580811643 \tabularnewline
58 & 195635 & 193747.230947702 & 1887.76905229830 \tabularnewline
59 & 190062 & 187812.283688406 & 2249.71631159392 \tabularnewline
60 & 193134 & 189588.730635712 & 3545.26936428761 \tabularnewline
61 & 194795 & 194132.928944042 & 662.071055957844 \tabularnewline
62 & 190835 & 193112.285459732 & -2277.28545973162 \tabularnewline
63 & 185045 & 188431.967071973 & -3386.9670719734 \tabularnewline
64 & 184425 & 181957.894262301 & 2467.10573769888 \tabularnewline
65 & 177293 & 179283.777727809 & -1990.77772780877 \tabularnewline
66 & 180549 & 174194.553457322 & 6354.44654267828 \tabularnewline
67 & 195344 & 191855.138118321 & 3488.86188167922 \tabularnewline
68 & 196597 & 194801.001029687 & 1795.99897031314 \tabularnewline
69 & 189102 & 192465.600555133 & -3363.60055513267 \tabularnewline
70 & 185749 & 185941.896486569 & -192.896486569283 \tabularnewline
71 & 185145 & 179687.410847424 & 5457.58915257579 \tabularnewline
72 & 192243 & 185861.655828502 & 6381.34417149783 \tabularnewline
73 & 197356 & 193936.640966452 & 3419.35903354763 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=42260&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]246861[/C][C]241488.400106838[/C][C]5372.59989316217[/C][/ROW]
[ROW][C]14[/C][C]246843[/C][C]246698.146581664[/C][C]144.85341833625[/C][/ROW]
[ROW][C]15[/C][C]246947[/C][C]247998.863442649[/C][C]-1051.86344264919[/C][/ROW]
[ROW][C]16[/C][C]241679[/C][C]242722.692366167[/C][C]-1043.69236616709[/C][/ROW]
[ROW][C]17[/C][C]240085[/C][C]240859.204807568[/C][C]-774.204807568109[/C][/ROW]
[ROW][C]18[/C][C]241514[/C][C]242143.140954864[/C][C]-629.140954863891[/C][/ROW]
[ROW][C]19[/C][C]250525[/C][C]255381.855706619[/C][C]-4856.85570661904[/C][/ROW]
[ROW][C]20[/C][C]250567[/C][C]251883.004897147[/C][C]-1316.00489714718[/C][/ROW]
[ROW][C]21[/C][C]252145[/C][C]250182.939933752[/C][C]1962.06006624809[/C][/ROW]
[ROW][C]22[/C][C]251877[/C][C]248511.174232739[/C][C]3365.82576726069[/C][/ROW]
[ROW][C]23[/C][C]245817[/C][C]244126.325549484[/C][C]1690.67445051644[/C][/ROW]
[ROW][C]24[/C][C]248269[/C][C]249390.446220837[/C][C]-1121.44622083745[/C][/ROW]
[ROW][C]25[/C][C]246310[/C][C]254368.315305939[/C][C]-8058.31530593935[/C][/ROW]
[ROW][C]26[/C][C]246733[/C][C]246493.671715601[/C][C]239.328284399002[/C][/ROW]
[ROW][C]27[/C][C]245028[/C][C]246098.710705382[/C][C]-1070.71070538196[/C][/ROW]
[ROW][C]28[/C][C]240022[/C][C]239309.458568613[/C][C]712.541431387013[/C][/ROW]
[ROW][C]29[/C][C]238614[/C][C]237592.264456122[/C][C]1021.73554387782[/C][/ROW]
[ROW][C]30[/C][C]238096[/C][C]239257.090559623[/C][C]-1161.09055962315[/C][/ROW]
[ROW][C]31[/C][C]248530[/C][C]250017.251528366[/C][C]-1487.25152836612[/C][/ROW]
[ROW][C]32[/C][C]248381[/C][C]249251.989465183[/C][C]-870.989465183375[/C][/ROW]
[ROW][C]33[/C][C]247567[/C][C]248020.874131474[/C][C]-453.874131474324[/C][/ROW]
[ROW][C]34[/C][C]241783[/C][C]243868.277593915[/C][C]-2085.27759391547[/C][/ROW]
[ROW][C]35[/C][C]235000[/C][C]233253.237179674[/C][C]1746.76282032573[/C][/ROW]
[ROW][C]36[/C][C]237384[/C][C]236297.813684912[/C][C]1086.18631508760[/C][/ROW]
[ROW][C]37[/C][C]238020[/C][C]240072.381781725[/C][C]-2052.38178172495[/C][/ROW]
[ROW][C]38[/C][C]236412[/C][C]238157.101756682[/C][C]-1745.1017566823[/C][/ROW]
[ROW][C]39[/C][C]232279[/C][C]235108.697450088[/C][C]-2829.69745008802[/C][/ROW]
[ROW][C]40[/C][C]230408[/C][C]226313.269489641[/C][C]4094.73051035873[/C][/ROW]
[ROW][C]41[/C][C]230254[/C][C]226670.815243843[/C][C]3583.18475615731[/C][/ROW]
[ROW][C]42[/C][C]229217[/C][C]229542.318780281[/C][C]-325.318780280533[/C][/ROW]
[ROW][C]43[/C][C]239658[/C][C]240702.263864742[/C][C]-1044.26386474186[/C][/ROW]
[ROW][C]44[/C][C]239906[/C][C]240303.437453434[/C][C]-397.437453433929[/C][/ROW]
[ROW][C]45[/C][C]236558[/C][C]239478.514574015[/C][C]-2920.51457401496[/C][/ROW]
[ROW][C]46[/C][C]223566[/C][C]232675.039548096[/C][C]-9109.03954809584[/C][/ROW]
[ROW][C]47[/C][C]216054[/C][C]216212.500823049[/C][C]-158.500823049166[/C][/ROW]
[ROW][C]48[/C][C]214685[/C][C]216106.605027618[/C][C]-1421.60502761812[/C][/ROW]
[ROW][C]49[/C][C]216086[/C][C]215379.684192603[/C][C]706.315807397041[/C][/ROW]
[ROW][C]50[/C][C]211692[/C][C]214173.761210970[/C][C]-2481.76121096950[/C][/ROW]
[ROW][C]51[/C][C]204681[/C][C]208720.266064819[/C][C]-4039.26606481895[/C][/ROW]
[ROW][C]52[/C][C]203075[/C][C]198810.298835002[/C][C]4264.70116499774[/C][/ROW]
[ROW][C]53[/C][C]198401[/C][C]197459.566253684[/C][C]941.433746316208[/C][/ROW]
[ROW][C]54[/C][C]191246[/C][C]195337.293807303[/C][C]-4091.29380730292[/C][/ROW]
[ROW][C]55[/C][C]206750[/C][C]200869.019659909[/C][C]5880.98034009055[/C][/ROW]
[ROW][C]56[/C][C]209611[/C][C]204317.290777901[/C][C]5293.70922209925[/C][/ROW]
[ROW][C]57[/C][C]199573[/C][C]206402.535808116[/C][C]-6829.53580811643[/C][/ROW]
[ROW][C]58[/C][C]195635[/C][C]193747.230947702[/C][C]1887.76905229830[/C][/ROW]
[ROW][C]59[/C][C]190062[/C][C]187812.283688406[/C][C]2249.71631159392[/C][/ROW]
[ROW][C]60[/C][C]193134[/C][C]189588.730635712[/C][C]3545.26936428761[/C][/ROW]
[ROW][C]61[/C][C]194795[/C][C]194132.928944042[/C][C]662.071055957844[/C][/ROW]
[ROW][C]62[/C][C]190835[/C][C]193112.285459732[/C][C]-2277.28545973162[/C][/ROW]
[ROW][C]63[/C][C]185045[/C][C]188431.967071973[/C][C]-3386.9670719734[/C][/ROW]
[ROW][C]64[/C][C]184425[/C][C]181957.894262301[/C][C]2467.10573769888[/C][/ROW]
[ROW][C]65[/C][C]177293[/C][C]179283.777727809[/C][C]-1990.77772780877[/C][/ROW]
[ROW][C]66[/C][C]180549[/C][C]174194.553457322[/C][C]6354.44654267828[/C][/ROW]
[ROW][C]67[/C][C]195344[/C][C]191855.138118321[/C][C]3488.86188167922[/C][/ROW]
[ROW][C]68[/C][C]196597[/C][C]194801.001029687[/C][C]1795.99897031314[/C][/ROW]
[ROW][C]69[/C][C]189102[/C][C]192465.600555133[/C][C]-3363.60055513267[/C][/ROW]
[ROW][C]70[/C][C]185749[/C][C]185941.896486569[/C][C]-192.896486569283[/C][/ROW]
[ROW][C]71[/C][C]185145[/C][C]179687.410847424[/C][C]5457.58915257579[/C][/ROW]
[ROW][C]72[/C][C]192243[/C][C]185861.655828502[/C][C]6381.34417149783[/C][/ROW]
[ROW][C]73[/C][C]197356[/C][C]193936.640966452[/C][C]3419.35903354763[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=42260&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=42260&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
13246861241488.4001068385372.59989316217
14246843246698.146581664144.85341833625
15246947247998.863442649-1051.86344264919
16241679242722.692366167-1043.69236616709
17240085240859.204807568-774.204807568109
18241514242143.140954864-629.140954863891
19250525255381.855706619-4856.85570661904
20250567251883.004897147-1316.00489714718
21252145250182.9399337521962.06006624809
22251877248511.1742327393365.82576726069
23245817244126.3255494841690.67445051644
24248269249390.446220837-1121.44622083745
25246310254368.315305939-8058.31530593935
26246733246493.671715601239.328284399002
27245028246098.710705382-1070.71070538196
28240022239309.458568613712.541431387013
29238614237592.2644561221021.73554387782
30238096239257.090559623-1161.09055962315
31248530250017.251528366-1487.25152836612
32248381249251.989465183-870.989465183375
33247567248020.874131474-453.874131474324
34241783243868.277593915-2085.27759391547
35235000233253.2371796741746.76282032573
36237384236297.8136849121086.18631508760
37238020240072.381781725-2052.38178172495
38236412238157.101756682-1745.1017566823
39232279235108.697450088-2829.69745008802
40230408226313.2694896414094.73051035873
41230254226670.8152438433583.18475615731
42229217229542.318780281-325.318780280533
43239658240702.263864742-1044.26386474186
44239906240303.437453434-397.437453433929
45236558239478.514574015-2920.51457401496
46223566232675.039548096-9109.03954809584
47216054216212.500823049-158.500823049166
48214685216106.605027618-1421.60502761812
49216086215379.684192603706.315807397041
50211692214173.761210970-2481.76121096950
51204681208720.266064819-4039.26606481895
52203075198810.2988350024264.70116499774
53198401197459.566253684941.433746316208
54191246195337.293807303-4091.29380730292
55206750200869.0196599095880.98034009055
56209611204317.2907779015293.70922209925
57199573206402.535808116-6829.53580811643
58195635193747.2309477021887.76905229830
59190062187812.2836884062249.71631159392
60193134189588.7306357123545.26936428761
61194795194132.928944042662.071055957844
62190835193112.285459732-2277.28545973162
63185045188431.967071973-3386.9670719734
64184425181957.8942623012467.10573769888
65177293179283.777727809-1990.77772780877
66180549174194.5534573226354.44654267828
67195344191855.1381183213488.86188167922
68196597194801.0010296871795.99897031314
69189102192465.600555133-3363.60055513267
70185749185941.896486569-192.896486569283
71185145179687.4108474245457.58915257579
72192243185861.6558285026381.34417149783
73197356193936.6409664523419.35903354763







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
74196729.364533671190215.115827812203243.613239530
75196199.394646408187422.857105238204975.932187578
76196747.920877436185692.22057359207803.621181282
77193914.612306293180518.535279166207310.689333420
78195270.087796205179454.795441633211085.380150776
79209560.569096801191239.787553311227881.350640291
80211167.997265687190252.588554592232083.405976781
81207787.193338659184187.403565266231386.983112051
82206529.901214780180156.523477426232903.278952134
83203674.935570431174439.922335222232909.94880564
84207102.162732279174918.942513823239285.382950736
85210011.502391167174795.131239360245227.873542974

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
74 & 196729.364533671 & 190215.115827812 & 203243.613239530 \tabularnewline
75 & 196199.394646408 & 187422.857105238 & 204975.932187578 \tabularnewline
76 & 196747.920877436 & 185692.22057359 & 207803.621181282 \tabularnewline
77 & 193914.612306293 & 180518.535279166 & 207310.689333420 \tabularnewline
78 & 195270.087796205 & 179454.795441633 & 211085.380150776 \tabularnewline
79 & 209560.569096801 & 191239.787553311 & 227881.350640291 \tabularnewline
80 & 211167.997265687 & 190252.588554592 & 232083.405976781 \tabularnewline
81 & 207787.193338659 & 184187.403565266 & 231386.983112051 \tabularnewline
82 & 206529.901214780 & 180156.523477426 & 232903.278952134 \tabularnewline
83 & 203674.935570431 & 174439.922335222 & 232909.94880564 \tabularnewline
84 & 207102.162732279 & 174918.942513823 & 239285.382950736 \tabularnewline
85 & 210011.502391167 & 174795.131239360 & 245227.873542974 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=42260&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]196729.364533671[/C][C]190215.115827812[/C][C]203243.613239530[/C][/ROW]
[ROW][C]75[/C][C]196199.394646408[/C][C]187422.857105238[/C][C]204975.932187578[/C][/ROW]
[ROW][C]76[/C][C]196747.920877436[/C][C]185692.22057359[/C][C]207803.621181282[/C][/ROW]
[ROW][C]77[/C][C]193914.612306293[/C][C]180518.535279166[/C][C]207310.689333420[/C][/ROW]
[ROW][C]78[/C][C]195270.087796205[/C][C]179454.795441633[/C][C]211085.380150776[/C][/ROW]
[ROW][C]79[/C][C]209560.569096801[/C][C]191239.787553311[/C][C]227881.350640291[/C][/ROW]
[ROW][C]80[/C][C]211167.997265687[/C][C]190252.588554592[/C][C]232083.405976781[/C][/ROW]
[ROW][C]81[/C][C]207787.193338659[/C][C]184187.403565266[/C][C]231386.983112051[/C][/ROW]
[ROW][C]82[/C][C]206529.901214780[/C][C]180156.523477426[/C][C]232903.278952134[/C][/ROW]
[ROW][C]83[/C][C]203674.935570431[/C][C]174439.922335222[/C][C]232909.94880564[/C][/ROW]
[ROW][C]84[/C][C]207102.162732279[/C][C]174918.942513823[/C][C]239285.382950736[/C][/ROW]
[ROW][C]85[/C][C]210011.502391167[/C][C]174795.131239360[/C][C]245227.873542974[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=42260&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=42260&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
74196729.364533671190215.115827812203243.613239530
75196199.394646408187422.857105238204975.932187578
76196747.920877436185692.22057359207803.621181282
77193914.612306293180518.535279166207310.689333420
78195270.087796205179454.795441633211085.380150776
79209560.569096801191239.787553311227881.350640291
80211167.997265687190252.588554592232083.405976781
81207787.193338659184187.403565266231386.983112051
82206529.901214780180156.523477426232903.278952134
83203674.935570431174439.922335222232909.94880564
84207102.162732279174918.942513823239285.382950736
85210011.502391167174795.131239360245227.873542974



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')