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Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationThu, 28 Apr 2016 10:15:18 +0100
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2016/Apr/28/t1461834956gxwhb8ld0944g8x.htm/, Retrieved Sat, 04 May 2024 19:05:38 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=295008, Retrieved Sat, 04 May 2024 19:05:38 +0000
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Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact122
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [] [2016-04-28 09:15:18] [4c0c83f68a39c2484f611b00ec7d20d3] [Current]
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Dataseries X:
214320
212588
205816
202196
195722
198563
229139
229527
211868
203555
195770
199834
203089
198480
192684
187827
182414
182510
211524
211451
200140
191568
186424
191987
203583
201920
195978
191395
188222
189422
214419
224325
216222
210506
207221
210027
215191
215177
211701
210176
205491
206996
235980
241292
236675
229127
225436
229570
239973
236168
230703
224790
217811
219576
245472
248511
242084
235572
229827
229697
239567
237201
233164
227755
220189
221270
245413
247826
237736
230079
225939
228987




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time1 seconds
R Server'Gertrude Mary Cox' @ cox.wessa.net

\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 & 'Gertrude Mary Cox' @ cox.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=295008&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]'Gertrude Mary Cox' @ cox.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=295008&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=295008&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'Gertrude Mary Cox' @ cox.wessa.net







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.753544580924858
beta0.086765385215168
gamma1

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.753544580924858 \tabularnewline
beta & 0.086765385215168 \tabularnewline
gamma & 1 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=295008&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]0.753544580924858[/C][/ROW]
[ROW][C]beta[/C][C]0.086765385215168[/C][/ROW]
[ROW][C]gamma[/C][C]1[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=295008&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=295008&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
alpha0.753544580924858
beta0.086765385215168
gamma1







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
13203089210227.258547009-7138.25854700859
14198480200072.263667562-1592.26366756187
15192684192560.026785031123.97321496933
16187827187034.448136977792.551863022585
17182414181409.2416037521004.75839624775
18182510181346.1348510091163.86514899074
19211524214857.225812063-3333.22581206344
20211451212014.834993264-563.834993264347
21200140193254.6475257566885.3524742444
22191568189914.805170521653.19482948002
23186424183275.7206085163148.27939148387
24191987189888.2550821862098.74491781372
25203583193458.33364339410124.666356606
26201920199084.6632147752835.33678522531
27195978197027.380525724-1049.3805257238
28191395192401.270613101-1006.2706131009
29188222186974.1289922361247.87100776445
30189422188650.584631171771.415368828719
31214419222249.109239975-7830.10923997458
32224325217898.1287782956426.87122170455
33216222207896.1872939138325.81270608693
34210506206101.0264886364404.97351136446
35207221203832.6413398793388.3586601209
36210027212311.759357519-2284.75935751927
37215191216214.439967828-1023.43996782796
38215177212572.534895532604.46510446951
39211701210297.630952051403.36904795023
40210176208604.5269997651571.47300023539
41205491206918.037632046-1427.03763204647
42206996207529.177622448-533.177622447954
43235980239007.216877197-3027.21687719697
44241292243085.636718967-1793.63671896691
45236675228116.207293488558.79270651977
46229127226304.5546907342822.44530926552
47225436223263.9050010372172.09499896324
48229570230019.613451481-449.613451480953
49239973236327.2720649973645.72793500341
50236168238114.442382039-1946.44238203909
51230703232833.196937143-2130.19693714319
52224790229006.780272974-4216.78027297353
53217811222329.096302992-4518.09630299205
54219576220738.695587273-1162.6955872727
55245472250993.94977989-5521.9497798896
56248511253199.644361988-4688.64436198823
57242084238113.9744422973970.02555770261
58235572230644.5709408664927.42905913357
59229827228381.3087874641445.69121253633
60229697233247.482711636-3550.48271163637
61239567237329.0547913542237.94520864569
62237201235686.3719333231514.62806667731
63233164232203.394886533960.605113466707
64227755229629.351950596-1874.35195059585
65220189224233.249221881-4044.24922188101
66221270223448.569010673-2178.56901067292
67245413251419.234970644-6006.23497064449
68247826252988.987873203-5162.98787320332
69237736239172.457929423-1436.45792942299
70230079227004.1037459613074.89625403934
71225939221504.7792139644434.2207860357
72228987226605.0009055382381.99909446223

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 203089 & 210227.258547009 & -7138.25854700859 \tabularnewline
14 & 198480 & 200072.263667562 & -1592.26366756187 \tabularnewline
15 & 192684 & 192560.026785031 & 123.97321496933 \tabularnewline
16 & 187827 & 187034.448136977 & 792.551863022585 \tabularnewline
17 & 182414 & 181409.241603752 & 1004.75839624775 \tabularnewline
18 & 182510 & 181346.134851009 & 1163.86514899074 \tabularnewline
19 & 211524 & 214857.225812063 & -3333.22581206344 \tabularnewline
20 & 211451 & 212014.834993264 & -563.834993264347 \tabularnewline
21 & 200140 & 193254.647525756 & 6885.3524742444 \tabularnewline
22 & 191568 & 189914.80517052 & 1653.19482948002 \tabularnewline
23 & 186424 & 183275.720608516 & 3148.27939148387 \tabularnewline
24 & 191987 & 189888.255082186 & 2098.74491781372 \tabularnewline
25 & 203583 & 193458.333643394 & 10124.666356606 \tabularnewline
26 & 201920 & 199084.663214775 & 2835.33678522531 \tabularnewline
27 & 195978 & 197027.380525724 & -1049.3805257238 \tabularnewline
28 & 191395 & 192401.270613101 & -1006.2706131009 \tabularnewline
29 & 188222 & 186974.128992236 & 1247.87100776445 \tabularnewline
30 & 189422 & 188650.584631171 & 771.415368828719 \tabularnewline
31 & 214419 & 222249.109239975 & -7830.10923997458 \tabularnewline
32 & 224325 & 217898.128778295 & 6426.87122170455 \tabularnewline
33 & 216222 & 207896.187293913 & 8325.81270608693 \tabularnewline
34 & 210506 & 206101.026488636 & 4404.97351136446 \tabularnewline
35 & 207221 & 203832.641339879 & 3388.3586601209 \tabularnewline
36 & 210027 & 212311.759357519 & -2284.75935751927 \tabularnewline
37 & 215191 & 216214.439967828 & -1023.43996782796 \tabularnewline
38 & 215177 & 212572.53489553 & 2604.46510446951 \tabularnewline
39 & 211701 & 210297.63095205 & 1403.36904795023 \tabularnewline
40 & 210176 & 208604.526999765 & 1571.47300023539 \tabularnewline
41 & 205491 & 206918.037632046 & -1427.03763204647 \tabularnewline
42 & 206996 & 207529.177622448 & -533.177622447954 \tabularnewline
43 & 235980 & 239007.216877197 & -3027.21687719697 \tabularnewline
44 & 241292 & 243085.636718967 & -1793.63671896691 \tabularnewline
45 & 236675 & 228116.20729348 & 8558.79270651977 \tabularnewline
46 & 229127 & 226304.554690734 & 2822.44530926552 \tabularnewline
47 & 225436 & 223263.905001037 & 2172.09499896324 \tabularnewline
48 & 229570 & 230019.613451481 & -449.613451480953 \tabularnewline
49 & 239973 & 236327.272064997 & 3645.72793500341 \tabularnewline
50 & 236168 & 238114.442382039 & -1946.44238203909 \tabularnewline
51 & 230703 & 232833.196937143 & -2130.19693714319 \tabularnewline
52 & 224790 & 229006.780272974 & -4216.78027297353 \tabularnewline
53 & 217811 & 222329.096302992 & -4518.09630299205 \tabularnewline
54 & 219576 & 220738.695587273 & -1162.6955872727 \tabularnewline
55 & 245472 & 250993.94977989 & -5521.9497798896 \tabularnewline
56 & 248511 & 253199.644361988 & -4688.64436198823 \tabularnewline
57 & 242084 & 238113.974442297 & 3970.02555770261 \tabularnewline
58 & 235572 & 230644.570940866 & 4927.42905913357 \tabularnewline
59 & 229827 & 228381.308787464 & 1445.69121253633 \tabularnewline
60 & 229697 & 233247.482711636 & -3550.48271163637 \tabularnewline
61 & 239567 & 237329.054791354 & 2237.94520864569 \tabularnewline
62 & 237201 & 235686.371933323 & 1514.62806667731 \tabularnewline
63 & 233164 & 232203.394886533 & 960.605113466707 \tabularnewline
64 & 227755 & 229629.351950596 & -1874.35195059585 \tabularnewline
65 & 220189 & 224233.249221881 & -4044.24922188101 \tabularnewline
66 & 221270 & 223448.569010673 & -2178.56901067292 \tabularnewline
67 & 245413 & 251419.234970644 & -6006.23497064449 \tabularnewline
68 & 247826 & 252988.987873203 & -5162.98787320332 \tabularnewline
69 & 237736 & 239172.457929423 & -1436.45792942299 \tabularnewline
70 & 230079 & 227004.103745961 & 3074.89625403934 \tabularnewline
71 & 225939 & 221504.779213964 & 4434.2207860357 \tabularnewline
72 & 228987 & 226605.000905538 & 2381.99909446223 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=295008&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]203089[/C][C]210227.258547009[/C][C]-7138.25854700859[/C][/ROW]
[ROW][C]14[/C][C]198480[/C][C]200072.263667562[/C][C]-1592.26366756187[/C][/ROW]
[ROW][C]15[/C][C]192684[/C][C]192560.026785031[/C][C]123.97321496933[/C][/ROW]
[ROW][C]16[/C][C]187827[/C][C]187034.448136977[/C][C]792.551863022585[/C][/ROW]
[ROW][C]17[/C][C]182414[/C][C]181409.241603752[/C][C]1004.75839624775[/C][/ROW]
[ROW][C]18[/C][C]182510[/C][C]181346.134851009[/C][C]1163.86514899074[/C][/ROW]
[ROW][C]19[/C][C]211524[/C][C]214857.225812063[/C][C]-3333.22581206344[/C][/ROW]
[ROW][C]20[/C][C]211451[/C][C]212014.834993264[/C][C]-563.834993264347[/C][/ROW]
[ROW][C]21[/C][C]200140[/C][C]193254.647525756[/C][C]6885.3524742444[/C][/ROW]
[ROW][C]22[/C][C]191568[/C][C]189914.80517052[/C][C]1653.19482948002[/C][/ROW]
[ROW][C]23[/C][C]186424[/C][C]183275.720608516[/C][C]3148.27939148387[/C][/ROW]
[ROW][C]24[/C][C]191987[/C][C]189888.255082186[/C][C]2098.74491781372[/C][/ROW]
[ROW][C]25[/C][C]203583[/C][C]193458.333643394[/C][C]10124.666356606[/C][/ROW]
[ROW][C]26[/C][C]201920[/C][C]199084.663214775[/C][C]2835.33678522531[/C][/ROW]
[ROW][C]27[/C][C]195978[/C][C]197027.380525724[/C][C]-1049.3805257238[/C][/ROW]
[ROW][C]28[/C][C]191395[/C][C]192401.270613101[/C][C]-1006.2706131009[/C][/ROW]
[ROW][C]29[/C][C]188222[/C][C]186974.128992236[/C][C]1247.87100776445[/C][/ROW]
[ROW][C]30[/C][C]189422[/C][C]188650.584631171[/C][C]771.415368828719[/C][/ROW]
[ROW][C]31[/C][C]214419[/C][C]222249.109239975[/C][C]-7830.10923997458[/C][/ROW]
[ROW][C]32[/C][C]224325[/C][C]217898.128778295[/C][C]6426.87122170455[/C][/ROW]
[ROW][C]33[/C][C]216222[/C][C]207896.187293913[/C][C]8325.81270608693[/C][/ROW]
[ROW][C]34[/C][C]210506[/C][C]206101.026488636[/C][C]4404.97351136446[/C][/ROW]
[ROW][C]35[/C][C]207221[/C][C]203832.641339879[/C][C]3388.3586601209[/C][/ROW]
[ROW][C]36[/C][C]210027[/C][C]212311.759357519[/C][C]-2284.75935751927[/C][/ROW]
[ROW][C]37[/C][C]215191[/C][C]216214.439967828[/C][C]-1023.43996782796[/C][/ROW]
[ROW][C]38[/C][C]215177[/C][C]212572.53489553[/C][C]2604.46510446951[/C][/ROW]
[ROW][C]39[/C][C]211701[/C][C]210297.63095205[/C][C]1403.36904795023[/C][/ROW]
[ROW][C]40[/C][C]210176[/C][C]208604.526999765[/C][C]1571.47300023539[/C][/ROW]
[ROW][C]41[/C][C]205491[/C][C]206918.037632046[/C][C]-1427.03763204647[/C][/ROW]
[ROW][C]42[/C][C]206996[/C][C]207529.177622448[/C][C]-533.177622447954[/C][/ROW]
[ROW][C]43[/C][C]235980[/C][C]239007.216877197[/C][C]-3027.21687719697[/C][/ROW]
[ROW][C]44[/C][C]241292[/C][C]243085.636718967[/C][C]-1793.63671896691[/C][/ROW]
[ROW][C]45[/C][C]236675[/C][C]228116.20729348[/C][C]8558.79270651977[/C][/ROW]
[ROW][C]46[/C][C]229127[/C][C]226304.554690734[/C][C]2822.44530926552[/C][/ROW]
[ROW][C]47[/C][C]225436[/C][C]223263.905001037[/C][C]2172.09499896324[/C][/ROW]
[ROW][C]48[/C][C]229570[/C][C]230019.613451481[/C][C]-449.613451480953[/C][/ROW]
[ROW][C]49[/C][C]239973[/C][C]236327.272064997[/C][C]3645.72793500341[/C][/ROW]
[ROW][C]50[/C][C]236168[/C][C]238114.442382039[/C][C]-1946.44238203909[/C][/ROW]
[ROW][C]51[/C][C]230703[/C][C]232833.196937143[/C][C]-2130.19693714319[/C][/ROW]
[ROW][C]52[/C][C]224790[/C][C]229006.780272974[/C][C]-4216.78027297353[/C][/ROW]
[ROW][C]53[/C][C]217811[/C][C]222329.096302992[/C][C]-4518.09630299205[/C][/ROW]
[ROW][C]54[/C][C]219576[/C][C]220738.695587273[/C][C]-1162.6955872727[/C][/ROW]
[ROW][C]55[/C][C]245472[/C][C]250993.94977989[/C][C]-5521.9497798896[/C][/ROW]
[ROW][C]56[/C][C]248511[/C][C]253199.644361988[/C][C]-4688.64436198823[/C][/ROW]
[ROW][C]57[/C][C]242084[/C][C]238113.974442297[/C][C]3970.02555770261[/C][/ROW]
[ROW][C]58[/C][C]235572[/C][C]230644.570940866[/C][C]4927.42905913357[/C][/ROW]
[ROW][C]59[/C][C]229827[/C][C]228381.308787464[/C][C]1445.69121253633[/C][/ROW]
[ROW][C]60[/C][C]229697[/C][C]233247.482711636[/C][C]-3550.48271163637[/C][/ROW]
[ROW][C]61[/C][C]239567[/C][C]237329.054791354[/C][C]2237.94520864569[/C][/ROW]
[ROW][C]62[/C][C]237201[/C][C]235686.371933323[/C][C]1514.62806667731[/C][/ROW]
[ROW][C]63[/C][C]233164[/C][C]232203.394886533[/C][C]960.605113466707[/C][/ROW]
[ROW][C]64[/C][C]227755[/C][C]229629.351950596[/C][C]-1874.35195059585[/C][/ROW]
[ROW][C]65[/C][C]220189[/C][C]224233.249221881[/C][C]-4044.24922188101[/C][/ROW]
[ROW][C]66[/C][C]221270[/C][C]223448.569010673[/C][C]-2178.56901067292[/C][/ROW]
[ROW][C]67[/C][C]245413[/C][C]251419.234970644[/C][C]-6006.23497064449[/C][/ROW]
[ROW][C]68[/C][C]247826[/C][C]252988.987873203[/C][C]-5162.98787320332[/C][/ROW]
[ROW][C]69[/C][C]237736[/C][C]239172.457929423[/C][C]-1436.45792942299[/C][/ROW]
[ROW][C]70[/C][C]230079[/C][C]227004.103745961[/C][C]3074.89625403934[/C][/ROW]
[ROW][C]71[/C][C]225939[/C][C]221504.779213964[/C][C]4434.2207860357[/C][/ROW]
[ROW][C]72[/C][C]228987[/C][C]226605.000905538[/C][C]2381.99909446223[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=295008&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=295008&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
13203089210227.258547009-7138.25854700859
14198480200072.263667562-1592.26366756187
15192684192560.026785031123.97321496933
16187827187034.448136977792.551863022585
17182414181409.2416037521004.75839624775
18182510181346.1348510091163.86514899074
19211524214857.225812063-3333.22581206344
20211451212014.834993264-563.834993264347
21200140193254.6475257566885.3524742444
22191568189914.805170521653.19482948002
23186424183275.7206085163148.27939148387
24191987189888.2550821862098.74491781372
25203583193458.33364339410124.666356606
26201920199084.6632147752835.33678522531
27195978197027.380525724-1049.3805257238
28191395192401.270613101-1006.2706131009
29188222186974.1289922361247.87100776445
30189422188650.584631171771.415368828719
31214419222249.109239975-7830.10923997458
32224325217898.1287782956426.87122170455
33216222207896.1872939138325.81270608693
34210506206101.0264886364404.97351136446
35207221203832.6413398793388.3586601209
36210027212311.759357519-2284.75935751927
37215191216214.439967828-1023.43996782796
38215177212572.534895532604.46510446951
39211701210297.630952051403.36904795023
40210176208604.5269997651571.47300023539
41205491206918.037632046-1427.03763204647
42206996207529.177622448-533.177622447954
43235980239007.216877197-3027.21687719697
44241292243085.636718967-1793.63671896691
45236675228116.207293488558.79270651977
46229127226304.5546907342822.44530926552
47225436223263.9050010372172.09499896324
48229570230019.613451481-449.613451480953
49239973236327.2720649973645.72793500341
50236168238114.442382039-1946.44238203909
51230703232833.196937143-2130.19693714319
52224790229006.780272974-4216.78027297353
53217811222329.096302992-4518.09630299205
54219576220738.695587273-1162.6955872727
55245472250993.94977989-5521.9497798896
56248511253199.644361988-4688.64436198823
57242084238113.9744422973970.02555770261
58235572230644.5709408664927.42905913357
59229827228381.3087874641445.69121253633
60229697233247.482711636-3550.48271163637
61239567237329.0547913542237.94520864569
62237201235686.3719333231514.62806667731
63233164232203.394886533960.605113466707
64227755229629.351950596-1874.35195059585
65220189224233.249221881-4044.24922188101
66221270223448.569010673-2178.56901067292
67245413251419.234970644-6006.23497064449
68247826252988.987873203-5162.98787320332
69237736239172.457929423-1436.45792942299
70230079227004.1037459613074.89625403934
71225939221504.7792139644434.2207860357
72228987226605.0009055382381.99909446223







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
73236184.818639621228692.956449237243676.680830005
74232132.425170159222448.950374333241815.899965984
75226727.483909838214994.547759778238460.420059898
76222024.003296611208302.334835881235745.671757341
77216921.185116278201233.077053727232609.29317883
78219323.913150713201670.604539119236977.221762307
79247815.396423656228185.527271408267445.265575903
80254334.152583254232708.381496347275959.923670161
81245879.366632889222233.102488853269525.630776926
82236551.992082363210857.106831412262246.877333314
83229516.264303647201742.21523082257290.313376474
84230925.060672515201039.651255597260810.470089433

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
73 & 236184.818639621 & 228692.956449237 & 243676.680830005 \tabularnewline
74 & 232132.425170159 & 222448.950374333 & 241815.899965984 \tabularnewline
75 & 226727.483909838 & 214994.547759778 & 238460.420059898 \tabularnewline
76 & 222024.003296611 & 208302.334835881 & 235745.671757341 \tabularnewline
77 & 216921.185116278 & 201233.077053727 & 232609.29317883 \tabularnewline
78 & 219323.913150713 & 201670.604539119 & 236977.221762307 \tabularnewline
79 & 247815.396423656 & 228185.527271408 & 267445.265575903 \tabularnewline
80 & 254334.152583254 & 232708.381496347 & 275959.923670161 \tabularnewline
81 & 245879.366632889 & 222233.102488853 & 269525.630776926 \tabularnewline
82 & 236551.992082363 & 210857.106831412 & 262246.877333314 \tabularnewline
83 & 229516.264303647 & 201742.21523082 & 257290.313376474 \tabularnewline
84 & 230925.060672515 & 201039.651255597 & 260810.470089433 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=295008&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]236184.818639621[/C][C]228692.956449237[/C][C]243676.680830005[/C][/ROW]
[ROW][C]74[/C][C]232132.425170159[/C][C]222448.950374333[/C][C]241815.899965984[/C][/ROW]
[ROW][C]75[/C][C]226727.483909838[/C][C]214994.547759778[/C][C]238460.420059898[/C][/ROW]
[ROW][C]76[/C][C]222024.003296611[/C][C]208302.334835881[/C][C]235745.671757341[/C][/ROW]
[ROW][C]77[/C][C]216921.185116278[/C][C]201233.077053727[/C][C]232609.29317883[/C][/ROW]
[ROW][C]78[/C][C]219323.913150713[/C][C]201670.604539119[/C][C]236977.221762307[/C][/ROW]
[ROW][C]79[/C][C]247815.396423656[/C][C]228185.527271408[/C][C]267445.265575903[/C][/ROW]
[ROW][C]80[/C][C]254334.152583254[/C][C]232708.381496347[/C][C]275959.923670161[/C][/ROW]
[ROW][C]81[/C][C]245879.366632889[/C][C]222233.102488853[/C][C]269525.630776926[/C][/ROW]
[ROW][C]82[/C][C]236551.992082363[/C][C]210857.106831412[/C][C]262246.877333314[/C][/ROW]
[ROW][C]83[/C][C]229516.264303647[/C][C]201742.21523082[/C][C]257290.313376474[/C][/ROW]
[ROW][C]84[/C][C]230925.060672515[/C][C]201039.651255597[/C][C]260810.470089433[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=295008&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=295008&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
73236184.818639621228692.956449237243676.680830005
74232132.425170159222448.950374333241815.899965984
75226727.483909838214994.547759778238460.420059898
76222024.003296611208302.334835881235745.671757341
77216921.185116278201233.077053727232609.29317883
78219323.913150713201670.604539119236977.221762307
79247815.396423656228185.527271408267445.265575903
80254334.152583254232708.381496347275959.923670161
81245879.366632889222233.102488853269525.630776926
82236551.992082363210857.106831412262246.877333314
83229516.264303647201742.21523082257290.313376474
84230925.060672515201039.651255597260810.470089433



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=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')