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Author's title

Author*The author of this computation has been verified*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationWed, 08 Dec 2010 17:06:15 +0000
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2010/Dec/08/t1291829676ibzqyvznorfwrrf.htm/, Retrieved Fri, 03 May 2024 13:58:15 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=107028, Retrieved Fri, 03 May 2024 13:58:15 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact146
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [] [2010-12-08 17:06:15] [b7dd4adfab743bef2d672ff51f950617] [Current]
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Dataseries X:
186448
190530
194207
190855
200779
204428
207617
212071
214239
215883
223484
221529
225247
226699
231406
232324
237192
236727
240698
240688
245283
243556
247826
245798
250479
249216
251896
247616
249994
246552
248771
247551
249745
245742
249019
245841
248771
244723
246878
246014
248496
244351
248016
246509
249426
247840
251035
250161
254278
250801
253985
249174
251287
247947
249992
243805
255812
250417
253033
248705
253950
251484
251093
245996
252721
248019
250464
245571
252690
250183
253639
254436
265280
268705
270643
271480




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'RServer@AstonUniversity' @ vre.aston.ac.uk

\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 & 2 seconds \tabularnewline
R Server & 'RServer@AstonUniversity' @ vre.aston.ac.uk \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=107028&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]2 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'RServer@AstonUniversity' @ vre.aston.ac.uk[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=107028&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=107028&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 time2 seconds
R Server'RServer@AstonUniversity' @ vre.aston.ac.uk







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.594091053904783
beta0.374196561823787
gamma0.693700862612219

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.594091053904783 \tabularnewline
beta & 0.374196561823787 \tabularnewline
gamma & 0.693700862612219 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=107028&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]0.594091053904783[/C][/ROW]
[ROW][C]beta[/C][C]0.374196561823787[/C][/ROW]
[ROW][C]gamma[/C][C]0.693700862612219[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=107028&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=107028&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
alpha0.594091053904783
beta0.374196561823787
gamma0.693700862612219







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
5200779193857.868756921.13124999998
6204428202551.4781552151876.52184478543
7207617210393.918864677-2776.91886467711
8212071206924.4640494055146.53595059502
9214239224646.345835572-10407.3458355723
10215883220255.125632632-4372.12563263174
11223484220316.1924129983167.80758700179
12221529221172.28584846356.714151539549
13225247229166.872676244-3919.87267624363
14226699229269.353236709-2570.35323670949
15231406231864.630352412-458.630352412263
16232324228309.2652720534014.73472794739
17237192236620.575448753571.424551246804
18236727240117.463158815-3390.46315881546
19240698242983.992694058-2285.99269405808
20240688239360.2350123651327.76498763464
21245283244265.96323921017.03676079967
22243556246171.349805591-2615.34980559099
23247826249241.026895512-1415.0268955116
24245798246777.547048244-979.547048243956
25250479249337.3811245571141.61887544286
26249216249434.025038334-218.025038333988
27251896253938.908589686-2042.90858968601
28247616250758.440679939-3142.44067993888
29249994251683.178258106-1689.17825810626
30246552248138.500344917-1586.50034491657
31248771249435.591086078-664.59108607826
32247551245189.828815352361.17118465033
33249745249442.377324503302.622675496677
34245742247201.669079551-1459.66907955092
35249019248953.64180910665.3581908937776
36245841246275.742891004-434.742891004193
37248771247948.28297532822.717024679645
38244723245296.617566287-573.617566287227
39246878247977.661584934-1099.66158493413
40246014244181.0846010351832.91539896512
41248496247773.278821491722.721178508742
42244351244865.181820142-514.181820142257
43248016247642.779986517373.220013483427
44246509246083.780703617425.21929638306
45249426248750.925691315675.074308685347
46247840245679.5017347092160.49826529145
47251035251103.843136672-68.8431366720179
48250161250006.452020969154.547979031107
49254278253232.5675427821045.43245721792
50250801251531.187881904-730.187881904189
51253985254699.595714861-714.595714860945
52249174253227.049688093-4053.04968809334
53251287253214.524668936-1927.52466893601
54247947247596.251904122350.748095877643
55249992250000.816227863-8.8162278632517
56243805246754.018924213-2949.01892421348
57255812246987.8175781338824.18242186715
58250417249780.655217727636.344782272761
59253033253699.236931496-666.23693149563
60248705250533.415141752-1828.41514175225
61253950256296.606901658-2346.60690165771
62251484249212.6710998042271.32890019621
63251093253164.489084398-2071.48908439768
64245996247952.863976388-1956.86397638821
65252721252581.568103102139.431896898343
66248019247915.279431006103.720568993769
67250464248515.0167315041948.98326849574
68245571245776.496867017-205.496867017326
69252690252477.589619012212.410380987654
70250183248302.4682416211880.53175837855
71253639251330.2453788332308.75462116735
72254436249131.6491580655304.35084193503
73265280261381.4878808573898.51211914272
74268705262843.1214270615861.87857293943
75270643272219.00667257-1576.00667256973
76271480271554.64455014-74.644550140365

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
5 & 200779 & 193857.86875 & 6921.13124999998 \tabularnewline
6 & 204428 & 202551.478155215 & 1876.52184478543 \tabularnewline
7 & 207617 & 210393.918864677 & -2776.91886467711 \tabularnewline
8 & 212071 & 206924.464049405 & 5146.53595059502 \tabularnewline
9 & 214239 & 224646.345835572 & -10407.3458355723 \tabularnewline
10 & 215883 & 220255.125632632 & -4372.12563263174 \tabularnewline
11 & 223484 & 220316.192412998 & 3167.80758700179 \tabularnewline
12 & 221529 & 221172.28584846 & 356.714151539549 \tabularnewline
13 & 225247 & 229166.872676244 & -3919.87267624363 \tabularnewline
14 & 226699 & 229269.353236709 & -2570.35323670949 \tabularnewline
15 & 231406 & 231864.630352412 & -458.630352412263 \tabularnewline
16 & 232324 & 228309.265272053 & 4014.73472794739 \tabularnewline
17 & 237192 & 236620.575448753 & 571.424551246804 \tabularnewline
18 & 236727 & 240117.463158815 & -3390.46315881546 \tabularnewline
19 & 240698 & 242983.992694058 & -2285.99269405808 \tabularnewline
20 & 240688 & 239360.235012365 & 1327.76498763464 \tabularnewline
21 & 245283 & 244265.9632392 & 1017.03676079967 \tabularnewline
22 & 243556 & 246171.349805591 & -2615.34980559099 \tabularnewline
23 & 247826 & 249241.026895512 & -1415.0268955116 \tabularnewline
24 & 245798 & 246777.547048244 & -979.547048243956 \tabularnewline
25 & 250479 & 249337.381124557 & 1141.61887544286 \tabularnewline
26 & 249216 & 249434.025038334 & -218.025038333988 \tabularnewline
27 & 251896 & 253938.908589686 & -2042.90858968601 \tabularnewline
28 & 247616 & 250758.440679939 & -3142.44067993888 \tabularnewline
29 & 249994 & 251683.178258106 & -1689.17825810626 \tabularnewline
30 & 246552 & 248138.500344917 & -1586.50034491657 \tabularnewline
31 & 248771 & 249435.591086078 & -664.59108607826 \tabularnewline
32 & 247551 & 245189.82881535 & 2361.17118465033 \tabularnewline
33 & 249745 & 249442.377324503 & 302.622675496677 \tabularnewline
34 & 245742 & 247201.669079551 & -1459.66907955092 \tabularnewline
35 & 249019 & 248953.641809106 & 65.3581908937776 \tabularnewline
36 & 245841 & 246275.742891004 & -434.742891004193 \tabularnewline
37 & 248771 & 247948.28297532 & 822.717024679645 \tabularnewline
38 & 244723 & 245296.617566287 & -573.617566287227 \tabularnewline
39 & 246878 & 247977.661584934 & -1099.66158493413 \tabularnewline
40 & 246014 & 244181.084601035 & 1832.91539896512 \tabularnewline
41 & 248496 & 247773.278821491 & 722.721178508742 \tabularnewline
42 & 244351 & 244865.181820142 & -514.181820142257 \tabularnewline
43 & 248016 & 247642.779986517 & 373.220013483427 \tabularnewline
44 & 246509 & 246083.780703617 & 425.21929638306 \tabularnewline
45 & 249426 & 248750.925691315 & 675.074308685347 \tabularnewline
46 & 247840 & 245679.501734709 & 2160.49826529145 \tabularnewline
47 & 251035 & 251103.843136672 & -68.8431366720179 \tabularnewline
48 & 250161 & 250006.452020969 & 154.547979031107 \tabularnewline
49 & 254278 & 253232.567542782 & 1045.43245721792 \tabularnewline
50 & 250801 & 251531.187881904 & -730.187881904189 \tabularnewline
51 & 253985 & 254699.595714861 & -714.595714860945 \tabularnewline
52 & 249174 & 253227.049688093 & -4053.04968809334 \tabularnewline
53 & 251287 & 253214.524668936 & -1927.52466893601 \tabularnewline
54 & 247947 & 247596.251904122 & 350.748095877643 \tabularnewline
55 & 249992 & 250000.816227863 & -8.8162278632517 \tabularnewline
56 & 243805 & 246754.018924213 & -2949.01892421348 \tabularnewline
57 & 255812 & 246987.817578133 & 8824.18242186715 \tabularnewline
58 & 250417 & 249780.655217727 & 636.344782272761 \tabularnewline
59 & 253033 & 253699.236931496 & -666.23693149563 \tabularnewline
60 & 248705 & 250533.415141752 & -1828.41514175225 \tabularnewline
61 & 253950 & 256296.606901658 & -2346.60690165771 \tabularnewline
62 & 251484 & 249212.671099804 & 2271.32890019621 \tabularnewline
63 & 251093 & 253164.489084398 & -2071.48908439768 \tabularnewline
64 & 245996 & 247952.863976388 & -1956.86397638821 \tabularnewline
65 & 252721 & 252581.568103102 & 139.431896898343 \tabularnewline
66 & 248019 & 247915.279431006 & 103.720568993769 \tabularnewline
67 & 250464 & 248515.016731504 & 1948.98326849574 \tabularnewline
68 & 245571 & 245776.496867017 & -205.496867017326 \tabularnewline
69 & 252690 & 252477.589619012 & 212.410380987654 \tabularnewline
70 & 250183 & 248302.468241621 & 1880.53175837855 \tabularnewline
71 & 253639 & 251330.245378833 & 2308.75462116735 \tabularnewline
72 & 254436 & 249131.649158065 & 5304.35084193503 \tabularnewline
73 & 265280 & 261381.487880857 & 3898.51211914272 \tabularnewline
74 & 268705 & 262843.121427061 & 5861.87857293943 \tabularnewline
75 & 270643 & 272219.00667257 & -1576.00667256973 \tabularnewline
76 & 271480 & 271554.64455014 & -74.644550140365 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=107028&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]5[/C][C]200779[/C][C]193857.86875[/C][C]6921.13124999998[/C][/ROW]
[ROW][C]6[/C][C]204428[/C][C]202551.478155215[/C][C]1876.52184478543[/C][/ROW]
[ROW][C]7[/C][C]207617[/C][C]210393.918864677[/C][C]-2776.91886467711[/C][/ROW]
[ROW][C]8[/C][C]212071[/C][C]206924.464049405[/C][C]5146.53595059502[/C][/ROW]
[ROW][C]9[/C][C]214239[/C][C]224646.345835572[/C][C]-10407.3458355723[/C][/ROW]
[ROW][C]10[/C][C]215883[/C][C]220255.125632632[/C][C]-4372.12563263174[/C][/ROW]
[ROW][C]11[/C][C]223484[/C][C]220316.192412998[/C][C]3167.80758700179[/C][/ROW]
[ROW][C]12[/C][C]221529[/C][C]221172.28584846[/C][C]356.714151539549[/C][/ROW]
[ROW][C]13[/C][C]225247[/C][C]229166.872676244[/C][C]-3919.87267624363[/C][/ROW]
[ROW][C]14[/C][C]226699[/C][C]229269.353236709[/C][C]-2570.35323670949[/C][/ROW]
[ROW][C]15[/C][C]231406[/C][C]231864.630352412[/C][C]-458.630352412263[/C][/ROW]
[ROW][C]16[/C][C]232324[/C][C]228309.265272053[/C][C]4014.73472794739[/C][/ROW]
[ROW][C]17[/C][C]237192[/C][C]236620.575448753[/C][C]571.424551246804[/C][/ROW]
[ROW][C]18[/C][C]236727[/C][C]240117.463158815[/C][C]-3390.46315881546[/C][/ROW]
[ROW][C]19[/C][C]240698[/C][C]242983.992694058[/C][C]-2285.99269405808[/C][/ROW]
[ROW][C]20[/C][C]240688[/C][C]239360.235012365[/C][C]1327.76498763464[/C][/ROW]
[ROW][C]21[/C][C]245283[/C][C]244265.9632392[/C][C]1017.03676079967[/C][/ROW]
[ROW][C]22[/C][C]243556[/C][C]246171.349805591[/C][C]-2615.34980559099[/C][/ROW]
[ROW][C]23[/C][C]247826[/C][C]249241.026895512[/C][C]-1415.0268955116[/C][/ROW]
[ROW][C]24[/C][C]245798[/C][C]246777.547048244[/C][C]-979.547048243956[/C][/ROW]
[ROW][C]25[/C][C]250479[/C][C]249337.381124557[/C][C]1141.61887544286[/C][/ROW]
[ROW][C]26[/C][C]249216[/C][C]249434.025038334[/C][C]-218.025038333988[/C][/ROW]
[ROW][C]27[/C][C]251896[/C][C]253938.908589686[/C][C]-2042.90858968601[/C][/ROW]
[ROW][C]28[/C][C]247616[/C][C]250758.440679939[/C][C]-3142.44067993888[/C][/ROW]
[ROW][C]29[/C][C]249994[/C][C]251683.178258106[/C][C]-1689.17825810626[/C][/ROW]
[ROW][C]30[/C][C]246552[/C][C]248138.500344917[/C][C]-1586.50034491657[/C][/ROW]
[ROW][C]31[/C][C]248771[/C][C]249435.591086078[/C][C]-664.59108607826[/C][/ROW]
[ROW][C]32[/C][C]247551[/C][C]245189.82881535[/C][C]2361.17118465033[/C][/ROW]
[ROW][C]33[/C][C]249745[/C][C]249442.377324503[/C][C]302.622675496677[/C][/ROW]
[ROW][C]34[/C][C]245742[/C][C]247201.669079551[/C][C]-1459.66907955092[/C][/ROW]
[ROW][C]35[/C][C]249019[/C][C]248953.641809106[/C][C]65.3581908937776[/C][/ROW]
[ROW][C]36[/C][C]245841[/C][C]246275.742891004[/C][C]-434.742891004193[/C][/ROW]
[ROW][C]37[/C][C]248771[/C][C]247948.28297532[/C][C]822.717024679645[/C][/ROW]
[ROW][C]38[/C][C]244723[/C][C]245296.617566287[/C][C]-573.617566287227[/C][/ROW]
[ROW][C]39[/C][C]246878[/C][C]247977.661584934[/C][C]-1099.66158493413[/C][/ROW]
[ROW][C]40[/C][C]246014[/C][C]244181.084601035[/C][C]1832.91539896512[/C][/ROW]
[ROW][C]41[/C][C]248496[/C][C]247773.278821491[/C][C]722.721178508742[/C][/ROW]
[ROW][C]42[/C][C]244351[/C][C]244865.181820142[/C][C]-514.181820142257[/C][/ROW]
[ROW][C]43[/C][C]248016[/C][C]247642.779986517[/C][C]373.220013483427[/C][/ROW]
[ROW][C]44[/C][C]246509[/C][C]246083.780703617[/C][C]425.21929638306[/C][/ROW]
[ROW][C]45[/C][C]249426[/C][C]248750.925691315[/C][C]675.074308685347[/C][/ROW]
[ROW][C]46[/C][C]247840[/C][C]245679.501734709[/C][C]2160.49826529145[/C][/ROW]
[ROW][C]47[/C][C]251035[/C][C]251103.843136672[/C][C]-68.8431366720179[/C][/ROW]
[ROW][C]48[/C][C]250161[/C][C]250006.452020969[/C][C]154.547979031107[/C][/ROW]
[ROW][C]49[/C][C]254278[/C][C]253232.567542782[/C][C]1045.43245721792[/C][/ROW]
[ROW][C]50[/C][C]250801[/C][C]251531.187881904[/C][C]-730.187881904189[/C][/ROW]
[ROW][C]51[/C][C]253985[/C][C]254699.595714861[/C][C]-714.595714860945[/C][/ROW]
[ROW][C]52[/C][C]249174[/C][C]253227.049688093[/C][C]-4053.04968809334[/C][/ROW]
[ROW][C]53[/C][C]251287[/C][C]253214.524668936[/C][C]-1927.52466893601[/C][/ROW]
[ROW][C]54[/C][C]247947[/C][C]247596.251904122[/C][C]350.748095877643[/C][/ROW]
[ROW][C]55[/C][C]249992[/C][C]250000.816227863[/C][C]-8.8162278632517[/C][/ROW]
[ROW][C]56[/C][C]243805[/C][C]246754.018924213[/C][C]-2949.01892421348[/C][/ROW]
[ROW][C]57[/C][C]255812[/C][C]246987.817578133[/C][C]8824.18242186715[/C][/ROW]
[ROW][C]58[/C][C]250417[/C][C]249780.655217727[/C][C]636.344782272761[/C][/ROW]
[ROW][C]59[/C][C]253033[/C][C]253699.236931496[/C][C]-666.23693149563[/C][/ROW]
[ROW][C]60[/C][C]248705[/C][C]250533.415141752[/C][C]-1828.41514175225[/C][/ROW]
[ROW][C]61[/C][C]253950[/C][C]256296.606901658[/C][C]-2346.60690165771[/C][/ROW]
[ROW][C]62[/C][C]251484[/C][C]249212.671099804[/C][C]2271.32890019621[/C][/ROW]
[ROW][C]63[/C][C]251093[/C][C]253164.489084398[/C][C]-2071.48908439768[/C][/ROW]
[ROW][C]64[/C][C]245996[/C][C]247952.863976388[/C][C]-1956.86397638821[/C][/ROW]
[ROW][C]65[/C][C]252721[/C][C]252581.568103102[/C][C]139.431896898343[/C][/ROW]
[ROW][C]66[/C][C]248019[/C][C]247915.279431006[/C][C]103.720568993769[/C][/ROW]
[ROW][C]67[/C][C]250464[/C][C]248515.016731504[/C][C]1948.98326849574[/C][/ROW]
[ROW][C]68[/C][C]245571[/C][C]245776.496867017[/C][C]-205.496867017326[/C][/ROW]
[ROW][C]69[/C][C]252690[/C][C]252477.589619012[/C][C]212.410380987654[/C][/ROW]
[ROW][C]70[/C][C]250183[/C][C]248302.468241621[/C][C]1880.53175837855[/C][/ROW]
[ROW][C]71[/C][C]253639[/C][C]251330.245378833[/C][C]2308.75462116735[/C][/ROW]
[ROW][C]72[/C][C]254436[/C][C]249131.649158065[/C][C]5304.35084193503[/C][/ROW]
[ROW][C]73[/C][C]265280[/C][C]261381.487880857[/C][C]3898.51211914272[/C][/ROW]
[ROW][C]74[/C][C]268705[/C][C]262843.121427061[/C][C]5861.87857293943[/C][/ROW]
[ROW][C]75[/C][C]270643[/C][C]272219.00667257[/C][C]-1576.00667256973[/C][/ROW]
[ROW][C]76[/C][C]271480[/C][C]271554.64455014[/C][C]-74.644550140365[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=107028&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=107028&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
5200779193857.868756921.13124999998
6204428202551.4781552151876.52184478543
7207617210393.918864677-2776.91886467711
8212071206924.4640494055146.53595059502
9214239224646.345835572-10407.3458355723
10215883220255.125632632-4372.12563263174
11223484220316.1924129983167.80758700179
12221529221172.28584846356.714151539549
13225247229166.872676244-3919.87267624363
14226699229269.353236709-2570.35323670949
15231406231864.630352412-458.630352412263
16232324228309.2652720534014.73472794739
17237192236620.575448753571.424551246804
18236727240117.463158815-3390.46315881546
19240698242983.992694058-2285.99269405808
20240688239360.2350123651327.76498763464
21245283244265.96323921017.03676079967
22243556246171.349805591-2615.34980559099
23247826249241.026895512-1415.0268955116
24245798246777.547048244-979.547048243956
25250479249337.3811245571141.61887544286
26249216249434.025038334-218.025038333988
27251896253938.908589686-2042.90858968601
28247616250758.440679939-3142.44067993888
29249994251683.178258106-1689.17825810626
30246552248138.500344917-1586.50034491657
31248771249435.591086078-664.59108607826
32247551245189.828815352361.17118465033
33249745249442.377324503302.622675496677
34245742247201.669079551-1459.66907955092
35249019248953.64180910665.3581908937776
36245841246275.742891004-434.742891004193
37248771247948.28297532822.717024679645
38244723245296.617566287-573.617566287227
39246878247977.661584934-1099.66158493413
40246014244181.0846010351832.91539896512
41248496247773.278821491722.721178508742
42244351244865.181820142-514.181820142257
43248016247642.779986517373.220013483427
44246509246083.780703617425.21929638306
45249426248750.925691315675.074308685347
46247840245679.5017347092160.49826529145
47251035251103.843136672-68.8431366720179
48250161250006.452020969154.547979031107
49254278253232.5675427821045.43245721792
50250801251531.187881904-730.187881904189
51253985254699.595714861-714.595714860945
52249174253227.049688093-4053.04968809334
53251287253214.524668936-1927.52466893601
54247947247596.251904122350.748095877643
55249992250000.816227863-8.8162278632517
56243805246754.018924213-2949.01892421348
57255812246987.8175781338824.18242186715
58250417249780.655217727636.344782272761
59253033253699.236931496-666.23693149563
60248705250533.415141752-1828.41514175225
61253950256296.606901658-2346.60690165771
62251484249212.6710998042271.32890019621
63251093253164.489084398-2071.48908439768
64245996247952.863976388-1956.86397638821
65252721252581.568103102139.431896898343
66248019247915.279431006103.720568993769
67250464248515.0167315041948.98326849574
68245571245776.496867017-205.496867017326
69252690252477.589619012212.410380987654
70250183248302.4682416211880.53175837855
71253639251330.2453788332308.75462116735
72254436249131.6491580655304.35084193503
73265280261381.4878808573898.51211914272
74268705262843.1214270615861.87857293943
75270643272219.00667257-1576.00667256973
76271480271554.64455014-74.644550140365







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
77282015.865498848276525.680709346287506.050288351
78282650.455993896275563.000601895289737.911385897
79286082.545418822276985.700226495295179.390611149
80286760.633392828275328.962373197298192.304412459

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
77 & 282015.865498848 & 276525.680709346 & 287506.050288351 \tabularnewline
78 & 282650.455993896 & 275563.000601895 & 289737.911385897 \tabularnewline
79 & 286082.545418822 & 276985.700226495 & 295179.390611149 \tabularnewline
80 & 286760.633392828 & 275328.962373197 & 298192.304412459 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=107028&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]77[/C][C]282015.865498848[/C][C]276525.680709346[/C][C]287506.050288351[/C][/ROW]
[ROW][C]78[/C][C]282650.455993896[/C][C]275563.000601895[/C][C]289737.911385897[/C][/ROW]
[ROW][C]79[/C][C]286082.545418822[/C][C]276985.700226495[/C][C]295179.390611149[/C][/ROW]
[ROW][C]80[/C][C]286760.633392828[/C][C]275328.962373197[/C][C]298192.304412459[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=107028&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=107028&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
77282015.865498848276525.680709346287506.050288351
78282650.455993896275563.000601895289737.911385897
79286082.545418822276985.700226495295179.390611149
80286760.633392828275328.962373197298192.304412459



Parameters (Session):
par1 = 4 ; par2 = Triple ; par3 = additive ;
Parameters (R input):
par1 = 4 ; 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')