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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 computationThu, 21 Jan 2016 20:36:54 +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/2016/Jan/21/t1453409712ip441hoqdnqtabj.htm/, Retrieved Sun, 28 Apr 2024 21:40:35 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=289960, Retrieved Sun, 28 Apr 2024 21:40:35 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact68
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [Multiple Regression] [HPC Retail Sales] [2008-03-08 13:40:54] [1c0f2c85e8a48e42648374b3bcceca26]
- RMPD    [Exponential Smoothing] [Blog] [2016-01-21 20:36:54] [2ea4f5baf6c33ea976d37beb530b55ab] [Current]
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Dataseries X:
13328
12873
14000
13477
14237
13674
13529
14058
12975
14326
14008
16193
14483
14011
15057
14884
15414
14440
14900
15074
14442
15307
14938
17193
15528
14765
15838
15723
16150
15486
15986
15983
15692
16490
15686
18897
16316
15636
17163
16534
16518
16375
16290
16352
15943
16362
16393
19051
16747
16320
17910
16961
17480
17049
16879
17473
16998
17307
17418
20169
17871
17226
19062
17804
19100
18522
18060
18869
18127
18871
18890
21263
19547
18450
20254
19240
20216
19420
19415
20018
18652
19978
19509
21971




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'Herman Ole Andreas Wold' @ wold.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 & 2 seconds \tabularnewline
R Server & 'Herman Ole Andreas Wold' @ wold.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=289960&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]'Herman Ole Andreas Wold' @ wold.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=289960&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=289960&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'Herman Ole Andreas Wold' @ wold.wessa.net







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.283896982915226
betaFALSE
gammaFALSE

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.283896982915226 \tabularnewline
beta & FALSE \tabularnewline
gamma & FALSE \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=289960&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]0.283896982915226[/C][/ROW]
[ROW][C]beta[/C][C]FALSE[/C][/ROW]
[ROW][C]gamma[/C][C]FALSE[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=289960&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=289960&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
alpha0.283896982915226
betaFALSE
gammaFALSE







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
21287313328-455
31400013198.8268727736801.173127226426
41347713426.277506385950.7224936140883
51423713440.6774692889796.322530711112
61367413666.75103318527.24896681480823
71352913668.8089929932-139.80899299317
81405813629.117641698428.882358302006
91297513750.8760492455-775.8760492455
101432613530.6071797485795.392820251482
111400813756.4168016503251.583198349654
121619313827.8405126142365.15948738602
131448314499.3021551962-16.3021551961901
141401114494.674022521-483.674022520976
151505714357.3604268128699.6395731872
161488414555.9859907687328.014009231258
171541414649.1081783434764.891821656576
181444014866.2586587683-426.258658768256
191490014745.2451116025154.754888397543
201507414789.1795575099284.820442490098
211444214870.0392218054-428.03922180542
221530714748.5201781655558.47982183452
231493814907.070914603330.9290853966668
241719314915.85158863182277.14841136823
251552815562.3271522694-34.3271522694122
261476515552.5817773081-787.581777308054
271583815328.9896869313509.010313068713
281572315473.4961790842249.503820915772
291615015544.329561068605.670438931964
301548615716.2775713218-230.27757132176
311598615650.9024635905335.097536409534
321598315746.0356431595236.964356840541
331569215813.3091091249-121.309109124935
341649015778.8698190442711.130180955768
351568615980.7575318775-294.757531877533
361889715897.0767578862999.92324211404
371631616748.7459152994-432.745915299402
381563616625.890655577-989.890655577015
391716316344.8636850427818.136314957275
401653416577.1301164725-43.1301164724755
411651816564.8856065332-46.8856065331565
421637516551.5749242962-176.574924296241
431629016501.4458360301-211.445836030056
441635216441.4170011311-89.4170011311362
451594316416.0317842887-473.03178428868
461636216281.739487906180.2605120938824
471639316304.525205136888.4747948631975
481905116329.64293246252721.35706753749
491674717102.2279933714-355.227993371427
501632017001.3798378062-681.379837806249
511791016807.93815763381102.06184236621
521696117120.8101896676-159.810189667551
531748017075.4405589818404.559441018177
541704917190.2937636968-141.293763696754
551687917150.1808904785-271.18089047851
561747317073.1934538474399.806546152602
571699817186.6973260499-188.697326049878
581730717133.1267245001173.873275499853
591741817182.4888228241235.511177175857
602016917249.34973546722919.65026453282
611787118078.2296367357-207.22963673569
621722618019.3977680958-793.397768095809
631906217794.15453548171267.84546451826
641780418154.0920376612-350.092037661223
651910018054.70196442661045.29803557344
661852218351.4589229731170.54107702693
671806018399.8750202041-339.87502020413
681886918303.3855273999565.614472600075
691812718463.9617696643-336.961769664274
701887118368.2993398988502.700660101189
711889018511.014540611378.985459388969
722126318618.60736910032644.3926308997
731954719369.342458656177.657541344019
741845019419.7788986357-969.778898635686
752025419144.46159521821109.53840478184
761924019459.4562007643-219.4562007643
772021619397.1532474853818.846752514721
781942019629.6213699941-209.62136999414
791941519570.1104954982-155.110495498247
802001819526.0750938078491.924906192191
811865219665.7310904966-1013.73109049663
821997819377.9358924173600.064107582726
831950919548.2922821157-39.2922821157263
842197119537.13732177122433.86267822878

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
2 & 12873 & 13328 & -455 \tabularnewline
3 & 14000 & 13198.8268727736 & 801.173127226426 \tabularnewline
4 & 13477 & 13426.2775063859 & 50.7224936140883 \tabularnewline
5 & 14237 & 13440.6774692889 & 796.322530711112 \tabularnewline
6 & 13674 & 13666.7510331852 & 7.24896681480823 \tabularnewline
7 & 13529 & 13668.8089929932 & -139.80899299317 \tabularnewline
8 & 14058 & 13629.117641698 & 428.882358302006 \tabularnewline
9 & 12975 & 13750.8760492455 & -775.8760492455 \tabularnewline
10 & 14326 & 13530.6071797485 & 795.392820251482 \tabularnewline
11 & 14008 & 13756.4168016503 & 251.583198349654 \tabularnewline
12 & 16193 & 13827.840512614 & 2365.15948738602 \tabularnewline
13 & 14483 & 14499.3021551962 & -16.3021551961901 \tabularnewline
14 & 14011 & 14494.674022521 & -483.674022520976 \tabularnewline
15 & 15057 & 14357.3604268128 & 699.6395731872 \tabularnewline
16 & 14884 & 14555.9859907687 & 328.014009231258 \tabularnewline
17 & 15414 & 14649.1081783434 & 764.891821656576 \tabularnewline
18 & 14440 & 14866.2586587683 & -426.258658768256 \tabularnewline
19 & 14900 & 14745.2451116025 & 154.754888397543 \tabularnewline
20 & 15074 & 14789.1795575099 & 284.820442490098 \tabularnewline
21 & 14442 & 14870.0392218054 & -428.03922180542 \tabularnewline
22 & 15307 & 14748.5201781655 & 558.47982183452 \tabularnewline
23 & 14938 & 14907.0709146033 & 30.9290853966668 \tabularnewline
24 & 17193 & 14915.8515886318 & 2277.14841136823 \tabularnewline
25 & 15528 & 15562.3271522694 & -34.3271522694122 \tabularnewline
26 & 14765 & 15552.5817773081 & -787.581777308054 \tabularnewline
27 & 15838 & 15328.9896869313 & 509.010313068713 \tabularnewline
28 & 15723 & 15473.4961790842 & 249.503820915772 \tabularnewline
29 & 16150 & 15544.329561068 & 605.670438931964 \tabularnewline
30 & 15486 & 15716.2775713218 & -230.27757132176 \tabularnewline
31 & 15986 & 15650.9024635905 & 335.097536409534 \tabularnewline
32 & 15983 & 15746.0356431595 & 236.964356840541 \tabularnewline
33 & 15692 & 15813.3091091249 & -121.309109124935 \tabularnewline
34 & 16490 & 15778.8698190442 & 711.130180955768 \tabularnewline
35 & 15686 & 15980.7575318775 & -294.757531877533 \tabularnewline
36 & 18897 & 15897.076757886 & 2999.92324211404 \tabularnewline
37 & 16316 & 16748.7459152994 & -432.745915299402 \tabularnewline
38 & 15636 & 16625.890655577 & -989.890655577015 \tabularnewline
39 & 17163 & 16344.8636850427 & 818.136314957275 \tabularnewline
40 & 16534 & 16577.1301164725 & -43.1301164724755 \tabularnewline
41 & 16518 & 16564.8856065332 & -46.8856065331565 \tabularnewline
42 & 16375 & 16551.5749242962 & -176.574924296241 \tabularnewline
43 & 16290 & 16501.4458360301 & -211.445836030056 \tabularnewline
44 & 16352 & 16441.4170011311 & -89.4170011311362 \tabularnewline
45 & 15943 & 16416.0317842887 & -473.03178428868 \tabularnewline
46 & 16362 & 16281.7394879061 & 80.2605120938824 \tabularnewline
47 & 16393 & 16304.5252051368 & 88.4747948631975 \tabularnewline
48 & 19051 & 16329.6429324625 & 2721.35706753749 \tabularnewline
49 & 16747 & 17102.2279933714 & -355.227993371427 \tabularnewline
50 & 16320 & 17001.3798378062 & -681.379837806249 \tabularnewline
51 & 17910 & 16807.9381576338 & 1102.06184236621 \tabularnewline
52 & 16961 & 17120.8101896676 & -159.810189667551 \tabularnewline
53 & 17480 & 17075.4405589818 & 404.559441018177 \tabularnewline
54 & 17049 & 17190.2937636968 & -141.293763696754 \tabularnewline
55 & 16879 & 17150.1808904785 & -271.18089047851 \tabularnewline
56 & 17473 & 17073.1934538474 & 399.806546152602 \tabularnewline
57 & 16998 & 17186.6973260499 & -188.697326049878 \tabularnewline
58 & 17307 & 17133.1267245001 & 173.873275499853 \tabularnewline
59 & 17418 & 17182.4888228241 & 235.511177175857 \tabularnewline
60 & 20169 & 17249.3497354672 & 2919.65026453282 \tabularnewline
61 & 17871 & 18078.2296367357 & -207.22963673569 \tabularnewline
62 & 17226 & 18019.3977680958 & -793.397768095809 \tabularnewline
63 & 19062 & 17794.1545354817 & 1267.84546451826 \tabularnewline
64 & 17804 & 18154.0920376612 & -350.092037661223 \tabularnewline
65 & 19100 & 18054.7019644266 & 1045.29803557344 \tabularnewline
66 & 18522 & 18351.4589229731 & 170.54107702693 \tabularnewline
67 & 18060 & 18399.8750202041 & -339.87502020413 \tabularnewline
68 & 18869 & 18303.3855273999 & 565.614472600075 \tabularnewline
69 & 18127 & 18463.9617696643 & -336.961769664274 \tabularnewline
70 & 18871 & 18368.2993398988 & 502.700660101189 \tabularnewline
71 & 18890 & 18511.014540611 & 378.985459388969 \tabularnewline
72 & 21263 & 18618.6073691003 & 2644.3926308997 \tabularnewline
73 & 19547 & 19369.342458656 & 177.657541344019 \tabularnewline
74 & 18450 & 19419.7788986357 & -969.778898635686 \tabularnewline
75 & 20254 & 19144.4615952182 & 1109.53840478184 \tabularnewline
76 & 19240 & 19459.4562007643 & -219.4562007643 \tabularnewline
77 & 20216 & 19397.1532474853 & 818.846752514721 \tabularnewline
78 & 19420 & 19629.6213699941 & -209.62136999414 \tabularnewline
79 & 19415 & 19570.1104954982 & -155.110495498247 \tabularnewline
80 & 20018 & 19526.0750938078 & 491.924906192191 \tabularnewline
81 & 18652 & 19665.7310904966 & -1013.73109049663 \tabularnewline
82 & 19978 & 19377.9358924173 & 600.064107582726 \tabularnewline
83 & 19509 & 19548.2922821157 & -39.2922821157263 \tabularnewline
84 & 21971 & 19537.1373217712 & 2433.86267822878 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=289960&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]2[/C][C]12873[/C][C]13328[/C][C]-455[/C][/ROW]
[ROW][C]3[/C][C]14000[/C][C]13198.8268727736[/C][C]801.173127226426[/C][/ROW]
[ROW][C]4[/C][C]13477[/C][C]13426.2775063859[/C][C]50.7224936140883[/C][/ROW]
[ROW][C]5[/C][C]14237[/C][C]13440.6774692889[/C][C]796.322530711112[/C][/ROW]
[ROW][C]6[/C][C]13674[/C][C]13666.7510331852[/C][C]7.24896681480823[/C][/ROW]
[ROW][C]7[/C][C]13529[/C][C]13668.8089929932[/C][C]-139.80899299317[/C][/ROW]
[ROW][C]8[/C][C]14058[/C][C]13629.117641698[/C][C]428.882358302006[/C][/ROW]
[ROW][C]9[/C][C]12975[/C][C]13750.8760492455[/C][C]-775.8760492455[/C][/ROW]
[ROW][C]10[/C][C]14326[/C][C]13530.6071797485[/C][C]795.392820251482[/C][/ROW]
[ROW][C]11[/C][C]14008[/C][C]13756.4168016503[/C][C]251.583198349654[/C][/ROW]
[ROW][C]12[/C][C]16193[/C][C]13827.840512614[/C][C]2365.15948738602[/C][/ROW]
[ROW][C]13[/C][C]14483[/C][C]14499.3021551962[/C][C]-16.3021551961901[/C][/ROW]
[ROW][C]14[/C][C]14011[/C][C]14494.674022521[/C][C]-483.674022520976[/C][/ROW]
[ROW][C]15[/C][C]15057[/C][C]14357.3604268128[/C][C]699.6395731872[/C][/ROW]
[ROW][C]16[/C][C]14884[/C][C]14555.9859907687[/C][C]328.014009231258[/C][/ROW]
[ROW][C]17[/C][C]15414[/C][C]14649.1081783434[/C][C]764.891821656576[/C][/ROW]
[ROW][C]18[/C][C]14440[/C][C]14866.2586587683[/C][C]-426.258658768256[/C][/ROW]
[ROW][C]19[/C][C]14900[/C][C]14745.2451116025[/C][C]154.754888397543[/C][/ROW]
[ROW][C]20[/C][C]15074[/C][C]14789.1795575099[/C][C]284.820442490098[/C][/ROW]
[ROW][C]21[/C][C]14442[/C][C]14870.0392218054[/C][C]-428.03922180542[/C][/ROW]
[ROW][C]22[/C][C]15307[/C][C]14748.5201781655[/C][C]558.47982183452[/C][/ROW]
[ROW][C]23[/C][C]14938[/C][C]14907.0709146033[/C][C]30.9290853966668[/C][/ROW]
[ROW][C]24[/C][C]17193[/C][C]14915.8515886318[/C][C]2277.14841136823[/C][/ROW]
[ROW][C]25[/C][C]15528[/C][C]15562.3271522694[/C][C]-34.3271522694122[/C][/ROW]
[ROW][C]26[/C][C]14765[/C][C]15552.5817773081[/C][C]-787.581777308054[/C][/ROW]
[ROW][C]27[/C][C]15838[/C][C]15328.9896869313[/C][C]509.010313068713[/C][/ROW]
[ROW][C]28[/C][C]15723[/C][C]15473.4961790842[/C][C]249.503820915772[/C][/ROW]
[ROW][C]29[/C][C]16150[/C][C]15544.329561068[/C][C]605.670438931964[/C][/ROW]
[ROW][C]30[/C][C]15486[/C][C]15716.2775713218[/C][C]-230.27757132176[/C][/ROW]
[ROW][C]31[/C][C]15986[/C][C]15650.9024635905[/C][C]335.097536409534[/C][/ROW]
[ROW][C]32[/C][C]15983[/C][C]15746.0356431595[/C][C]236.964356840541[/C][/ROW]
[ROW][C]33[/C][C]15692[/C][C]15813.3091091249[/C][C]-121.309109124935[/C][/ROW]
[ROW][C]34[/C][C]16490[/C][C]15778.8698190442[/C][C]711.130180955768[/C][/ROW]
[ROW][C]35[/C][C]15686[/C][C]15980.7575318775[/C][C]-294.757531877533[/C][/ROW]
[ROW][C]36[/C][C]18897[/C][C]15897.076757886[/C][C]2999.92324211404[/C][/ROW]
[ROW][C]37[/C][C]16316[/C][C]16748.7459152994[/C][C]-432.745915299402[/C][/ROW]
[ROW][C]38[/C][C]15636[/C][C]16625.890655577[/C][C]-989.890655577015[/C][/ROW]
[ROW][C]39[/C][C]17163[/C][C]16344.8636850427[/C][C]818.136314957275[/C][/ROW]
[ROW][C]40[/C][C]16534[/C][C]16577.1301164725[/C][C]-43.1301164724755[/C][/ROW]
[ROW][C]41[/C][C]16518[/C][C]16564.8856065332[/C][C]-46.8856065331565[/C][/ROW]
[ROW][C]42[/C][C]16375[/C][C]16551.5749242962[/C][C]-176.574924296241[/C][/ROW]
[ROW][C]43[/C][C]16290[/C][C]16501.4458360301[/C][C]-211.445836030056[/C][/ROW]
[ROW][C]44[/C][C]16352[/C][C]16441.4170011311[/C][C]-89.4170011311362[/C][/ROW]
[ROW][C]45[/C][C]15943[/C][C]16416.0317842887[/C][C]-473.03178428868[/C][/ROW]
[ROW][C]46[/C][C]16362[/C][C]16281.7394879061[/C][C]80.2605120938824[/C][/ROW]
[ROW][C]47[/C][C]16393[/C][C]16304.5252051368[/C][C]88.4747948631975[/C][/ROW]
[ROW][C]48[/C][C]19051[/C][C]16329.6429324625[/C][C]2721.35706753749[/C][/ROW]
[ROW][C]49[/C][C]16747[/C][C]17102.2279933714[/C][C]-355.227993371427[/C][/ROW]
[ROW][C]50[/C][C]16320[/C][C]17001.3798378062[/C][C]-681.379837806249[/C][/ROW]
[ROW][C]51[/C][C]17910[/C][C]16807.9381576338[/C][C]1102.06184236621[/C][/ROW]
[ROW][C]52[/C][C]16961[/C][C]17120.8101896676[/C][C]-159.810189667551[/C][/ROW]
[ROW][C]53[/C][C]17480[/C][C]17075.4405589818[/C][C]404.559441018177[/C][/ROW]
[ROW][C]54[/C][C]17049[/C][C]17190.2937636968[/C][C]-141.293763696754[/C][/ROW]
[ROW][C]55[/C][C]16879[/C][C]17150.1808904785[/C][C]-271.18089047851[/C][/ROW]
[ROW][C]56[/C][C]17473[/C][C]17073.1934538474[/C][C]399.806546152602[/C][/ROW]
[ROW][C]57[/C][C]16998[/C][C]17186.6973260499[/C][C]-188.697326049878[/C][/ROW]
[ROW][C]58[/C][C]17307[/C][C]17133.1267245001[/C][C]173.873275499853[/C][/ROW]
[ROW][C]59[/C][C]17418[/C][C]17182.4888228241[/C][C]235.511177175857[/C][/ROW]
[ROW][C]60[/C][C]20169[/C][C]17249.3497354672[/C][C]2919.65026453282[/C][/ROW]
[ROW][C]61[/C][C]17871[/C][C]18078.2296367357[/C][C]-207.22963673569[/C][/ROW]
[ROW][C]62[/C][C]17226[/C][C]18019.3977680958[/C][C]-793.397768095809[/C][/ROW]
[ROW][C]63[/C][C]19062[/C][C]17794.1545354817[/C][C]1267.84546451826[/C][/ROW]
[ROW][C]64[/C][C]17804[/C][C]18154.0920376612[/C][C]-350.092037661223[/C][/ROW]
[ROW][C]65[/C][C]19100[/C][C]18054.7019644266[/C][C]1045.29803557344[/C][/ROW]
[ROW][C]66[/C][C]18522[/C][C]18351.4589229731[/C][C]170.54107702693[/C][/ROW]
[ROW][C]67[/C][C]18060[/C][C]18399.8750202041[/C][C]-339.87502020413[/C][/ROW]
[ROW][C]68[/C][C]18869[/C][C]18303.3855273999[/C][C]565.614472600075[/C][/ROW]
[ROW][C]69[/C][C]18127[/C][C]18463.9617696643[/C][C]-336.961769664274[/C][/ROW]
[ROW][C]70[/C][C]18871[/C][C]18368.2993398988[/C][C]502.700660101189[/C][/ROW]
[ROW][C]71[/C][C]18890[/C][C]18511.014540611[/C][C]378.985459388969[/C][/ROW]
[ROW][C]72[/C][C]21263[/C][C]18618.6073691003[/C][C]2644.3926308997[/C][/ROW]
[ROW][C]73[/C][C]19547[/C][C]19369.342458656[/C][C]177.657541344019[/C][/ROW]
[ROW][C]74[/C][C]18450[/C][C]19419.7788986357[/C][C]-969.778898635686[/C][/ROW]
[ROW][C]75[/C][C]20254[/C][C]19144.4615952182[/C][C]1109.53840478184[/C][/ROW]
[ROW][C]76[/C][C]19240[/C][C]19459.4562007643[/C][C]-219.4562007643[/C][/ROW]
[ROW][C]77[/C][C]20216[/C][C]19397.1532474853[/C][C]818.846752514721[/C][/ROW]
[ROW][C]78[/C][C]19420[/C][C]19629.6213699941[/C][C]-209.62136999414[/C][/ROW]
[ROW][C]79[/C][C]19415[/C][C]19570.1104954982[/C][C]-155.110495498247[/C][/ROW]
[ROW][C]80[/C][C]20018[/C][C]19526.0750938078[/C][C]491.924906192191[/C][/ROW]
[ROW][C]81[/C][C]18652[/C][C]19665.7310904966[/C][C]-1013.73109049663[/C][/ROW]
[ROW][C]82[/C][C]19978[/C][C]19377.9358924173[/C][C]600.064107582726[/C][/ROW]
[ROW][C]83[/C][C]19509[/C][C]19548.2922821157[/C][C]-39.2922821157263[/C][/ROW]
[ROW][C]84[/C][C]21971[/C][C]19537.1373217712[/C][C]2433.86267822878[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=289960&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=289960&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
21287313328-455
31400013198.8268727736801.173127226426
41347713426.277506385950.7224936140883
51423713440.6774692889796.322530711112
61367413666.75103318527.24896681480823
71352913668.8089929932-139.80899299317
81405813629.117641698428.882358302006
91297513750.8760492455-775.8760492455
101432613530.6071797485795.392820251482
111400813756.4168016503251.583198349654
121619313827.8405126142365.15948738602
131448314499.3021551962-16.3021551961901
141401114494.674022521-483.674022520976
151505714357.3604268128699.6395731872
161488414555.9859907687328.014009231258
171541414649.1081783434764.891821656576
181444014866.2586587683-426.258658768256
191490014745.2451116025154.754888397543
201507414789.1795575099284.820442490098
211444214870.0392218054-428.03922180542
221530714748.5201781655558.47982183452
231493814907.070914603330.9290853966668
241719314915.85158863182277.14841136823
251552815562.3271522694-34.3271522694122
261476515552.5817773081-787.581777308054
271583815328.9896869313509.010313068713
281572315473.4961790842249.503820915772
291615015544.329561068605.670438931964
301548615716.2775713218-230.27757132176
311598615650.9024635905335.097536409534
321598315746.0356431595236.964356840541
331569215813.3091091249-121.309109124935
341649015778.8698190442711.130180955768
351568615980.7575318775-294.757531877533
361889715897.0767578862999.92324211404
371631616748.7459152994-432.745915299402
381563616625.890655577-989.890655577015
391716316344.8636850427818.136314957275
401653416577.1301164725-43.1301164724755
411651816564.8856065332-46.8856065331565
421637516551.5749242962-176.574924296241
431629016501.4458360301-211.445836030056
441635216441.4170011311-89.4170011311362
451594316416.0317842887-473.03178428868
461636216281.739487906180.2605120938824
471639316304.525205136888.4747948631975
481905116329.64293246252721.35706753749
491674717102.2279933714-355.227993371427
501632017001.3798378062-681.379837806249
511791016807.93815763381102.06184236621
521696117120.8101896676-159.810189667551
531748017075.4405589818404.559441018177
541704917190.2937636968-141.293763696754
551687917150.1808904785-271.18089047851
561747317073.1934538474399.806546152602
571699817186.6973260499-188.697326049878
581730717133.1267245001173.873275499853
591741817182.4888228241235.511177175857
602016917249.34973546722919.65026453282
611787118078.2296367357-207.22963673569
621722618019.3977680958-793.397768095809
631906217794.15453548171267.84546451826
641780418154.0920376612-350.092037661223
651910018054.70196442661045.29803557344
661852218351.4589229731170.54107702693
671806018399.8750202041-339.87502020413
681886918303.3855273999565.614472600075
691812718463.9617696643-336.961769664274
701887118368.2993398988502.700660101189
711889018511.014540611378.985459388969
722126318618.60736910032644.3926308997
731954719369.342458656177.657541344019
741845019419.7788986357-969.778898635686
752025419144.46159521821109.53840478184
761924019459.4562007643-219.4562007643
772021619397.1532474853818.846752514721
781942019629.6213699941-209.62136999414
791941519570.1104954982-155.110495498247
802001819526.0750938078491.924906192191
811865219665.7310904966-1013.73109049663
821997819377.9358924173600.064107582726
831950919548.2922821157-39.2922821157263
842197119537.13732177122433.86267822878







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
8520228.103592950318517.598846209421938.6083396913
8620228.103592950318450.00326394922006.2039219516
8720228.103592950318384.884921341922071.3222645587
8820228.103592950318321.989912516522134.2172733842
8920228.103592950318261.104951845522195.1022340552
9020228.103592950318202.048819386822254.1583665139
9120228.103592950318144.665992048722311.541193852
9220228.103592950318088.821814356922367.3853715438
9320228.103592950318034.398776984222421.8084089165
9420228.103592950317981.293607445422474.9135784552
9520228.103592950317929.414966290422526.7922196103
9620228.103592950317878.681601543322577.5255843574

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
85 & 20228.1035929503 & 18517.5988462094 & 21938.6083396913 \tabularnewline
86 & 20228.1035929503 & 18450.003263949 & 22006.2039219516 \tabularnewline
87 & 20228.1035929503 & 18384.8849213419 & 22071.3222645587 \tabularnewline
88 & 20228.1035929503 & 18321.9899125165 & 22134.2172733842 \tabularnewline
89 & 20228.1035929503 & 18261.1049518455 & 22195.1022340552 \tabularnewline
90 & 20228.1035929503 & 18202.0488193868 & 22254.1583665139 \tabularnewline
91 & 20228.1035929503 & 18144.6659920487 & 22311.541193852 \tabularnewline
92 & 20228.1035929503 & 18088.8218143569 & 22367.3853715438 \tabularnewline
93 & 20228.1035929503 & 18034.3987769842 & 22421.8084089165 \tabularnewline
94 & 20228.1035929503 & 17981.2936074454 & 22474.9135784552 \tabularnewline
95 & 20228.1035929503 & 17929.4149662904 & 22526.7922196103 \tabularnewline
96 & 20228.1035929503 & 17878.6816015433 & 22577.5255843574 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=289960&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]85[/C][C]20228.1035929503[/C][C]18517.5988462094[/C][C]21938.6083396913[/C][/ROW]
[ROW][C]86[/C][C]20228.1035929503[/C][C]18450.003263949[/C][C]22006.2039219516[/C][/ROW]
[ROW][C]87[/C][C]20228.1035929503[/C][C]18384.8849213419[/C][C]22071.3222645587[/C][/ROW]
[ROW][C]88[/C][C]20228.1035929503[/C][C]18321.9899125165[/C][C]22134.2172733842[/C][/ROW]
[ROW][C]89[/C][C]20228.1035929503[/C][C]18261.1049518455[/C][C]22195.1022340552[/C][/ROW]
[ROW][C]90[/C][C]20228.1035929503[/C][C]18202.0488193868[/C][C]22254.1583665139[/C][/ROW]
[ROW][C]91[/C][C]20228.1035929503[/C][C]18144.6659920487[/C][C]22311.541193852[/C][/ROW]
[ROW][C]92[/C][C]20228.1035929503[/C][C]18088.8218143569[/C][C]22367.3853715438[/C][/ROW]
[ROW][C]93[/C][C]20228.1035929503[/C][C]18034.3987769842[/C][C]22421.8084089165[/C][/ROW]
[ROW][C]94[/C][C]20228.1035929503[/C][C]17981.2936074454[/C][C]22474.9135784552[/C][/ROW]
[ROW][C]95[/C][C]20228.1035929503[/C][C]17929.4149662904[/C][C]22526.7922196103[/C][/ROW]
[ROW][C]96[/C][C]20228.1035929503[/C][C]17878.6816015433[/C][C]22577.5255843574[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=289960&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=289960&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
8520228.103592950318517.598846209421938.6083396913
8620228.103592950318450.00326394922006.2039219516
8720228.103592950318384.884921341922071.3222645587
8820228.103592950318321.989912516522134.2172733842
8920228.103592950318261.104951845522195.1022340552
9020228.103592950318202.048819386822254.1583665139
9120228.103592950318144.665992048722311.541193852
9220228.103592950318088.821814356922367.3853715438
9320228.103592950318034.398776984222421.8084089165
9420228.103592950317981.293607445422474.9135784552
9520228.103592950317929.414966290422526.7922196103
9620228.103592950317878.681601543322577.5255843574



Parameters (Session):
par1 = 5 ; par2 = grey ; par3 = FALSE ; par4 = Unknown ;
Parameters (R input):
par1 = 12 ; par2 = Single ; 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')