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of Irreproducible Research!

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, 01 Dec 2011 17:12:13 -0500
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2011/Dec/01/t1322777596ptg3xuuuzx5ctrc.htm/, Retrieved Fri, 26 Apr 2024 13:55:25 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=150013, Retrieved Fri, 26 Apr 2024 13:55:25 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact93
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [Workshop 8 Questi...] [2011-12-01 22:12:13] [02ed7fa8d7b1f39a2d911dce6cf09d8a] [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'AstonUniversity' @ aston.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 & 'AstonUniversity' @ aston.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=150013&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]'AstonUniversity' @ aston.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=150013&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=150013&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'AstonUniversity' @ aston.wessa.net







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.283896982917142
betaFALSE
gammaFALSE

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.283896982917142 \tabularnewline
beta & FALSE \tabularnewline
gamma & FALSE \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=150013&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]0.283896982917142[/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=150013&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=150013&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
alpha0.283896982917142
betaFALSE
gammaFALSE







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
21287313328-455
31400013198.8268727727801.1731272273
41347713426.277506386850.722493613177
51423713440.6774692896796.322530710362
61367413666.75103318737.24896681274731
71352913668.8089929947-139.808992994658
81405813629.1176416988428.882358301209
91297513750.8760492469-775.876049246894
101432613530.607179748795.392820251971
111400813756.4168016515251.58319834848
121619313827.84051261532365.1594873847
131448314499.3021552017-16.3021552016689
141401114494.6740225249-483.674022524869
151505714357.3604268147699.639573185339
161488414555.9859907714328.014009228584
171541414649.108178346764.891821654033
181444014866.2586587715-426.258658771543
191490014745.245111604154.754888396006
201507414789.1795575113284.820442488701
211444214870.039221807-428.039221806966
221530714748.5201781658558.479821834233
231493814907.070914604630.9290853953917
241719314915.85158863272277.14841136725
251552815562.3271522745-34.3271522744726
261476515552.5817773116-787.581777311612
271583815328.9896869323509.010313067674
281572315473.4961790859249.503820914051
291615015544.3295610697605.670438930252
301548615716.2775713241-230.277571324148
311598615650.9024635917335.097536408264
321598315746.035643161236.964356838991
331569215813.3091091265-121.3091091265
341649015778.8698190451711.13018095488
351568615980.7575318795-294.757531879532
361889715897.07675788682999.92324211317
371631616748.7459153058-432.745915305768
381563616625.8906555807-989.890655580744
391716316344.8636850435818.1363149565
401653416577.1301164746-43.1301164746001
411651816564.8856065346-46.8856065345972
421637516551.5749242972-176.574924297183
431629016501.4458360304-211.445836030391
441635216441.417001131-89.4170011309689
451594316416.0317842884-473.031784288389
461636216281.73948790580.2605120949975
471639316304.525205136288.4747948638433
481905116329.64293246222721.35706753779
491674717102.2279933764-355.227993376433
501632017001.3798378092-681.379837809152
511791016807.93815763461102.06184236544
521696117120.8101896702-159.810189670217
531748017075.4405589834404.559441016572
541704917190.2937636987-141.293763698679
551687917150.1808904796-271.180890479616
561747317073.1934538477399.806546152329
571699817186.6973260508-188.697326050838
581730717133.1267245005173.873275499525
591741817182.4888228247235.511177175289
602016917249.3497354682919.65026453196
611787118078.2296367419-207.2296367419
621722618019.3977680999-793.397768099858
631906217794.15453548311267.84546451689
641780418154.0920376646-350.092037664639
651910018054.70196442831045.29803557167
661852218351.4589229763170.541077023656
671806018399.8750202068-339.8750202068
681886918303.3855274012565.614472598812
691812718463.9617696663-336.961769666261
701887118368.2993398996502.70066010041
711889018511.0145406126378.985459387448
722126318618.60736910212644.39263089788
731954719369.3424586623177.657541337652
741845019419.7788986406-969.778898640583
752025419144.46159521981109.53840478019
761924019459.4562007676-219.456200767607
772021619397.1532474872818.846752512774
781942019629.6213699971-209.621369997101
791941519570.1104955-155.110495499965
802001819526.0750938087491.92490619126
811865219665.7310904982-1013.73109049824
821997819377.9358924165600.064107583516
831950919548.2922821163-39.292282116312
842197119537.13732177162433.86267822844

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
2 & 12873 & 13328 & -455 \tabularnewline
3 & 14000 & 13198.8268727727 & 801.1731272273 \tabularnewline
4 & 13477 & 13426.2775063868 & 50.722493613177 \tabularnewline
5 & 14237 & 13440.6774692896 & 796.322530710362 \tabularnewline
6 & 13674 & 13666.7510331873 & 7.24896681274731 \tabularnewline
7 & 13529 & 13668.8089929947 & -139.808992994658 \tabularnewline
8 & 14058 & 13629.1176416988 & 428.882358301209 \tabularnewline
9 & 12975 & 13750.8760492469 & -775.876049246894 \tabularnewline
10 & 14326 & 13530.607179748 & 795.392820251971 \tabularnewline
11 & 14008 & 13756.4168016515 & 251.58319834848 \tabularnewline
12 & 16193 & 13827.8405126153 & 2365.1594873847 \tabularnewline
13 & 14483 & 14499.3021552017 & -16.3021552016689 \tabularnewline
14 & 14011 & 14494.6740225249 & -483.674022524869 \tabularnewline
15 & 15057 & 14357.3604268147 & 699.639573185339 \tabularnewline
16 & 14884 & 14555.9859907714 & 328.014009228584 \tabularnewline
17 & 15414 & 14649.108178346 & 764.891821654033 \tabularnewline
18 & 14440 & 14866.2586587715 & -426.258658771543 \tabularnewline
19 & 14900 & 14745.245111604 & 154.754888396006 \tabularnewline
20 & 15074 & 14789.1795575113 & 284.820442488701 \tabularnewline
21 & 14442 & 14870.039221807 & -428.039221806966 \tabularnewline
22 & 15307 & 14748.5201781658 & 558.479821834233 \tabularnewline
23 & 14938 & 14907.0709146046 & 30.9290853953917 \tabularnewline
24 & 17193 & 14915.8515886327 & 2277.14841136725 \tabularnewline
25 & 15528 & 15562.3271522745 & -34.3271522744726 \tabularnewline
26 & 14765 & 15552.5817773116 & -787.581777311612 \tabularnewline
27 & 15838 & 15328.9896869323 & 509.010313067674 \tabularnewline
28 & 15723 & 15473.4961790859 & 249.503820914051 \tabularnewline
29 & 16150 & 15544.3295610697 & 605.670438930252 \tabularnewline
30 & 15486 & 15716.2775713241 & -230.277571324148 \tabularnewline
31 & 15986 & 15650.9024635917 & 335.097536408264 \tabularnewline
32 & 15983 & 15746.035643161 & 236.964356838991 \tabularnewline
33 & 15692 & 15813.3091091265 & -121.3091091265 \tabularnewline
34 & 16490 & 15778.8698190451 & 711.13018095488 \tabularnewline
35 & 15686 & 15980.7575318795 & -294.757531879532 \tabularnewline
36 & 18897 & 15897.0767578868 & 2999.92324211317 \tabularnewline
37 & 16316 & 16748.7459153058 & -432.745915305768 \tabularnewline
38 & 15636 & 16625.8906555807 & -989.890655580744 \tabularnewline
39 & 17163 & 16344.8636850435 & 818.1363149565 \tabularnewline
40 & 16534 & 16577.1301164746 & -43.1301164746001 \tabularnewline
41 & 16518 & 16564.8856065346 & -46.8856065345972 \tabularnewline
42 & 16375 & 16551.5749242972 & -176.574924297183 \tabularnewline
43 & 16290 & 16501.4458360304 & -211.445836030391 \tabularnewline
44 & 16352 & 16441.417001131 & -89.4170011309689 \tabularnewline
45 & 15943 & 16416.0317842884 & -473.031784288389 \tabularnewline
46 & 16362 & 16281.739487905 & 80.2605120949975 \tabularnewline
47 & 16393 & 16304.5252051362 & 88.4747948638433 \tabularnewline
48 & 19051 & 16329.6429324622 & 2721.35706753779 \tabularnewline
49 & 16747 & 17102.2279933764 & -355.227993376433 \tabularnewline
50 & 16320 & 17001.3798378092 & -681.379837809152 \tabularnewline
51 & 17910 & 16807.9381576346 & 1102.06184236544 \tabularnewline
52 & 16961 & 17120.8101896702 & -159.810189670217 \tabularnewline
53 & 17480 & 17075.4405589834 & 404.559441016572 \tabularnewline
54 & 17049 & 17190.2937636987 & -141.293763698679 \tabularnewline
55 & 16879 & 17150.1808904796 & -271.180890479616 \tabularnewline
56 & 17473 & 17073.1934538477 & 399.806546152329 \tabularnewline
57 & 16998 & 17186.6973260508 & -188.697326050838 \tabularnewline
58 & 17307 & 17133.1267245005 & 173.873275499525 \tabularnewline
59 & 17418 & 17182.4888228247 & 235.511177175289 \tabularnewline
60 & 20169 & 17249.349735468 & 2919.65026453196 \tabularnewline
61 & 17871 & 18078.2296367419 & -207.2296367419 \tabularnewline
62 & 17226 & 18019.3977680999 & -793.397768099858 \tabularnewline
63 & 19062 & 17794.1545354831 & 1267.84546451689 \tabularnewline
64 & 17804 & 18154.0920376646 & -350.092037664639 \tabularnewline
65 & 19100 & 18054.7019644283 & 1045.29803557167 \tabularnewline
66 & 18522 & 18351.4589229763 & 170.541077023656 \tabularnewline
67 & 18060 & 18399.8750202068 & -339.8750202068 \tabularnewline
68 & 18869 & 18303.3855274012 & 565.614472598812 \tabularnewline
69 & 18127 & 18463.9617696663 & -336.961769666261 \tabularnewline
70 & 18871 & 18368.2993398996 & 502.70066010041 \tabularnewline
71 & 18890 & 18511.0145406126 & 378.985459387448 \tabularnewline
72 & 21263 & 18618.6073691021 & 2644.39263089788 \tabularnewline
73 & 19547 & 19369.3424586623 & 177.657541337652 \tabularnewline
74 & 18450 & 19419.7788986406 & -969.778898640583 \tabularnewline
75 & 20254 & 19144.4615952198 & 1109.53840478019 \tabularnewline
76 & 19240 & 19459.4562007676 & -219.456200767607 \tabularnewline
77 & 20216 & 19397.1532474872 & 818.846752512774 \tabularnewline
78 & 19420 & 19629.6213699971 & -209.621369997101 \tabularnewline
79 & 19415 & 19570.1104955 & -155.110495499965 \tabularnewline
80 & 20018 & 19526.0750938087 & 491.92490619126 \tabularnewline
81 & 18652 & 19665.7310904982 & -1013.73109049824 \tabularnewline
82 & 19978 & 19377.9358924165 & 600.064107583516 \tabularnewline
83 & 19509 & 19548.2922821163 & -39.292282116312 \tabularnewline
84 & 21971 & 19537.1373217716 & 2433.86267822844 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=150013&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]13198.8268727727[/C][C]801.1731272273[/C][/ROW]
[ROW][C]4[/C][C]13477[/C][C]13426.2775063868[/C][C]50.722493613177[/C][/ROW]
[ROW][C]5[/C][C]14237[/C][C]13440.6774692896[/C][C]796.322530710362[/C][/ROW]
[ROW][C]6[/C][C]13674[/C][C]13666.7510331873[/C][C]7.24896681274731[/C][/ROW]
[ROW][C]7[/C][C]13529[/C][C]13668.8089929947[/C][C]-139.808992994658[/C][/ROW]
[ROW][C]8[/C][C]14058[/C][C]13629.1176416988[/C][C]428.882358301209[/C][/ROW]
[ROW][C]9[/C][C]12975[/C][C]13750.8760492469[/C][C]-775.876049246894[/C][/ROW]
[ROW][C]10[/C][C]14326[/C][C]13530.607179748[/C][C]795.392820251971[/C][/ROW]
[ROW][C]11[/C][C]14008[/C][C]13756.4168016515[/C][C]251.58319834848[/C][/ROW]
[ROW][C]12[/C][C]16193[/C][C]13827.8405126153[/C][C]2365.1594873847[/C][/ROW]
[ROW][C]13[/C][C]14483[/C][C]14499.3021552017[/C][C]-16.3021552016689[/C][/ROW]
[ROW][C]14[/C][C]14011[/C][C]14494.6740225249[/C][C]-483.674022524869[/C][/ROW]
[ROW][C]15[/C][C]15057[/C][C]14357.3604268147[/C][C]699.639573185339[/C][/ROW]
[ROW][C]16[/C][C]14884[/C][C]14555.9859907714[/C][C]328.014009228584[/C][/ROW]
[ROW][C]17[/C][C]15414[/C][C]14649.108178346[/C][C]764.891821654033[/C][/ROW]
[ROW][C]18[/C][C]14440[/C][C]14866.2586587715[/C][C]-426.258658771543[/C][/ROW]
[ROW][C]19[/C][C]14900[/C][C]14745.245111604[/C][C]154.754888396006[/C][/ROW]
[ROW][C]20[/C][C]15074[/C][C]14789.1795575113[/C][C]284.820442488701[/C][/ROW]
[ROW][C]21[/C][C]14442[/C][C]14870.039221807[/C][C]-428.039221806966[/C][/ROW]
[ROW][C]22[/C][C]15307[/C][C]14748.5201781658[/C][C]558.479821834233[/C][/ROW]
[ROW][C]23[/C][C]14938[/C][C]14907.0709146046[/C][C]30.9290853953917[/C][/ROW]
[ROW][C]24[/C][C]17193[/C][C]14915.8515886327[/C][C]2277.14841136725[/C][/ROW]
[ROW][C]25[/C][C]15528[/C][C]15562.3271522745[/C][C]-34.3271522744726[/C][/ROW]
[ROW][C]26[/C][C]14765[/C][C]15552.5817773116[/C][C]-787.581777311612[/C][/ROW]
[ROW][C]27[/C][C]15838[/C][C]15328.9896869323[/C][C]509.010313067674[/C][/ROW]
[ROW][C]28[/C][C]15723[/C][C]15473.4961790859[/C][C]249.503820914051[/C][/ROW]
[ROW][C]29[/C][C]16150[/C][C]15544.3295610697[/C][C]605.670438930252[/C][/ROW]
[ROW][C]30[/C][C]15486[/C][C]15716.2775713241[/C][C]-230.277571324148[/C][/ROW]
[ROW][C]31[/C][C]15986[/C][C]15650.9024635917[/C][C]335.097536408264[/C][/ROW]
[ROW][C]32[/C][C]15983[/C][C]15746.035643161[/C][C]236.964356838991[/C][/ROW]
[ROW][C]33[/C][C]15692[/C][C]15813.3091091265[/C][C]-121.3091091265[/C][/ROW]
[ROW][C]34[/C][C]16490[/C][C]15778.8698190451[/C][C]711.13018095488[/C][/ROW]
[ROW][C]35[/C][C]15686[/C][C]15980.7575318795[/C][C]-294.757531879532[/C][/ROW]
[ROW][C]36[/C][C]18897[/C][C]15897.0767578868[/C][C]2999.92324211317[/C][/ROW]
[ROW][C]37[/C][C]16316[/C][C]16748.7459153058[/C][C]-432.745915305768[/C][/ROW]
[ROW][C]38[/C][C]15636[/C][C]16625.8906555807[/C][C]-989.890655580744[/C][/ROW]
[ROW][C]39[/C][C]17163[/C][C]16344.8636850435[/C][C]818.1363149565[/C][/ROW]
[ROW][C]40[/C][C]16534[/C][C]16577.1301164746[/C][C]-43.1301164746001[/C][/ROW]
[ROW][C]41[/C][C]16518[/C][C]16564.8856065346[/C][C]-46.8856065345972[/C][/ROW]
[ROW][C]42[/C][C]16375[/C][C]16551.5749242972[/C][C]-176.574924297183[/C][/ROW]
[ROW][C]43[/C][C]16290[/C][C]16501.4458360304[/C][C]-211.445836030391[/C][/ROW]
[ROW][C]44[/C][C]16352[/C][C]16441.417001131[/C][C]-89.4170011309689[/C][/ROW]
[ROW][C]45[/C][C]15943[/C][C]16416.0317842884[/C][C]-473.031784288389[/C][/ROW]
[ROW][C]46[/C][C]16362[/C][C]16281.739487905[/C][C]80.2605120949975[/C][/ROW]
[ROW][C]47[/C][C]16393[/C][C]16304.5252051362[/C][C]88.4747948638433[/C][/ROW]
[ROW][C]48[/C][C]19051[/C][C]16329.6429324622[/C][C]2721.35706753779[/C][/ROW]
[ROW][C]49[/C][C]16747[/C][C]17102.2279933764[/C][C]-355.227993376433[/C][/ROW]
[ROW][C]50[/C][C]16320[/C][C]17001.3798378092[/C][C]-681.379837809152[/C][/ROW]
[ROW][C]51[/C][C]17910[/C][C]16807.9381576346[/C][C]1102.06184236544[/C][/ROW]
[ROW][C]52[/C][C]16961[/C][C]17120.8101896702[/C][C]-159.810189670217[/C][/ROW]
[ROW][C]53[/C][C]17480[/C][C]17075.4405589834[/C][C]404.559441016572[/C][/ROW]
[ROW][C]54[/C][C]17049[/C][C]17190.2937636987[/C][C]-141.293763698679[/C][/ROW]
[ROW][C]55[/C][C]16879[/C][C]17150.1808904796[/C][C]-271.180890479616[/C][/ROW]
[ROW][C]56[/C][C]17473[/C][C]17073.1934538477[/C][C]399.806546152329[/C][/ROW]
[ROW][C]57[/C][C]16998[/C][C]17186.6973260508[/C][C]-188.697326050838[/C][/ROW]
[ROW][C]58[/C][C]17307[/C][C]17133.1267245005[/C][C]173.873275499525[/C][/ROW]
[ROW][C]59[/C][C]17418[/C][C]17182.4888228247[/C][C]235.511177175289[/C][/ROW]
[ROW][C]60[/C][C]20169[/C][C]17249.349735468[/C][C]2919.65026453196[/C][/ROW]
[ROW][C]61[/C][C]17871[/C][C]18078.2296367419[/C][C]-207.2296367419[/C][/ROW]
[ROW][C]62[/C][C]17226[/C][C]18019.3977680999[/C][C]-793.397768099858[/C][/ROW]
[ROW][C]63[/C][C]19062[/C][C]17794.1545354831[/C][C]1267.84546451689[/C][/ROW]
[ROW][C]64[/C][C]17804[/C][C]18154.0920376646[/C][C]-350.092037664639[/C][/ROW]
[ROW][C]65[/C][C]19100[/C][C]18054.7019644283[/C][C]1045.29803557167[/C][/ROW]
[ROW][C]66[/C][C]18522[/C][C]18351.4589229763[/C][C]170.541077023656[/C][/ROW]
[ROW][C]67[/C][C]18060[/C][C]18399.8750202068[/C][C]-339.8750202068[/C][/ROW]
[ROW][C]68[/C][C]18869[/C][C]18303.3855274012[/C][C]565.614472598812[/C][/ROW]
[ROW][C]69[/C][C]18127[/C][C]18463.9617696663[/C][C]-336.961769666261[/C][/ROW]
[ROW][C]70[/C][C]18871[/C][C]18368.2993398996[/C][C]502.70066010041[/C][/ROW]
[ROW][C]71[/C][C]18890[/C][C]18511.0145406126[/C][C]378.985459387448[/C][/ROW]
[ROW][C]72[/C][C]21263[/C][C]18618.6073691021[/C][C]2644.39263089788[/C][/ROW]
[ROW][C]73[/C][C]19547[/C][C]19369.3424586623[/C][C]177.657541337652[/C][/ROW]
[ROW][C]74[/C][C]18450[/C][C]19419.7788986406[/C][C]-969.778898640583[/C][/ROW]
[ROW][C]75[/C][C]20254[/C][C]19144.4615952198[/C][C]1109.53840478019[/C][/ROW]
[ROW][C]76[/C][C]19240[/C][C]19459.4562007676[/C][C]-219.456200767607[/C][/ROW]
[ROW][C]77[/C][C]20216[/C][C]19397.1532474872[/C][C]818.846752512774[/C][/ROW]
[ROW][C]78[/C][C]19420[/C][C]19629.6213699971[/C][C]-209.621369997101[/C][/ROW]
[ROW][C]79[/C][C]19415[/C][C]19570.1104955[/C][C]-155.110495499965[/C][/ROW]
[ROW][C]80[/C][C]20018[/C][C]19526.0750938087[/C][C]491.92490619126[/C][/ROW]
[ROW][C]81[/C][C]18652[/C][C]19665.7310904982[/C][C]-1013.73109049824[/C][/ROW]
[ROW][C]82[/C][C]19978[/C][C]19377.9358924165[/C][C]600.064107583516[/C][/ROW]
[ROW][C]83[/C][C]19509[/C][C]19548.2922821163[/C][C]-39.292282116312[/C][/ROW]
[ROW][C]84[/C][C]21971[/C][C]19537.1373217716[/C][C]2433.86267822844[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=150013&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=150013&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
31400013198.8268727727801.1731272273
41347713426.277506386850.722493613177
51423713440.6774692896796.322530710362
61367413666.75103318737.24896681274731
71352913668.8089929947-139.808992994658
81405813629.1176416988428.882358301209
91297513750.8760492469-775.876049246894
101432613530.607179748795.392820251971
111400813756.4168016515251.58319834848
121619313827.84051261532365.1594873847
131448314499.3021552017-16.3021552016689
141401114494.6740225249-483.674022524869
151505714357.3604268147699.639573185339
161488414555.9859907714328.014009228584
171541414649.108178346764.891821654033
181444014866.2586587715-426.258658771543
191490014745.245111604154.754888396006
201507414789.1795575113284.820442488701
211444214870.039221807-428.039221806966
221530714748.5201781658558.479821834233
231493814907.070914604630.9290853953917
241719314915.85158863272277.14841136725
251552815562.3271522745-34.3271522744726
261476515552.5817773116-787.581777311612
271583815328.9896869323509.010313067674
281572315473.4961790859249.503820914051
291615015544.3295610697605.670438930252
301548615716.2775713241-230.277571324148
311598615650.9024635917335.097536408264
321598315746.035643161236.964356838991
331569215813.3091091265-121.3091091265
341649015778.8698190451711.13018095488
351568615980.7575318795-294.757531879532
361889715897.07675788682999.92324211317
371631616748.7459153058-432.745915305768
381563616625.8906555807-989.890655580744
391716316344.8636850435818.1363149565
401653416577.1301164746-43.1301164746001
411651816564.8856065346-46.8856065345972
421637516551.5749242972-176.574924297183
431629016501.4458360304-211.445836030391
441635216441.417001131-89.4170011309689
451594316416.0317842884-473.031784288389
461636216281.73948790580.2605120949975
471639316304.525205136288.4747948638433
481905116329.64293246222721.35706753779
491674717102.2279933764-355.227993376433
501632017001.3798378092-681.379837809152
511791016807.93815763461102.06184236544
521696117120.8101896702-159.810189670217
531748017075.4405589834404.559441016572
541704917190.2937636987-141.293763698679
551687917150.1808904796-271.180890479616
561747317073.1934538477399.806546152329
571699817186.6973260508-188.697326050838
581730717133.1267245005173.873275499525
591741817182.4888228247235.511177175289
602016917249.3497354682919.65026453196
611787118078.2296367419-207.2296367419
621722618019.3977680999-793.397768099858
631906217794.15453548311267.84546451689
641780418154.0920376646-350.092037664639
651910018054.70196442831045.29803557167
661852218351.4589229763170.541077023656
671806018399.8750202068-339.8750202068
681886918303.3855274012565.614472598812
691812718463.9617696663-336.961769666261
701887118368.2993398996502.70066010041
711889018511.0145406126378.985459387448
722126318618.60736910212644.39263089788
731954719369.3424586623177.657541337652
741845019419.7788986406-969.778898640583
752025419144.46159521981109.53840478019
761924019459.4562007676-219.456200767607
772021619397.1532474872818.846752512774
781942019629.6213699971-209.621369997101
791941519570.1104955-155.110495499965
802001819526.0750938087491.92490619126
811865219665.7310904982-1013.73109049824
821997819377.9358924165600.064107583516
831950919548.2922821163-39.292282116312
842197119537.13732177162433.86267822844







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
8520228.103592955318517.598846213121938.6083396974
8620228.103592955318450.003263951822006.2039219587
8720228.103592955318384.884921343922071.3222645666
8820228.103592955318321.989912517622134.2172733929
8920228.103592955318261.104951845822195.1022340647
9020228.103592955318202.048819386422254.1583665241
9120228.103592955318144.665992047622311.5411938629
9220228.103592955318088.821814355122367.3853715554
9320228.103592955318034.398776981822421.8084089288
9420228.103592955317981.293607442422474.9135784681
9520228.103592955317929.414966286822526.7922196237
9620228.103592955317878.681601539222577.5255843713

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
85 & 20228.1035929553 & 18517.5988462131 & 21938.6083396974 \tabularnewline
86 & 20228.1035929553 & 18450.0032639518 & 22006.2039219587 \tabularnewline
87 & 20228.1035929553 & 18384.8849213439 & 22071.3222645666 \tabularnewline
88 & 20228.1035929553 & 18321.9899125176 & 22134.2172733929 \tabularnewline
89 & 20228.1035929553 & 18261.1049518458 & 22195.1022340647 \tabularnewline
90 & 20228.1035929553 & 18202.0488193864 & 22254.1583665241 \tabularnewline
91 & 20228.1035929553 & 18144.6659920476 & 22311.5411938629 \tabularnewline
92 & 20228.1035929553 & 18088.8218143551 & 22367.3853715554 \tabularnewline
93 & 20228.1035929553 & 18034.3987769818 & 22421.8084089288 \tabularnewline
94 & 20228.1035929553 & 17981.2936074424 & 22474.9135784681 \tabularnewline
95 & 20228.1035929553 & 17929.4149662868 & 22526.7922196237 \tabularnewline
96 & 20228.1035929553 & 17878.6816015392 & 22577.5255843713 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=150013&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]20228.1035929553[/C][C]18517.5988462131[/C][C]21938.6083396974[/C][/ROW]
[ROW][C]86[/C][C]20228.1035929553[/C][C]18450.0032639518[/C][C]22006.2039219587[/C][/ROW]
[ROW][C]87[/C][C]20228.1035929553[/C][C]18384.8849213439[/C][C]22071.3222645666[/C][/ROW]
[ROW][C]88[/C][C]20228.1035929553[/C][C]18321.9899125176[/C][C]22134.2172733929[/C][/ROW]
[ROW][C]89[/C][C]20228.1035929553[/C][C]18261.1049518458[/C][C]22195.1022340647[/C][/ROW]
[ROW][C]90[/C][C]20228.1035929553[/C][C]18202.0488193864[/C][C]22254.1583665241[/C][/ROW]
[ROW][C]91[/C][C]20228.1035929553[/C][C]18144.6659920476[/C][C]22311.5411938629[/C][/ROW]
[ROW][C]92[/C][C]20228.1035929553[/C][C]18088.8218143551[/C][C]22367.3853715554[/C][/ROW]
[ROW][C]93[/C][C]20228.1035929553[/C][C]18034.3987769818[/C][C]22421.8084089288[/C][/ROW]
[ROW][C]94[/C][C]20228.1035929553[/C][C]17981.2936074424[/C][C]22474.9135784681[/C][/ROW]
[ROW][C]95[/C][C]20228.1035929553[/C][C]17929.4149662868[/C][C]22526.7922196237[/C][/ROW]
[ROW][C]96[/C][C]20228.1035929553[/C][C]17878.6816015392[/C][C]22577.5255843713[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=150013&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=150013&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
8520228.103592955318517.598846213121938.6083396974
8620228.103592955318450.003263951822006.2039219587
8720228.103592955318384.884921343922071.3222645666
8820228.103592955318321.989912517622134.2172733929
8920228.103592955318261.104951845822195.1022340647
9020228.103592955318202.048819386422254.1583665241
9120228.103592955318144.665992047622311.5411938629
9220228.103592955318088.821814355122367.3853715554
9320228.103592955318034.398776981822421.8084089288
9420228.103592955317981.293607442422474.9135784681
9520228.103592955317929.414966286822526.7922196237
9620228.103592955317878.681601539222577.5255843713



Parameters (Session):
par1 = 12 ; par2 = Single ; par3 = additive ;
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')