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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 computationMon, 23 Jan 2017 09:48:04 +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/2017/Jan/23/t1485161328s1p1mwkfddnk53u.htm/, Retrieved Thu, 31 Oct 2024 23:53:47 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=304097, Retrieved Thu, 31 Oct 2024 23:53:47 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact87
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [ff] [2017-01-23 08:48:04] [60937726ec8f1328d8735dbe11c01121] [Current]
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Dataseries X:
3035
2552
2704
2554
2014
1655
1721
1524
1596
2074
2199
2512
2933
2889
2938
2497
1870
1726
1607
1545
1396
1787
2076
2837
2787
3891
3179
2011
1636
1580
1489
1300
1356
1653
2013
2823
3102
2294
2385
2444
1748
1554
1498
1361
1346
1564
1640
2293
2815
3137
2679
1969
1870
1633
1529
1366
1357
1570
1535
2491
3084
2605
2573
2143
1693
1504
1461
1354
1333
1492
1781
1915




Summary of computational transaction
Raw Input view raw input (R code)
Raw Outputview raw output of R engine
Computing time1 seconds
R ServerBig Analytics Cloud Computing Center

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input view raw input (R code)  \tabularnewline
Raw Outputview raw output of R engine  \tabularnewline
Computing time1 seconds \tabularnewline
R ServerBig Analytics Cloud Computing Center \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=304097&T=0

[TABLE]
[ROW]
Summary of computational transaction[/C][/ROW] [ROW]Raw Input[/C] view raw input (R code) [/C][/ROW] [ROW]Raw Output[/C]view raw output of R engine [/C][/ROW] [ROW]Computing time[/C]1 seconds[/C][/ROW] [ROW]R Server[/C]Big Analytics Cloud Computing Center[/C][/ROW] [/TABLE] Source: https://freestatistics.org/blog/index.php?pk=304097&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=304097&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 Input view raw input (R code)
Raw Outputview raw output of R engine
Computing time1 seconds
R ServerBig Analytics Cloud Computing Center







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.999933893038648
betaFALSE
gammaFALSE

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.999933893038648 \tabularnewline
beta & FALSE \tabularnewline
gamma & FALSE \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=304097&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]0.999933893038648[/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=304097&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=304097&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
alpha0.999933893038648
betaFALSE
gammaFALSE







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
225523035-483
327042552.03192966233151.968070337667
425542703.98995385265-149.989953852647
520142554.00991538008-540.009915380082
616552014.03569841461-359.035698414606
717211655.0237347590465.9762652409611
815241720.99563850958-196.995638509584
915961524.0130227830671.9869772169386
1020741595.99524115968478.004758840321
1121992073.96840055788125.031599442119
1225122198.99173454089313.008265459112
1329332511.97930797469421.020692025308
1428892932.97216760138-43.9721676013837
1529382889.0029068663848.9970931336156
1624972937.99676095106-440.996760951058
1718702497.02915295583-627.029152955832
1817261870.04145099198-144.041450991981
1916071726.00952214263-119.009522142634
2015451607.00786735788-62.0078673578807
2113961545.00409915169-149.004099151691
2217871396.00985020822390.990149791776
2320761786.97415282928289.025847170721
2428372075.98089337949761.019106620508
2527872836.94969133933-49.9496913393309
2638912787.003302022311103.99669797769
2731793890.92701813295-711.927018132954
2820113179.04706333187-1168.04706333187
2916362011.07721604207-375.077216042073
3015801636.02479521502-56.0247952150248
3114891580.00370362897-91.0037036289721
3213001489.00601597832-189.006015978319
3313561300.0124946133955.9875053866062
3416531355.99629883615297.003701163855
3520131652.98036598781360.019634012194
3628232012.97620019597810.023799804032
3731022822.94645178797279.053548212028
3822943101.98155261787-807.981552617873
3923852294.0534132052790.9465867947279
4024442384.993987797559.0060122024984
4117482443.99609929183-695.996099291832
4215541748.04601018724-194.046010187237
4314981554.0128277921-56.0128277920958
4413611498.00370283784-137.003702837842
4513461361.00905689849-15.0090568984886
4615641346.00099220314217.999007796856
4716401563.9855887480276.0144112519831
4822931639.99497491825653.005025081747
4928152292.95683182204522.043168177956
5031372814.96548931246322.034510687542
5126793136.97871127705-457.978711277048
5219692679.03027558097-710.030275580967
5318701969.04693794399-99.0469379439864
5416331870.0065476921-237.006547692099
5515291633.01566778269-104.015667782688
5613661529.00687615973-163.00687615973
5713571366.01077588926-9.01077588926228
5815701357.00059567501212.999404324986
5915351569.98591925661-34.9859192566105
6024911535.00231281281955.997687187188
6130842490.93680189784593.063198102159
6226053083.96079439408-478.960794394084
6325732605.03166264272-32.0316626427243
6421432573.00211751588-430.002117515884
6516932143.02842613336-450.028426133364
6615041693.02975001177-189.029750011774
6714611504.01249618238-43.0124961823783
6813541461.00284342542-107.002843425423
6913331354.00707363283-21.0070736328348
7014921333.0013887138158.998611286195
7117811491.98948908495289.010510915051
7219151780.98089439332134.019105606675

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
2 & 2552 & 3035 & -483 \tabularnewline
3 & 2704 & 2552.03192966233 & 151.968070337667 \tabularnewline
4 & 2554 & 2703.98995385265 & -149.989953852647 \tabularnewline
5 & 2014 & 2554.00991538008 & -540.009915380082 \tabularnewline
6 & 1655 & 2014.03569841461 & -359.035698414606 \tabularnewline
7 & 1721 & 1655.02373475904 & 65.9762652409611 \tabularnewline
8 & 1524 & 1720.99563850958 & -196.995638509584 \tabularnewline
9 & 1596 & 1524.01302278306 & 71.9869772169386 \tabularnewline
10 & 2074 & 1595.99524115968 & 478.004758840321 \tabularnewline
11 & 2199 & 2073.96840055788 & 125.031599442119 \tabularnewline
12 & 2512 & 2198.99173454089 & 313.008265459112 \tabularnewline
13 & 2933 & 2511.97930797469 & 421.020692025308 \tabularnewline
14 & 2889 & 2932.97216760138 & -43.9721676013837 \tabularnewline
15 & 2938 & 2889.00290686638 & 48.9970931336156 \tabularnewline
16 & 2497 & 2937.99676095106 & -440.996760951058 \tabularnewline
17 & 1870 & 2497.02915295583 & -627.029152955832 \tabularnewline
18 & 1726 & 1870.04145099198 & -144.041450991981 \tabularnewline
19 & 1607 & 1726.00952214263 & -119.009522142634 \tabularnewline
20 & 1545 & 1607.00786735788 & -62.0078673578807 \tabularnewline
21 & 1396 & 1545.00409915169 & -149.004099151691 \tabularnewline
22 & 1787 & 1396.00985020822 & 390.990149791776 \tabularnewline
23 & 2076 & 1786.97415282928 & 289.025847170721 \tabularnewline
24 & 2837 & 2075.98089337949 & 761.019106620508 \tabularnewline
25 & 2787 & 2836.94969133933 & -49.9496913393309 \tabularnewline
26 & 3891 & 2787.00330202231 & 1103.99669797769 \tabularnewline
27 & 3179 & 3890.92701813295 & -711.927018132954 \tabularnewline
28 & 2011 & 3179.04706333187 & -1168.04706333187 \tabularnewline
29 & 1636 & 2011.07721604207 & -375.077216042073 \tabularnewline
30 & 1580 & 1636.02479521502 & -56.0247952150248 \tabularnewline
31 & 1489 & 1580.00370362897 & -91.0037036289721 \tabularnewline
32 & 1300 & 1489.00601597832 & -189.006015978319 \tabularnewline
33 & 1356 & 1300.01249461339 & 55.9875053866062 \tabularnewline
34 & 1653 & 1355.99629883615 & 297.003701163855 \tabularnewline
35 & 2013 & 1652.98036598781 & 360.019634012194 \tabularnewline
36 & 2823 & 2012.97620019597 & 810.023799804032 \tabularnewline
37 & 3102 & 2822.94645178797 & 279.053548212028 \tabularnewline
38 & 2294 & 3101.98155261787 & -807.981552617873 \tabularnewline
39 & 2385 & 2294.05341320527 & 90.9465867947279 \tabularnewline
40 & 2444 & 2384.9939877975 & 59.0060122024984 \tabularnewline
41 & 1748 & 2443.99609929183 & -695.996099291832 \tabularnewline
42 & 1554 & 1748.04601018724 & -194.046010187237 \tabularnewline
43 & 1498 & 1554.0128277921 & -56.0128277920958 \tabularnewline
44 & 1361 & 1498.00370283784 & -137.003702837842 \tabularnewline
45 & 1346 & 1361.00905689849 & -15.0090568984886 \tabularnewline
46 & 1564 & 1346.00099220314 & 217.999007796856 \tabularnewline
47 & 1640 & 1563.98558874802 & 76.0144112519831 \tabularnewline
48 & 2293 & 1639.99497491825 & 653.005025081747 \tabularnewline
49 & 2815 & 2292.95683182204 & 522.043168177956 \tabularnewline
50 & 3137 & 2814.96548931246 & 322.034510687542 \tabularnewline
51 & 2679 & 3136.97871127705 & -457.978711277048 \tabularnewline
52 & 1969 & 2679.03027558097 & -710.030275580967 \tabularnewline
53 & 1870 & 1969.04693794399 & -99.0469379439864 \tabularnewline
54 & 1633 & 1870.0065476921 & -237.006547692099 \tabularnewline
55 & 1529 & 1633.01566778269 & -104.015667782688 \tabularnewline
56 & 1366 & 1529.00687615973 & -163.00687615973 \tabularnewline
57 & 1357 & 1366.01077588926 & -9.01077588926228 \tabularnewline
58 & 1570 & 1357.00059567501 & 212.999404324986 \tabularnewline
59 & 1535 & 1569.98591925661 & -34.9859192566105 \tabularnewline
60 & 2491 & 1535.00231281281 & 955.997687187188 \tabularnewline
61 & 3084 & 2490.93680189784 & 593.063198102159 \tabularnewline
62 & 2605 & 3083.96079439408 & -478.960794394084 \tabularnewline
63 & 2573 & 2605.03166264272 & -32.0316626427243 \tabularnewline
64 & 2143 & 2573.00211751588 & -430.002117515884 \tabularnewline
65 & 1693 & 2143.02842613336 & -450.028426133364 \tabularnewline
66 & 1504 & 1693.02975001177 & -189.029750011774 \tabularnewline
67 & 1461 & 1504.01249618238 & -43.0124961823783 \tabularnewline
68 & 1354 & 1461.00284342542 & -107.002843425423 \tabularnewline
69 & 1333 & 1354.00707363283 & -21.0070736328348 \tabularnewline
70 & 1492 & 1333.0013887138 & 158.998611286195 \tabularnewline
71 & 1781 & 1491.98948908495 & 289.010510915051 \tabularnewline
72 & 1915 & 1780.98089439332 & 134.019105606675 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=304097&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]2552[/C][C]3035[/C][C]-483[/C][/ROW]
[ROW][C]3[/C][C]2704[/C][C]2552.03192966233[/C][C]151.968070337667[/C][/ROW]
[ROW][C]4[/C][C]2554[/C][C]2703.98995385265[/C][C]-149.989953852647[/C][/ROW]
[ROW][C]5[/C][C]2014[/C][C]2554.00991538008[/C][C]-540.009915380082[/C][/ROW]
[ROW][C]6[/C][C]1655[/C][C]2014.03569841461[/C][C]-359.035698414606[/C][/ROW]
[ROW][C]7[/C][C]1721[/C][C]1655.02373475904[/C][C]65.9762652409611[/C][/ROW]
[ROW][C]8[/C][C]1524[/C][C]1720.99563850958[/C][C]-196.995638509584[/C][/ROW]
[ROW][C]9[/C][C]1596[/C][C]1524.01302278306[/C][C]71.9869772169386[/C][/ROW]
[ROW][C]10[/C][C]2074[/C][C]1595.99524115968[/C][C]478.004758840321[/C][/ROW]
[ROW][C]11[/C][C]2199[/C][C]2073.96840055788[/C][C]125.031599442119[/C][/ROW]
[ROW][C]12[/C][C]2512[/C][C]2198.99173454089[/C][C]313.008265459112[/C][/ROW]
[ROW][C]13[/C][C]2933[/C][C]2511.97930797469[/C][C]421.020692025308[/C][/ROW]
[ROW][C]14[/C][C]2889[/C][C]2932.97216760138[/C][C]-43.9721676013837[/C][/ROW]
[ROW][C]15[/C][C]2938[/C][C]2889.00290686638[/C][C]48.9970931336156[/C][/ROW]
[ROW][C]16[/C][C]2497[/C][C]2937.99676095106[/C][C]-440.996760951058[/C][/ROW]
[ROW][C]17[/C][C]1870[/C][C]2497.02915295583[/C][C]-627.029152955832[/C][/ROW]
[ROW][C]18[/C][C]1726[/C][C]1870.04145099198[/C][C]-144.041450991981[/C][/ROW]
[ROW][C]19[/C][C]1607[/C][C]1726.00952214263[/C][C]-119.009522142634[/C][/ROW]
[ROW][C]20[/C][C]1545[/C][C]1607.00786735788[/C][C]-62.0078673578807[/C][/ROW]
[ROW][C]21[/C][C]1396[/C][C]1545.00409915169[/C][C]-149.004099151691[/C][/ROW]
[ROW][C]22[/C][C]1787[/C][C]1396.00985020822[/C][C]390.990149791776[/C][/ROW]
[ROW][C]23[/C][C]2076[/C][C]1786.97415282928[/C][C]289.025847170721[/C][/ROW]
[ROW][C]24[/C][C]2837[/C][C]2075.98089337949[/C][C]761.019106620508[/C][/ROW]
[ROW][C]25[/C][C]2787[/C][C]2836.94969133933[/C][C]-49.9496913393309[/C][/ROW]
[ROW][C]26[/C][C]3891[/C][C]2787.00330202231[/C][C]1103.99669797769[/C][/ROW]
[ROW][C]27[/C][C]3179[/C][C]3890.92701813295[/C][C]-711.927018132954[/C][/ROW]
[ROW][C]28[/C][C]2011[/C][C]3179.04706333187[/C][C]-1168.04706333187[/C][/ROW]
[ROW][C]29[/C][C]1636[/C][C]2011.07721604207[/C][C]-375.077216042073[/C][/ROW]
[ROW][C]30[/C][C]1580[/C][C]1636.02479521502[/C][C]-56.0247952150248[/C][/ROW]
[ROW][C]31[/C][C]1489[/C][C]1580.00370362897[/C][C]-91.0037036289721[/C][/ROW]
[ROW][C]32[/C][C]1300[/C][C]1489.00601597832[/C][C]-189.006015978319[/C][/ROW]
[ROW][C]33[/C][C]1356[/C][C]1300.01249461339[/C][C]55.9875053866062[/C][/ROW]
[ROW][C]34[/C][C]1653[/C][C]1355.99629883615[/C][C]297.003701163855[/C][/ROW]
[ROW][C]35[/C][C]2013[/C][C]1652.98036598781[/C][C]360.019634012194[/C][/ROW]
[ROW][C]36[/C][C]2823[/C][C]2012.97620019597[/C][C]810.023799804032[/C][/ROW]
[ROW][C]37[/C][C]3102[/C][C]2822.94645178797[/C][C]279.053548212028[/C][/ROW]
[ROW][C]38[/C][C]2294[/C][C]3101.98155261787[/C][C]-807.981552617873[/C][/ROW]
[ROW][C]39[/C][C]2385[/C][C]2294.05341320527[/C][C]90.9465867947279[/C][/ROW]
[ROW][C]40[/C][C]2444[/C][C]2384.9939877975[/C][C]59.0060122024984[/C][/ROW]
[ROW][C]41[/C][C]1748[/C][C]2443.99609929183[/C][C]-695.996099291832[/C][/ROW]
[ROW][C]42[/C][C]1554[/C][C]1748.04601018724[/C][C]-194.046010187237[/C][/ROW]
[ROW][C]43[/C][C]1498[/C][C]1554.0128277921[/C][C]-56.0128277920958[/C][/ROW]
[ROW][C]44[/C][C]1361[/C][C]1498.00370283784[/C][C]-137.003702837842[/C][/ROW]
[ROW][C]45[/C][C]1346[/C][C]1361.00905689849[/C][C]-15.0090568984886[/C][/ROW]
[ROW][C]46[/C][C]1564[/C][C]1346.00099220314[/C][C]217.999007796856[/C][/ROW]
[ROW][C]47[/C][C]1640[/C][C]1563.98558874802[/C][C]76.0144112519831[/C][/ROW]
[ROW][C]48[/C][C]2293[/C][C]1639.99497491825[/C][C]653.005025081747[/C][/ROW]
[ROW][C]49[/C][C]2815[/C][C]2292.95683182204[/C][C]522.043168177956[/C][/ROW]
[ROW][C]50[/C][C]3137[/C][C]2814.96548931246[/C][C]322.034510687542[/C][/ROW]
[ROW][C]51[/C][C]2679[/C][C]3136.97871127705[/C][C]-457.978711277048[/C][/ROW]
[ROW][C]52[/C][C]1969[/C][C]2679.03027558097[/C][C]-710.030275580967[/C][/ROW]
[ROW][C]53[/C][C]1870[/C][C]1969.04693794399[/C][C]-99.0469379439864[/C][/ROW]
[ROW][C]54[/C][C]1633[/C][C]1870.0065476921[/C][C]-237.006547692099[/C][/ROW]
[ROW][C]55[/C][C]1529[/C][C]1633.01566778269[/C][C]-104.015667782688[/C][/ROW]
[ROW][C]56[/C][C]1366[/C][C]1529.00687615973[/C][C]-163.00687615973[/C][/ROW]
[ROW][C]57[/C][C]1357[/C][C]1366.01077588926[/C][C]-9.01077588926228[/C][/ROW]
[ROW][C]58[/C][C]1570[/C][C]1357.00059567501[/C][C]212.999404324986[/C][/ROW]
[ROW][C]59[/C][C]1535[/C][C]1569.98591925661[/C][C]-34.9859192566105[/C][/ROW]
[ROW][C]60[/C][C]2491[/C][C]1535.00231281281[/C][C]955.997687187188[/C][/ROW]
[ROW][C]61[/C][C]3084[/C][C]2490.93680189784[/C][C]593.063198102159[/C][/ROW]
[ROW][C]62[/C][C]2605[/C][C]3083.96079439408[/C][C]-478.960794394084[/C][/ROW]
[ROW][C]63[/C][C]2573[/C][C]2605.03166264272[/C][C]-32.0316626427243[/C][/ROW]
[ROW][C]64[/C][C]2143[/C][C]2573.00211751588[/C][C]-430.002117515884[/C][/ROW]
[ROW][C]65[/C][C]1693[/C][C]2143.02842613336[/C][C]-450.028426133364[/C][/ROW]
[ROW][C]66[/C][C]1504[/C][C]1693.02975001177[/C][C]-189.029750011774[/C][/ROW]
[ROW][C]67[/C][C]1461[/C][C]1504.01249618238[/C][C]-43.0124961823783[/C][/ROW]
[ROW][C]68[/C][C]1354[/C][C]1461.00284342542[/C][C]-107.002843425423[/C][/ROW]
[ROW][C]69[/C][C]1333[/C][C]1354.00707363283[/C][C]-21.0070736328348[/C][/ROW]
[ROW][C]70[/C][C]1492[/C][C]1333.0013887138[/C][C]158.998611286195[/C][/ROW]
[ROW][C]71[/C][C]1781[/C][C]1491.98948908495[/C][C]289.010510915051[/C][/ROW]
[ROW][C]72[/C][C]1915[/C][C]1780.98089439332[/C][C]134.019105606675[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=304097&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=304097&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
225523035-483
327042552.03192966233151.968070337667
425542703.98995385265-149.989953852647
520142554.00991538008-540.009915380082
616552014.03569841461-359.035698414606
717211655.0237347590465.9762652409611
815241720.99563850958-196.995638509584
915961524.0130227830671.9869772169386
1020741595.99524115968478.004758840321
1121992073.96840055788125.031599442119
1225122198.99173454089313.008265459112
1329332511.97930797469421.020692025308
1428892932.97216760138-43.9721676013837
1529382889.0029068663848.9970931336156
1624972937.99676095106-440.996760951058
1718702497.02915295583-627.029152955832
1817261870.04145099198-144.041450991981
1916071726.00952214263-119.009522142634
2015451607.00786735788-62.0078673578807
2113961545.00409915169-149.004099151691
2217871396.00985020822390.990149791776
2320761786.97415282928289.025847170721
2428372075.98089337949761.019106620508
2527872836.94969133933-49.9496913393309
2638912787.003302022311103.99669797769
2731793890.92701813295-711.927018132954
2820113179.04706333187-1168.04706333187
2916362011.07721604207-375.077216042073
3015801636.02479521502-56.0247952150248
3114891580.00370362897-91.0037036289721
3213001489.00601597832-189.006015978319
3313561300.0124946133955.9875053866062
3416531355.99629883615297.003701163855
3520131652.98036598781360.019634012194
3628232012.97620019597810.023799804032
3731022822.94645178797279.053548212028
3822943101.98155261787-807.981552617873
3923852294.0534132052790.9465867947279
4024442384.993987797559.0060122024984
4117482443.99609929183-695.996099291832
4215541748.04601018724-194.046010187237
4314981554.0128277921-56.0128277920958
4413611498.00370283784-137.003702837842
4513461361.00905689849-15.0090568984886
4615641346.00099220314217.999007796856
4716401563.9855887480276.0144112519831
4822931639.99497491825653.005025081747
4928152292.95683182204522.043168177956
5031372814.96548931246322.034510687542
5126793136.97871127705-457.978711277048
5219692679.03027558097-710.030275580967
5318701969.04693794399-99.0469379439864
5416331870.0065476921-237.006547692099
5515291633.01566778269-104.015667782688
5613661529.00687615973-163.00687615973
5713571366.01077588926-9.01077588926228
5815701357.00059567501212.999404324986
5915351569.98591925661-34.9859192566105
6024911535.00231281281955.997687187188
6130842490.93680189784593.063198102159
6226053083.96079439408-478.960794394084
6325732605.03166264272-32.0316626427243
6421432573.00211751588-430.002117515884
6516932143.02842613336-450.028426133364
6615041693.02975001177-189.029750011774
6714611504.01249618238-43.0124961823783
6813541461.00284342542-107.002843425423
6913331354.00707363283-21.0070736328348
7014921333.0013887138158.998611286195
7117811491.98948908495289.010510915051
7219151780.98089439332134.019105606675







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
731914.991140404171105.465380310722724.51690049761
741914.99114040417770.1866717873543059.79560902098
751914.99114040417512.9131873376583317.06909347067
761914.99114040417296.0198924861193533.96238832221
771914.99114040417104.9322417228373725.05003908549
781914.99114040417-67.8246684408253897.80694924916
791914.99114040417-226.6913400106514056.67362081898
801914.99114040417-374.5610345911784204.54331539951
811914.99114040417-513.4434329652844343.42571377361
821914.99114040417-644.801779393494474.78406020182
831914.99114040417-769.7407097731214599.72299058145
841914.99114040417-889.1184192362034719.10070004453

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
73 & 1914.99114040417 & 1105.46538031072 & 2724.51690049761 \tabularnewline
74 & 1914.99114040417 & 770.186671787354 & 3059.79560902098 \tabularnewline
75 & 1914.99114040417 & 512.913187337658 & 3317.06909347067 \tabularnewline
76 & 1914.99114040417 & 296.019892486119 & 3533.96238832221 \tabularnewline
77 & 1914.99114040417 & 104.932241722837 & 3725.05003908549 \tabularnewline
78 & 1914.99114040417 & -67.824668440825 & 3897.80694924916 \tabularnewline
79 & 1914.99114040417 & -226.691340010651 & 4056.67362081898 \tabularnewline
80 & 1914.99114040417 & -374.561034591178 & 4204.54331539951 \tabularnewline
81 & 1914.99114040417 & -513.443432965284 & 4343.42571377361 \tabularnewline
82 & 1914.99114040417 & -644.80177939349 & 4474.78406020182 \tabularnewline
83 & 1914.99114040417 & -769.740709773121 & 4599.72299058145 \tabularnewline
84 & 1914.99114040417 & -889.118419236203 & 4719.10070004453 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=304097&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]1914.99114040417[/C][C]1105.46538031072[/C][C]2724.51690049761[/C][/ROW]
[ROW][C]74[/C][C]1914.99114040417[/C][C]770.186671787354[/C][C]3059.79560902098[/C][/ROW]
[ROW][C]75[/C][C]1914.99114040417[/C][C]512.913187337658[/C][C]3317.06909347067[/C][/ROW]
[ROW][C]76[/C][C]1914.99114040417[/C][C]296.019892486119[/C][C]3533.96238832221[/C][/ROW]
[ROW][C]77[/C][C]1914.99114040417[/C][C]104.932241722837[/C][C]3725.05003908549[/C][/ROW]
[ROW][C]78[/C][C]1914.99114040417[/C][C]-67.824668440825[/C][C]3897.80694924916[/C][/ROW]
[ROW][C]79[/C][C]1914.99114040417[/C][C]-226.691340010651[/C][C]4056.67362081898[/C][/ROW]
[ROW][C]80[/C][C]1914.99114040417[/C][C]-374.561034591178[/C][C]4204.54331539951[/C][/ROW]
[ROW][C]81[/C][C]1914.99114040417[/C][C]-513.443432965284[/C][C]4343.42571377361[/C][/ROW]
[ROW][C]82[/C][C]1914.99114040417[/C][C]-644.80177939349[/C][C]4474.78406020182[/C][/ROW]
[ROW][C]83[/C][C]1914.99114040417[/C][C]-769.740709773121[/C][C]4599.72299058145[/C][/ROW]
[ROW][C]84[/C][C]1914.99114040417[/C][C]-889.118419236203[/C][C]4719.10070004453[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=304097&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=304097&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
731914.991140404171105.465380310722724.51690049761
741914.99114040417770.1866717873543059.79560902098
751914.99114040417512.9131873376583317.06909347067
761914.99114040417296.0198924861193533.96238832221
771914.99114040417104.9322417228373725.05003908549
781914.99114040417-67.8246684408253897.80694924916
791914.99114040417-226.6913400106514056.67362081898
801914.99114040417-374.5610345911784204.54331539951
811914.99114040417-513.4434329652844343.42571377361
821914.99114040417-644.801779393494474.78406020182
831914.99114040417-769.7407097731214599.72299058145
841914.99114040417-889.1184192362034719.10070004453



Parameters (Session):
Parameters (R input):
par1 = 12 ; par2 = Single ; par3 = additive ; par4 = 12 ;
R code (references can be found in the software module):
par1 <- as.numeric(par1)
par4 <- as.numeric(par4)
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$fitted[,'xhat']
bitmap(file='test1.png')
op <- par(mfrow=c(2,1))
plot(fit,ylab='Observed (black) / Fitted (red)',main='Interpolation Fit of Exponential Smoothing')
plot(myresid,ylab='Residuals',main='Interpolation Prediction Errors')
par(op)
dev.off()
bitmap(file='test2.png')
p <- predict(fit, par4, prediction.interval=TRUE)
np <- length(p[,1])
plot(fit,p,ylab='Observed (black) / Fitted (red)',main='Extrapolation Fit of Exponential Smoothing')
dev.off()
bitmap(file='test3.png')
op <- par(mfrow = c(2,2))
acf(as.numeric(myresid),lag.max = nx/2,main='Residual ACF')
spectrum(myresid,main='Residals Periodogram')
cpgram(myresid,main='Residal Cumulative Periodogram')
qqnorm(myresid,main='Residual Normal QQ Plot')
qqline(myresid)
par(op)
dev.off()
load(file='createtable')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Estimated Parameters of Exponential Smoothing',2,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'Parameter',header=TRUE)
a<-table.element(a,'Value',header=TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'alpha',header=TRUE)
a<-table.element(a,fit$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')