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Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationSun, 30 May 2010 01:03:56 +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/May/30/t127518160387stgt9f0qijylh.htm/, Retrieved Thu, 02 May 2024 20:13:03 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=76679, Retrieved Thu, 02 May 2024 20:13:03 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywordsKDGP2W62
Estimated Impact203
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [Univariate Data Series] [Uitvoer van België] [2010-02-04 08:24:53] [2ee36997fb1be82ef07372b18c1a823d]
- RMPD    [Exponential Smoothing] [invoer uitvoer] [2010-05-30 01:03:56] [d41d8cd98f00b204e9800998ecf8427e] [Current]
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Dataseries X:
18288.3
16049
16764.5
17880.2
16555.9
16087.1
16373.5
17842.2
22321.5
22786.7
18274.1
22392.9
23899.3
21343.5
22952.3
21374.4
21164.1
20906.5
17877.4
20664.3
22160
19813.6
17735.4
19640.2
20844.4
19823.1
18594.6
21350.6
18574.1
18924.2
17343.4
19961.2
19932.1
19464.6
16165.4
17574.9
19795.4
19439.5
17170
21072.4
17751.8
17515.5
18040.3
19090.1
17746.5
19202.1
15141.6
16258.1
18586.5
17209.4
17838.7
19123.5
16583.6
15991.2
16704.5
17422
17872
17823.2
13866.5
15912.8
17870.5
15420.3
16379.4
17903.9
15305.8
14583.3
14861
14968.9
16726.5
16283.6
11703.7
15101.8
15469.7
14956.9
15370.6
15998.1
14725.1
14768.9
13659.6
15070.3
16942.6
15761.3
12083
15023.6
15106.5




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'Sir Ronald Aylmer Fisher' @ 193.190.124.24

\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 & 'Sir Ronald Aylmer Fisher' @ 193.190.124.24 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=76679&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]'Sir Ronald Aylmer Fisher' @ 193.190.124.24[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=76679&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=76679&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'Sir Ronald Aylmer Fisher' @ 193.190.124.24







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.326901016459753
beta0.0446229444979951
gamma0.91238775163749

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.326901016459753 \tabularnewline
beta & 0.0446229444979951 \tabularnewline
gamma & 0.91238775163749 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=76679&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]0.326901016459753[/C][/ROW]
[ROW][C]beta[/C][C]0.0446229444979951[/C][/ROW]
[ROW][C]gamma[/C][C]0.91238775163749[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=76679&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=76679&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
alpha0.326901016459753
beta0.0446229444979951
gamma0.91238775163749







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
1323899.321615.74869123932283.55130876068
1421343.519874.15738799741469.34261200265
1522952.322121.8258216281830.474178371886
1621374.421227.5285458716146.871454128443
1721164.121495.2199672658-331.119967265779
1820906.521545.3420321796-638.842032179575
1917877.419280.1713032421-1402.77130324211
2020664.320084.9503596855579.349640314478
212216024532.7045728378-2372.70457283775
2219813.624041.7304430732-4228.1304430732
2317735.417970.5554293756-235.15542937558
2419640.221777.4410602050-2137.24106020496
2520844.423850.6933789375-3006.29337893752
2619823.119714.5998937978108.500106202198
2718594.620939.9911905536-2345.39119055362
2821350.618356.28415521872994.31584478128
2918574.119071.3998930772-497.299893077179
3018924.218685.9323628415238.267637158515
3117343.416058.849832141284.55016786001
3219961.218819.10220816861142.09779183138
3319932.121505.8020214568-1573.70202145675
3419464.620016.1299424397-551.529942439676
3516165.417532.2407550719-1366.84075507191
3617574.919717.7529811395-2142.85298113946
3719795.421172.0784989800-1376.67849898003
3819439.519421.975515034317.5244849656592
391717019049.6862691411-1879.68626914107
4021072.419843.33275053711229.06724946287
4117751.817757.1947173780-5.39471737795611
4217515.517911.5433523241-396.043352324094
4318040.315637.68145632282402.6185436772
4419090.118610.2841249505479.815875049546
4517746.519337.3121830273-1590.81218302726
4619202.118394.2165274608807.88347253915
4715141.615798.2725234051-656.672523405095
4816258.117693.9847830826-1435.88478308255
4918586.519814.8758977416-1228.37589774163
5017209.418936.5629197668-1727.16291976681
5117838.716770.44614120361068.25385879642
5219123.520421.5914093451-1298.09140934514
5316583.616698.9853570465-115.385357046503
5415991.216523.6449667608-532.44496676078
5516704.515868.113105563836.38689443701
561742217069.205713296352.794286703993
571787216402.56643946111469.43356053891
5817823.217897.0986252003-73.8986252002796
5913866.514064.7385634458-198.238563445804
6015912.815589.7283407549323.071659245112
6117870.518396.6698562816-526.169856281551
6215420.317435.4422031367-2015.14220313669
6316379.416881.5777051103-502.177705110318
6417903.918532.8531405357-628.953140535705
6515305.815731.8250137122-426.025013712208
6614583.315170.7810438640-587.481043864043
671486115309.0644964530-448.064496453022
6814968.915745.7142638718-776.814263871778
6916726.515331.51854266361394.98145733641
7016283.615788.7789360675494.821063932515
7111703.712009.1385039417-305.438503941714
7215101.813760.83671028971340.96328971034
7315469.716335.4353143074-865.735314307407
7414956.914300.2811613617656.618838638276
7515370.615539.4408733427-168.840873342739
7615998.117217.1607413557-1219.06074135574
7714725.114334.5740031767390.525996823339
7814768.913939.9425679843828.95743201572
7913659.614646.1784245800-986.578424580044
8015070.314716.3355113673353.964488632695
8116942.616033.4887465577909.111253442334
8215761.315799.9543649097-38.6543649097457
831208311367.5268237749715.473176225085
8415023.614492.0224358100531.577564189965
8515106.515462.9916007743-356.491600774285

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 23899.3 & 21615.7486912393 & 2283.55130876068 \tabularnewline
14 & 21343.5 & 19874.1573879974 & 1469.34261200265 \tabularnewline
15 & 22952.3 & 22121.8258216281 & 830.474178371886 \tabularnewline
16 & 21374.4 & 21227.5285458716 & 146.871454128443 \tabularnewline
17 & 21164.1 & 21495.2199672658 & -331.119967265779 \tabularnewline
18 & 20906.5 & 21545.3420321796 & -638.842032179575 \tabularnewline
19 & 17877.4 & 19280.1713032421 & -1402.77130324211 \tabularnewline
20 & 20664.3 & 20084.9503596855 & 579.349640314478 \tabularnewline
21 & 22160 & 24532.7045728378 & -2372.70457283775 \tabularnewline
22 & 19813.6 & 24041.7304430732 & -4228.1304430732 \tabularnewline
23 & 17735.4 & 17970.5554293756 & -235.15542937558 \tabularnewline
24 & 19640.2 & 21777.4410602050 & -2137.24106020496 \tabularnewline
25 & 20844.4 & 23850.6933789375 & -3006.29337893752 \tabularnewline
26 & 19823.1 & 19714.5998937978 & 108.500106202198 \tabularnewline
27 & 18594.6 & 20939.9911905536 & -2345.39119055362 \tabularnewline
28 & 21350.6 & 18356.2841552187 & 2994.31584478128 \tabularnewline
29 & 18574.1 & 19071.3998930772 & -497.299893077179 \tabularnewline
30 & 18924.2 & 18685.9323628415 & 238.267637158515 \tabularnewline
31 & 17343.4 & 16058.84983214 & 1284.55016786001 \tabularnewline
32 & 19961.2 & 18819.1022081686 & 1142.09779183138 \tabularnewline
33 & 19932.1 & 21505.8020214568 & -1573.70202145675 \tabularnewline
34 & 19464.6 & 20016.1299424397 & -551.529942439676 \tabularnewline
35 & 16165.4 & 17532.2407550719 & -1366.84075507191 \tabularnewline
36 & 17574.9 & 19717.7529811395 & -2142.85298113946 \tabularnewline
37 & 19795.4 & 21172.0784989800 & -1376.67849898003 \tabularnewline
38 & 19439.5 & 19421.9755150343 & 17.5244849656592 \tabularnewline
39 & 17170 & 19049.6862691411 & -1879.68626914107 \tabularnewline
40 & 21072.4 & 19843.3327505371 & 1229.06724946287 \tabularnewline
41 & 17751.8 & 17757.1947173780 & -5.39471737795611 \tabularnewline
42 & 17515.5 & 17911.5433523241 & -396.043352324094 \tabularnewline
43 & 18040.3 & 15637.6814563228 & 2402.6185436772 \tabularnewline
44 & 19090.1 & 18610.2841249505 & 479.815875049546 \tabularnewline
45 & 17746.5 & 19337.3121830273 & -1590.81218302726 \tabularnewline
46 & 19202.1 & 18394.2165274608 & 807.88347253915 \tabularnewline
47 & 15141.6 & 15798.2725234051 & -656.672523405095 \tabularnewline
48 & 16258.1 & 17693.9847830826 & -1435.88478308255 \tabularnewline
49 & 18586.5 & 19814.8758977416 & -1228.37589774163 \tabularnewline
50 & 17209.4 & 18936.5629197668 & -1727.16291976681 \tabularnewline
51 & 17838.7 & 16770.4461412036 & 1068.25385879642 \tabularnewline
52 & 19123.5 & 20421.5914093451 & -1298.09140934514 \tabularnewline
53 & 16583.6 & 16698.9853570465 & -115.385357046503 \tabularnewline
54 & 15991.2 & 16523.6449667608 & -532.44496676078 \tabularnewline
55 & 16704.5 & 15868.113105563 & 836.38689443701 \tabularnewline
56 & 17422 & 17069.205713296 & 352.794286703993 \tabularnewline
57 & 17872 & 16402.5664394611 & 1469.43356053891 \tabularnewline
58 & 17823.2 & 17897.0986252003 & -73.8986252002796 \tabularnewline
59 & 13866.5 & 14064.7385634458 & -198.238563445804 \tabularnewline
60 & 15912.8 & 15589.7283407549 & 323.071659245112 \tabularnewline
61 & 17870.5 & 18396.6698562816 & -526.169856281551 \tabularnewline
62 & 15420.3 & 17435.4422031367 & -2015.14220313669 \tabularnewline
63 & 16379.4 & 16881.5777051103 & -502.177705110318 \tabularnewline
64 & 17903.9 & 18532.8531405357 & -628.953140535705 \tabularnewline
65 & 15305.8 & 15731.8250137122 & -426.025013712208 \tabularnewline
66 & 14583.3 & 15170.7810438640 & -587.481043864043 \tabularnewline
67 & 14861 & 15309.0644964530 & -448.064496453022 \tabularnewline
68 & 14968.9 & 15745.7142638718 & -776.814263871778 \tabularnewline
69 & 16726.5 & 15331.5185426636 & 1394.98145733641 \tabularnewline
70 & 16283.6 & 15788.7789360675 & 494.821063932515 \tabularnewline
71 & 11703.7 & 12009.1385039417 & -305.438503941714 \tabularnewline
72 & 15101.8 & 13760.8367102897 & 1340.96328971034 \tabularnewline
73 & 15469.7 & 16335.4353143074 & -865.735314307407 \tabularnewline
74 & 14956.9 & 14300.2811613617 & 656.618838638276 \tabularnewline
75 & 15370.6 & 15539.4408733427 & -168.840873342739 \tabularnewline
76 & 15998.1 & 17217.1607413557 & -1219.06074135574 \tabularnewline
77 & 14725.1 & 14334.5740031767 & 390.525996823339 \tabularnewline
78 & 14768.9 & 13939.9425679843 & 828.95743201572 \tabularnewline
79 & 13659.6 & 14646.1784245800 & -986.578424580044 \tabularnewline
80 & 15070.3 & 14716.3355113673 & 353.964488632695 \tabularnewline
81 & 16942.6 & 16033.4887465577 & 909.111253442334 \tabularnewline
82 & 15761.3 & 15799.9543649097 & -38.6543649097457 \tabularnewline
83 & 12083 & 11367.5268237749 & 715.473176225085 \tabularnewline
84 & 15023.6 & 14492.0224358100 & 531.577564189965 \tabularnewline
85 & 15106.5 & 15462.9916007743 & -356.491600774285 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=76679&T=2

[TABLE]
[ROW][C]Interpolation Forecasts of Exponential Smoothing[/C][/ROW]
[ROW][C]t[/C][C]Observed[/C][C]Fitted[/C][C]Residuals[/C][/ROW]
[ROW][C]13[/C][C]23899.3[/C][C]21615.7486912393[/C][C]2283.55130876068[/C][/ROW]
[ROW][C]14[/C][C]21343.5[/C][C]19874.1573879974[/C][C]1469.34261200265[/C][/ROW]
[ROW][C]15[/C][C]22952.3[/C][C]22121.8258216281[/C][C]830.474178371886[/C][/ROW]
[ROW][C]16[/C][C]21374.4[/C][C]21227.5285458716[/C][C]146.871454128443[/C][/ROW]
[ROW][C]17[/C][C]21164.1[/C][C]21495.2199672658[/C][C]-331.119967265779[/C][/ROW]
[ROW][C]18[/C][C]20906.5[/C][C]21545.3420321796[/C][C]-638.842032179575[/C][/ROW]
[ROW][C]19[/C][C]17877.4[/C][C]19280.1713032421[/C][C]-1402.77130324211[/C][/ROW]
[ROW][C]20[/C][C]20664.3[/C][C]20084.9503596855[/C][C]579.349640314478[/C][/ROW]
[ROW][C]21[/C][C]22160[/C][C]24532.7045728378[/C][C]-2372.70457283775[/C][/ROW]
[ROW][C]22[/C][C]19813.6[/C][C]24041.7304430732[/C][C]-4228.1304430732[/C][/ROW]
[ROW][C]23[/C][C]17735.4[/C][C]17970.5554293756[/C][C]-235.15542937558[/C][/ROW]
[ROW][C]24[/C][C]19640.2[/C][C]21777.4410602050[/C][C]-2137.24106020496[/C][/ROW]
[ROW][C]25[/C][C]20844.4[/C][C]23850.6933789375[/C][C]-3006.29337893752[/C][/ROW]
[ROW][C]26[/C][C]19823.1[/C][C]19714.5998937978[/C][C]108.500106202198[/C][/ROW]
[ROW][C]27[/C][C]18594.6[/C][C]20939.9911905536[/C][C]-2345.39119055362[/C][/ROW]
[ROW][C]28[/C][C]21350.6[/C][C]18356.2841552187[/C][C]2994.31584478128[/C][/ROW]
[ROW][C]29[/C][C]18574.1[/C][C]19071.3998930772[/C][C]-497.299893077179[/C][/ROW]
[ROW][C]30[/C][C]18924.2[/C][C]18685.9323628415[/C][C]238.267637158515[/C][/ROW]
[ROW][C]31[/C][C]17343.4[/C][C]16058.84983214[/C][C]1284.55016786001[/C][/ROW]
[ROW][C]32[/C][C]19961.2[/C][C]18819.1022081686[/C][C]1142.09779183138[/C][/ROW]
[ROW][C]33[/C][C]19932.1[/C][C]21505.8020214568[/C][C]-1573.70202145675[/C][/ROW]
[ROW][C]34[/C][C]19464.6[/C][C]20016.1299424397[/C][C]-551.529942439676[/C][/ROW]
[ROW][C]35[/C][C]16165.4[/C][C]17532.2407550719[/C][C]-1366.84075507191[/C][/ROW]
[ROW][C]36[/C][C]17574.9[/C][C]19717.7529811395[/C][C]-2142.85298113946[/C][/ROW]
[ROW][C]37[/C][C]19795.4[/C][C]21172.0784989800[/C][C]-1376.67849898003[/C][/ROW]
[ROW][C]38[/C][C]19439.5[/C][C]19421.9755150343[/C][C]17.5244849656592[/C][/ROW]
[ROW][C]39[/C][C]17170[/C][C]19049.6862691411[/C][C]-1879.68626914107[/C][/ROW]
[ROW][C]40[/C][C]21072.4[/C][C]19843.3327505371[/C][C]1229.06724946287[/C][/ROW]
[ROW][C]41[/C][C]17751.8[/C][C]17757.1947173780[/C][C]-5.39471737795611[/C][/ROW]
[ROW][C]42[/C][C]17515.5[/C][C]17911.5433523241[/C][C]-396.043352324094[/C][/ROW]
[ROW][C]43[/C][C]18040.3[/C][C]15637.6814563228[/C][C]2402.6185436772[/C][/ROW]
[ROW][C]44[/C][C]19090.1[/C][C]18610.2841249505[/C][C]479.815875049546[/C][/ROW]
[ROW][C]45[/C][C]17746.5[/C][C]19337.3121830273[/C][C]-1590.81218302726[/C][/ROW]
[ROW][C]46[/C][C]19202.1[/C][C]18394.2165274608[/C][C]807.88347253915[/C][/ROW]
[ROW][C]47[/C][C]15141.6[/C][C]15798.2725234051[/C][C]-656.672523405095[/C][/ROW]
[ROW][C]48[/C][C]16258.1[/C][C]17693.9847830826[/C][C]-1435.88478308255[/C][/ROW]
[ROW][C]49[/C][C]18586.5[/C][C]19814.8758977416[/C][C]-1228.37589774163[/C][/ROW]
[ROW][C]50[/C][C]17209.4[/C][C]18936.5629197668[/C][C]-1727.16291976681[/C][/ROW]
[ROW][C]51[/C][C]17838.7[/C][C]16770.4461412036[/C][C]1068.25385879642[/C][/ROW]
[ROW][C]52[/C][C]19123.5[/C][C]20421.5914093451[/C][C]-1298.09140934514[/C][/ROW]
[ROW][C]53[/C][C]16583.6[/C][C]16698.9853570465[/C][C]-115.385357046503[/C][/ROW]
[ROW][C]54[/C][C]15991.2[/C][C]16523.6449667608[/C][C]-532.44496676078[/C][/ROW]
[ROW][C]55[/C][C]16704.5[/C][C]15868.113105563[/C][C]836.38689443701[/C][/ROW]
[ROW][C]56[/C][C]17422[/C][C]17069.205713296[/C][C]352.794286703993[/C][/ROW]
[ROW][C]57[/C][C]17872[/C][C]16402.5664394611[/C][C]1469.43356053891[/C][/ROW]
[ROW][C]58[/C][C]17823.2[/C][C]17897.0986252003[/C][C]-73.8986252002796[/C][/ROW]
[ROW][C]59[/C][C]13866.5[/C][C]14064.7385634458[/C][C]-198.238563445804[/C][/ROW]
[ROW][C]60[/C][C]15912.8[/C][C]15589.7283407549[/C][C]323.071659245112[/C][/ROW]
[ROW][C]61[/C][C]17870.5[/C][C]18396.6698562816[/C][C]-526.169856281551[/C][/ROW]
[ROW][C]62[/C][C]15420.3[/C][C]17435.4422031367[/C][C]-2015.14220313669[/C][/ROW]
[ROW][C]63[/C][C]16379.4[/C][C]16881.5777051103[/C][C]-502.177705110318[/C][/ROW]
[ROW][C]64[/C][C]17903.9[/C][C]18532.8531405357[/C][C]-628.953140535705[/C][/ROW]
[ROW][C]65[/C][C]15305.8[/C][C]15731.8250137122[/C][C]-426.025013712208[/C][/ROW]
[ROW][C]66[/C][C]14583.3[/C][C]15170.7810438640[/C][C]-587.481043864043[/C][/ROW]
[ROW][C]67[/C][C]14861[/C][C]15309.0644964530[/C][C]-448.064496453022[/C][/ROW]
[ROW][C]68[/C][C]14968.9[/C][C]15745.7142638718[/C][C]-776.814263871778[/C][/ROW]
[ROW][C]69[/C][C]16726.5[/C][C]15331.5185426636[/C][C]1394.98145733641[/C][/ROW]
[ROW][C]70[/C][C]16283.6[/C][C]15788.7789360675[/C][C]494.821063932515[/C][/ROW]
[ROW][C]71[/C][C]11703.7[/C][C]12009.1385039417[/C][C]-305.438503941714[/C][/ROW]
[ROW][C]72[/C][C]15101.8[/C][C]13760.8367102897[/C][C]1340.96328971034[/C][/ROW]
[ROW][C]73[/C][C]15469.7[/C][C]16335.4353143074[/C][C]-865.735314307407[/C][/ROW]
[ROW][C]74[/C][C]14956.9[/C][C]14300.2811613617[/C][C]656.618838638276[/C][/ROW]
[ROW][C]75[/C][C]15370.6[/C][C]15539.4408733427[/C][C]-168.840873342739[/C][/ROW]
[ROW][C]76[/C][C]15998.1[/C][C]17217.1607413557[/C][C]-1219.06074135574[/C][/ROW]
[ROW][C]77[/C][C]14725.1[/C][C]14334.5740031767[/C][C]390.525996823339[/C][/ROW]
[ROW][C]78[/C][C]14768.9[/C][C]13939.9425679843[/C][C]828.95743201572[/C][/ROW]
[ROW][C]79[/C][C]13659.6[/C][C]14646.1784245800[/C][C]-986.578424580044[/C][/ROW]
[ROW][C]80[/C][C]15070.3[/C][C]14716.3355113673[/C][C]353.964488632695[/C][/ROW]
[ROW][C]81[/C][C]16942.6[/C][C]16033.4887465577[/C][C]909.111253442334[/C][/ROW]
[ROW][C]82[/C][C]15761.3[/C][C]15799.9543649097[/C][C]-38.6543649097457[/C][/ROW]
[ROW][C]83[/C][C]12083[/C][C]11367.5268237749[/C][C]715.473176225085[/C][/ROW]
[ROW][C]84[/C][C]15023.6[/C][C]14492.0224358100[/C][C]531.577564189965[/C][/ROW]
[ROW][C]85[/C][C]15106.5[/C][C]15462.9916007743[/C][C]-356.491600774285[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=76679&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=76679&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
1323899.321615.74869123932283.55130876068
1421343.519874.15738799741469.34261200265
1522952.322121.8258216281830.474178371886
1621374.421227.5285458716146.871454128443
1721164.121495.2199672658-331.119967265779
1820906.521545.3420321796-638.842032179575
1917877.419280.1713032421-1402.77130324211
2020664.320084.9503596855579.349640314478
212216024532.7045728378-2372.70457283775
2219813.624041.7304430732-4228.1304430732
2317735.417970.5554293756-235.15542937558
2419640.221777.4410602050-2137.24106020496
2520844.423850.6933789375-3006.29337893752
2619823.119714.5998937978108.500106202198
2718594.620939.9911905536-2345.39119055362
2821350.618356.28415521872994.31584478128
2918574.119071.3998930772-497.299893077179
3018924.218685.9323628415238.267637158515
3117343.416058.849832141284.55016786001
3219961.218819.10220816861142.09779183138
3319932.121505.8020214568-1573.70202145675
3419464.620016.1299424397-551.529942439676
3516165.417532.2407550719-1366.84075507191
3617574.919717.7529811395-2142.85298113946
3719795.421172.0784989800-1376.67849898003
3819439.519421.975515034317.5244849656592
391717019049.6862691411-1879.68626914107
4021072.419843.33275053711229.06724946287
4117751.817757.1947173780-5.39471737795611
4217515.517911.5433523241-396.043352324094
4318040.315637.68145632282402.6185436772
4419090.118610.2841249505479.815875049546
4517746.519337.3121830273-1590.81218302726
4619202.118394.2165274608807.88347253915
4715141.615798.2725234051-656.672523405095
4816258.117693.9847830826-1435.88478308255
4918586.519814.8758977416-1228.37589774163
5017209.418936.5629197668-1727.16291976681
5117838.716770.44614120361068.25385879642
5219123.520421.5914093451-1298.09140934514
5316583.616698.9853570465-115.385357046503
5415991.216523.6449667608-532.44496676078
5516704.515868.113105563836.38689443701
561742217069.205713296352.794286703993
571787216402.56643946111469.43356053891
5817823.217897.0986252003-73.8986252002796
5913866.514064.7385634458-198.238563445804
6015912.815589.7283407549323.071659245112
6117870.518396.6698562816-526.169856281551
6215420.317435.4422031367-2015.14220313669
6316379.416881.5777051103-502.177705110318
6417903.918532.8531405357-628.953140535705
6515305.815731.8250137122-426.025013712208
6614583.315170.7810438640-587.481043864043
671486115309.0644964530-448.064496453022
6814968.915745.7142638718-776.814263871778
6916726.515331.51854266361394.98145733641
7016283.615788.7789360675494.821063932515
7111703.712009.1385039417-305.438503941714
7215101.813760.83671028971340.96328971034
7315469.716335.4353143074-865.735314307407
7414956.914300.2811613617656.618838638276
7515370.615539.4408733427-168.840873342739
7615998.117217.1607413557-1219.06074135574
7714725.114334.5740031767390.525996823339
7814768.913939.9425679843828.95743201572
7913659.614646.1784245800-986.578424580044
8015070.314716.3355113673353.964488632695
8116942.616033.4887465577909.111253442334
8215761.315799.9543649097-38.6543649097457
831208311367.5268237749715.473176225085
8415023.614492.0224358100531.577564189965
8515106.515462.9916007743-356.491600774285







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
8614552.810779073412052.697554254917052.9240038918
8715084.387367045712442.518466880217726.2562672113
8816188.799319407613400.972303674618976.6263351406
8914727.465160576511789.651212894917665.2791082581
9014502.975642682111411.302090606817594.6491947574
9113839.714720125310590.449686891817088.9797533587
9215086.501079451211676.040024948218496.9621339542
9316654.562173953413079.416093136420229.7082547704
9415554.216667887411811.001733742519297.4316020324
9511610.54640545327695.9748658501215525.1179450564
9614390.771828081410301.643988567218479.8996675956
9714637.380011806910370.57715800918904.1828656049

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
86 & 14552.8107790734 & 12052.6975542549 & 17052.9240038918 \tabularnewline
87 & 15084.3873670457 & 12442.5184668802 & 17726.2562672113 \tabularnewline
88 & 16188.7993194076 & 13400.9723036746 & 18976.6263351406 \tabularnewline
89 & 14727.4651605765 & 11789.6512128949 & 17665.2791082581 \tabularnewline
90 & 14502.9756426821 & 11411.3020906068 & 17594.6491947574 \tabularnewline
91 & 13839.7147201253 & 10590.4496868918 & 17088.9797533587 \tabularnewline
92 & 15086.5010794512 & 11676.0400249482 & 18496.9621339542 \tabularnewline
93 & 16654.5621739534 & 13079.4160931364 & 20229.7082547704 \tabularnewline
94 & 15554.2166678874 & 11811.0017337425 & 19297.4316020324 \tabularnewline
95 & 11610.5464054532 & 7695.97486585012 & 15525.1179450564 \tabularnewline
96 & 14390.7718280814 & 10301.6439885672 & 18479.8996675956 \tabularnewline
97 & 14637.3800118069 & 10370.577158009 & 18904.1828656049 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=76679&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]86[/C][C]14552.8107790734[/C][C]12052.6975542549[/C][C]17052.9240038918[/C][/ROW]
[ROW][C]87[/C][C]15084.3873670457[/C][C]12442.5184668802[/C][C]17726.2562672113[/C][/ROW]
[ROW][C]88[/C][C]16188.7993194076[/C][C]13400.9723036746[/C][C]18976.6263351406[/C][/ROW]
[ROW][C]89[/C][C]14727.4651605765[/C][C]11789.6512128949[/C][C]17665.2791082581[/C][/ROW]
[ROW][C]90[/C][C]14502.9756426821[/C][C]11411.3020906068[/C][C]17594.6491947574[/C][/ROW]
[ROW][C]91[/C][C]13839.7147201253[/C][C]10590.4496868918[/C][C]17088.9797533587[/C][/ROW]
[ROW][C]92[/C][C]15086.5010794512[/C][C]11676.0400249482[/C][C]18496.9621339542[/C][/ROW]
[ROW][C]93[/C][C]16654.5621739534[/C][C]13079.4160931364[/C][C]20229.7082547704[/C][/ROW]
[ROW][C]94[/C][C]15554.2166678874[/C][C]11811.0017337425[/C][C]19297.4316020324[/C][/ROW]
[ROW][C]95[/C][C]11610.5464054532[/C][C]7695.97486585012[/C][C]15525.1179450564[/C][/ROW]
[ROW][C]96[/C][C]14390.7718280814[/C][C]10301.6439885672[/C][C]18479.8996675956[/C][/ROW]
[ROW][C]97[/C][C]14637.3800118069[/C][C]10370.577158009[/C][C]18904.1828656049[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=76679&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=76679&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
8614552.810779073412052.697554254917052.9240038918
8715084.387367045712442.518466880217726.2562672113
8816188.799319407613400.972303674618976.6263351406
8914727.465160576511789.651212894917665.2791082581
9014502.975642682111411.302090606817594.6491947574
9113839.714720125310590.449686891817088.9797533587
9215086.501079451211676.040024948218496.9621339542
9316654.562173953413079.416093136420229.7082547704
9415554.216667887411811.001733742519297.4316020324
9511610.54640545327695.9748658501215525.1179450564
9614390.771828081410301.643988567218479.8996675956
9714637.380011806910370.57715800918904.1828656049



Parameters (Session):
par1 = 12 ; par2 = Triple ; par3 = additive ;
Parameters (R input):
par1 = 12 ; par2 = Triple ; par3 = additive ;
R code (references can be found in the software module):
par1 <- as.numeric(par1)
if (par2 == 'Single') K <- 1
if (par2 == 'Double') K <- 2
if (par2 == 'Triple') K <- par1
nx <- length(x)
nxmK <- nx - K
x <- ts(x, frequency = par1)
if (par2 == 'Single') fit <- HoltWinters(x, gamma=F, beta=F)
if (par2 == 'Double') fit <- HoltWinters(x, gamma=F)
if (par2 == 'Triple') fit <- HoltWinters(x, seasonal=par3)
fit
myresid <- x - fit$fitted[,'xhat']
bitmap(file='test1.png')
op <- par(mfrow=c(2,1))
plot(fit,ylab='Observed (black) / Fitted (red)',main='Interpolation Fit of Exponential Smoothing')
plot(myresid,ylab='Residuals',main='Interpolation Prediction Errors')
par(op)
dev.off()
bitmap(file='test2.png')
p <- predict(fit, par1, prediction.interval=TRUE)
np <- length(p[,1])
plot(fit,p,ylab='Observed (black) / Fitted (red)',main='Extrapolation Fit of Exponential Smoothing')
dev.off()
bitmap(file='test3.png')
op <- par(mfrow = c(2,2))
acf(as.numeric(myresid),lag.max = nx/2,main='Residual ACF')
spectrum(myresid,main='Residals Periodogram')
cpgram(myresid,main='Residal Cumulative Periodogram')
qqnorm(myresid,main='Residual Normal QQ Plot')
qqline(myresid)
par(op)
dev.off()
load(file='createtable')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Estimated Parameters of Exponential Smoothing',2,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'Parameter',header=TRUE)
a<-table.element(a,'Value',header=TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'alpha',header=TRUE)
a<-table.element(a,fit$alpha)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'beta',header=TRUE)
a<-table.element(a,fit$beta)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'gamma',header=TRUE)
a<-table.element(a,fit$gamma)
a<-table.row.end(a)
a<-table.end(a)
table.save(a,file='mytable.tab')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Interpolation Forecasts of Exponential Smoothing',4,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'t',header=TRUE)
a<-table.element(a,'Observed',header=TRUE)
a<-table.element(a,'Fitted',header=TRUE)
a<-table.element(a,'Residuals',header=TRUE)
a<-table.row.end(a)
for (i in 1:nxmK) {
a<-table.row.start(a)
a<-table.element(a,i+K,header=TRUE)
a<-table.element(a,x[i+K])
a<-table.element(a,fit$fitted[i,'xhat'])
a<-table.element(a,myresid[i])
a<-table.row.end(a)
}
a<-table.end(a)
table.save(a,file='mytable1.tab')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Extrapolation Forecasts of Exponential Smoothing',4,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'t',header=TRUE)
a<-table.element(a,'Forecast',header=TRUE)
a<-table.element(a,'95% Lower Bound',header=TRUE)
a<-table.element(a,'95% Upper Bound',header=TRUE)
a<-table.row.end(a)
for (i in 1:np) {
a<-table.row.start(a)
a<-table.element(a,nx+i,header=TRUE)
a<-table.element(a,p[i,'fit'])
a<-table.element(a,p[i,'lwr'])
a<-table.element(a,p[i,'upr'])
a<-table.row.end(a)
}
a<-table.end(a)
table.save(a,file='mytable2.tab')