Free Statistics

of Irreproducible Research!

Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationWed, 16 Aug 2017 21:33:44 +0200
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/Aug/16/t15029120674v2engbtsg7k8tv.htm/, Retrieved Sat, 11 May 2024 20:23:45 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=307503, Retrieved Sat, 11 May 2024 20:23:45 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact67
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [Exponential smoot...] [2017-08-16 19:33:44] [41db9c2917eeaa94887144dd7479aea5] [Current]
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Dataseries X:
1263600
1216800
1287000
1029600
1333800
1310400
1404000
1450800
1614600
1404000
1333800
1661400
1404000
1053000
1240200
936000
1310400
1076400
1427400
1287000
1357200
1521000
1497600
1778400
1287000
1076400
1193400
865800
1240200
959400
1357200
1287000
1146600
1638000
1474200
1684800
1263600
1170000
1053000
865800
1146600
1029600
1404000
1357200
1170000
1567800
1450800
1872000
1497600
912600
912600
912600
1076400
1076400
1450800
1333800
1193400
1497600
1380600
1989000
1567800
912600
959400
795600
1099800
1263600
1591200
1567800
1263600
1474200
1310400
1872000
1427400
1146600
1029600
772200
1146600
1380600
1614600
1521000
1123200
1614600
1263600
1942200
1614600
1170000
1076400
725400
1146600
1099800
1661400
1661400
1263600
1638000
1216800
1895400
1614600
1193400
912600
631800
1240200
1193400
1567800
1801800
1333800
1497600
1123200
1942200




Summary of computational transaction
Raw Input view raw input (R code)
Raw Outputview raw output of R engine
Computing time2 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 time2 seconds \tabularnewline
R ServerBig Analytics Cloud Computing Center \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=307503&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]2 seconds[/C][/ROW] [ROW]R Server[/C]Big Analytics Cloud Computing Center[/C][/ROW] [/TABLE] Source: https://freestatistics.org/blog/index.php?pk=307503&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=307503&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 time2 seconds
R ServerBig Analytics Cloud Computing Center







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.616435516556137
beta0.0182153483451572
gammaFALSE

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.616435516556137 \tabularnewline
beta & 0.0182153483451572 \tabularnewline
gamma & FALSE \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=307503&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]0.616435516556137[/C][/ROW]
[ROW][C]beta[/C][C]0.0182153483451572[/C][/ROW]
[ROW][C]gamma[/C][C]FALSE[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=307503&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=307503&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
alpha0.616435516556137
beta0.0182153483451572
gammaFALSE







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
312870001170000117000
410296001196636.70019404-167036.700194036
513338001046307.50415143287492.495848573
613104001179394.38255426131005.617445744
714040001217488.19929486186511.80070514
814508001291892.26289006158907.737109935
916146001351064.51074092263535.489259082
1014040001477692.15237829-73692.1523782909
1113338001395613.23975262-61813.2397526167
1216614001320162.83538597341237.164614031
1314040001496998.62665114-92998.6266511371
1410530001405111.81038839-352111.810388392
1512402001149544.7065307590655.2934692535
169360001167932.9019638-231932.901963796
171310400984861.997587739325538.002412261
1810764001149091.29011458-72691.2901145839
1914274001067021.68247122360378.317528777
2012870001255958.101651731041.8983482986
2113572001242228.41183085114971.588169152
2215210001281526.93226601239473.067733989
2314976001400261.5309035297338.4690964799
2417784001432472.28834298345927.71165702
2512870001621806.56356712-334806.563567122
2610764001387752.6493557-311352.649355703
2711934001164660.5103480128739.4896519913
288658001151535.94860525-285735.948605249
291240200941349.146487814298850.853512186
309594001094878.08471338-135478.08471338
311357200979150.011997511378049.988002489
3212870001184223.84948489102776.150515108
3311466001220763.14778242-74163.1477824233
3416380001147398.03092834490601.969071656
3514742001427682.9578341246517.0421658752
3616848001434740.48411389250059.515886113
3712636001570076.63551844-306476.635518442
3811700001358902.83718014-188902.837180145
3910530001218084.59188627-165084.591886274
408658001090095.09212123-224295.092121225
411146600923087.619953271223512.380046729
4210296001034634.30656275-5034.30656274746
4314040001005240.17020234398759.829797662
4413572001229236.59057832127963.409421682
4511700001287741.32803906-117741.32803906
4615678001193462.86991905374337.130080945
4714508001406722.327598344077.672401696
4818720001416893.05589419455106.944105811
4914976001685547.03383217-187947.033832171
509126001555689.32096045-643089.32096045
519126001138044.75239854-225444.752398539
52912600975319.703028718-62719.7030287181
531076400912199.899839937164200.100160063
541076400990805.25796612885594.7420338717
5514508001021916.58961643428883.41038357
5613338001269459.003840964340.9961590976
5711934001293006.98516221-99606.9851622062
5814976001214373.1621643283226.837835703
5913806001374911.941979385688.05802062084
6019890001364429.82955293624570.170447073
6115678001742461.67270011-174661.67270011
629126001625857.41786487-713257.417864873
639594001169234.74319885-209834.743198854
647956001020583.53722719-224983.53722719
651099800860067.829212215239732.170787785
661263600988711.242415348274888.757584652
6715912001142113.036874449086.963125995
6815678001407939.40448399159860.595516012
6912636001497271.37548581-233671.37548581
7014742001341392.463137132807.536863001
7113104001412915.40949928-102515.409499283
7218720001338225.8306005533774.169399499
7314274001661761.27700464-234361.277004637
7411466001509159.20657511-362559.206575105
7510296001273460.35137409-243860.351374087
767722001108193.47895977-335993.478959768
771146600882359.7422164264240.2577836
7813806001029498.44393636351101.556063635
7916146001234123.90953239380476.090467611
8015210001461129.0905541159870.9094458928
8111232001491174.11695751-367974.116957509
8216146001253348.44387273361251.556127267
8312636001469099.72002957-205499.720029565
8419422001333177.90888804609022.091111961
8516146001706194.7290846-91594.7290846023
8611700001646297.97837007-476297.978370073
8710764001343908.32785597-267508.327855974
887254001167220.29269729-441820.292697287
891146600878119.153560385268480.846439615
9010998001029887.5247587569912.4752412521
9116614001060036.31784296601363.682157042
9216614001424542.97501117236857.024988827
9312636001567014.35254924-303414.352549238
9416380001373036.34973729264963.650262712
9512168001532401.90226325-315601.902263251
9618954001330342.46489593565057.535104071
9716146001677497.58078164-62897.580781643
9811934001636852.60943247-443452.609432467
999126001356640.65591798-444040.65591798
1006318001071080.26023202-439280.260232017
1011240200783521.844607609456678.155392391
10211934001053391.8684346140008.131565396
10315678001129627.33612525438172.663874749
10418018001394582.07147807407217.92852193
10513338001645027.69076355-311227.690763552
10614976001449103.2661973548496.7338026545
10711232001475470.3029335-352270.302933505
10819422001250834.80638178691365.19361822

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
3 & 1287000 & 1170000 & 117000 \tabularnewline
4 & 1029600 & 1196636.70019404 & -167036.700194036 \tabularnewline
5 & 1333800 & 1046307.50415143 & 287492.495848573 \tabularnewline
6 & 1310400 & 1179394.38255426 & 131005.617445744 \tabularnewline
7 & 1404000 & 1217488.19929486 & 186511.80070514 \tabularnewline
8 & 1450800 & 1291892.26289006 & 158907.737109935 \tabularnewline
9 & 1614600 & 1351064.51074092 & 263535.489259082 \tabularnewline
10 & 1404000 & 1477692.15237829 & -73692.1523782909 \tabularnewline
11 & 1333800 & 1395613.23975262 & -61813.2397526167 \tabularnewline
12 & 1661400 & 1320162.83538597 & 341237.164614031 \tabularnewline
13 & 1404000 & 1496998.62665114 & -92998.6266511371 \tabularnewline
14 & 1053000 & 1405111.81038839 & -352111.810388392 \tabularnewline
15 & 1240200 & 1149544.70653075 & 90655.2934692535 \tabularnewline
16 & 936000 & 1167932.9019638 & -231932.901963796 \tabularnewline
17 & 1310400 & 984861.997587739 & 325538.002412261 \tabularnewline
18 & 1076400 & 1149091.29011458 & -72691.2901145839 \tabularnewline
19 & 1427400 & 1067021.68247122 & 360378.317528777 \tabularnewline
20 & 1287000 & 1255958.1016517 & 31041.8983482986 \tabularnewline
21 & 1357200 & 1242228.41183085 & 114971.588169152 \tabularnewline
22 & 1521000 & 1281526.93226601 & 239473.067733989 \tabularnewline
23 & 1497600 & 1400261.53090352 & 97338.4690964799 \tabularnewline
24 & 1778400 & 1432472.28834298 & 345927.71165702 \tabularnewline
25 & 1287000 & 1621806.56356712 & -334806.563567122 \tabularnewline
26 & 1076400 & 1387752.6493557 & -311352.649355703 \tabularnewline
27 & 1193400 & 1164660.51034801 & 28739.4896519913 \tabularnewline
28 & 865800 & 1151535.94860525 & -285735.948605249 \tabularnewline
29 & 1240200 & 941349.146487814 & 298850.853512186 \tabularnewline
30 & 959400 & 1094878.08471338 & -135478.08471338 \tabularnewline
31 & 1357200 & 979150.011997511 & 378049.988002489 \tabularnewline
32 & 1287000 & 1184223.84948489 & 102776.150515108 \tabularnewline
33 & 1146600 & 1220763.14778242 & -74163.1477824233 \tabularnewline
34 & 1638000 & 1147398.03092834 & 490601.969071656 \tabularnewline
35 & 1474200 & 1427682.95783412 & 46517.0421658752 \tabularnewline
36 & 1684800 & 1434740.48411389 & 250059.515886113 \tabularnewline
37 & 1263600 & 1570076.63551844 & -306476.635518442 \tabularnewline
38 & 1170000 & 1358902.83718014 & -188902.837180145 \tabularnewline
39 & 1053000 & 1218084.59188627 & -165084.591886274 \tabularnewline
40 & 865800 & 1090095.09212123 & -224295.092121225 \tabularnewline
41 & 1146600 & 923087.619953271 & 223512.380046729 \tabularnewline
42 & 1029600 & 1034634.30656275 & -5034.30656274746 \tabularnewline
43 & 1404000 & 1005240.17020234 & 398759.829797662 \tabularnewline
44 & 1357200 & 1229236.59057832 & 127963.409421682 \tabularnewline
45 & 1170000 & 1287741.32803906 & -117741.32803906 \tabularnewline
46 & 1567800 & 1193462.86991905 & 374337.130080945 \tabularnewline
47 & 1450800 & 1406722.3275983 & 44077.672401696 \tabularnewline
48 & 1872000 & 1416893.05589419 & 455106.944105811 \tabularnewline
49 & 1497600 & 1685547.03383217 & -187947.033832171 \tabularnewline
50 & 912600 & 1555689.32096045 & -643089.32096045 \tabularnewline
51 & 912600 & 1138044.75239854 & -225444.752398539 \tabularnewline
52 & 912600 & 975319.703028718 & -62719.7030287181 \tabularnewline
53 & 1076400 & 912199.899839937 & 164200.100160063 \tabularnewline
54 & 1076400 & 990805.257966128 & 85594.7420338717 \tabularnewline
55 & 1450800 & 1021916.58961643 & 428883.41038357 \tabularnewline
56 & 1333800 & 1269459.0038409 & 64340.9961590976 \tabularnewline
57 & 1193400 & 1293006.98516221 & -99606.9851622062 \tabularnewline
58 & 1497600 & 1214373.1621643 & 283226.837835703 \tabularnewline
59 & 1380600 & 1374911.94197938 & 5688.05802062084 \tabularnewline
60 & 1989000 & 1364429.82955293 & 624570.170447073 \tabularnewline
61 & 1567800 & 1742461.67270011 & -174661.67270011 \tabularnewline
62 & 912600 & 1625857.41786487 & -713257.417864873 \tabularnewline
63 & 959400 & 1169234.74319885 & -209834.743198854 \tabularnewline
64 & 795600 & 1020583.53722719 & -224983.53722719 \tabularnewline
65 & 1099800 & 860067.829212215 & 239732.170787785 \tabularnewline
66 & 1263600 & 988711.242415348 & 274888.757584652 \tabularnewline
67 & 1591200 & 1142113.036874 & 449086.963125995 \tabularnewline
68 & 1567800 & 1407939.40448399 & 159860.595516012 \tabularnewline
69 & 1263600 & 1497271.37548581 & -233671.37548581 \tabularnewline
70 & 1474200 & 1341392.463137 & 132807.536863001 \tabularnewline
71 & 1310400 & 1412915.40949928 & -102515.409499283 \tabularnewline
72 & 1872000 & 1338225.8306005 & 533774.169399499 \tabularnewline
73 & 1427400 & 1661761.27700464 & -234361.277004637 \tabularnewline
74 & 1146600 & 1509159.20657511 & -362559.206575105 \tabularnewline
75 & 1029600 & 1273460.35137409 & -243860.351374087 \tabularnewline
76 & 772200 & 1108193.47895977 & -335993.478959768 \tabularnewline
77 & 1146600 & 882359.7422164 & 264240.2577836 \tabularnewline
78 & 1380600 & 1029498.44393636 & 351101.556063635 \tabularnewline
79 & 1614600 & 1234123.90953239 & 380476.090467611 \tabularnewline
80 & 1521000 & 1461129.09055411 & 59870.9094458928 \tabularnewline
81 & 1123200 & 1491174.11695751 & -367974.116957509 \tabularnewline
82 & 1614600 & 1253348.44387273 & 361251.556127267 \tabularnewline
83 & 1263600 & 1469099.72002957 & -205499.720029565 \tabularnewline
84 & 1942200 & 1333177.90888804 & 609022.091111961 \tabularnewline
85 & 1614600 & 1706194.7290846 & -91594.7290846023 \tabularnewline
86 & 1170000 & 1646297.97837007 & -476297.978370073 \tabularnewline
87 & 1076400 & 1343908.32785597 & -267508.327855974 \tabularnewline
88 & 725400 & 1167220.29269729 & -441820.292697287 \tabularnewline
89 & 1146600 & 878119.153560385 & 268480.846439615 \tabularnewline
90 & 1099800 & 1029887.52475875 & 69912.4752412521 \tabularnewline
91 & 1661400 & 1060036.31784296 & 601363.682157042 \tabularnewline
92 & 1661400 & 1424542.97501117 & 236857.024988827 \tabularnewline
93 & 1263600 & 1567014.35254924 & -303414.352549238 \tabularnewline
94 & 1638000 & 1373036.34973729 & 264963.650262712 \tabularnewline
95 & 1216800 & 1532401.90226325 & -315601.902263251 \tabularnewline
96 & 1895400 & 1330342.46489593 & 565057.535104071 \tabularnewline
97 & 1614600 & 1677497.58078164 & -62897.580781643 \tabularnewline
98 & 1193400 & 1636852.60943247 & -443452.609432467 \tabularnewline
99 & 912600 & 1356640.65591798 & -444040.65591798 \tabularnewline
100 & 631800 & 1071080.26023202 & -439280.260232017 \tabularnewline
101 & 1240200 & 783521.844607609 & 456678.155392391 \tabularnewline
102 & 1193400 & 1053391.8684346 & 140008.131565396 \tabularnewline
103 & 1567800 & 1129627.33612525 & 438172.663874749 \tabularnewline
104 & 1801800 & 1394582.07147807 & 407217.92852193 \tabularnewline
105 & 1333800 & 1645027.69076355 & -311227.690763552 \tabularnewline
106 & 1497600 & 1449103.26619735 & 48496.7338026545 \tabularnewline
107 & 1123200 & 1475470.3029335 & -352270.302933505 \tabularnewline
108 & 1942200 & 1250834.80638178 & 691365.19361822 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=307503&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]3[/C][C]1287000[/C][C]1170000[/C][C]117000[/C][/ROW]
[ROW][C]4[/C][C]1029600[/C][C]1196636.70019404[/C][C]-167036.700194036[/C][/ROW]
[ROW][C]5[/C][C]1333800[/C][C]1046307.50415143[/C][C]287492.495848573[/C][/ROW]
[ROW][C]6[/C][C]1310400[/C][C]1179394.38255426[/C][C]131005.617445744[/C][/ROW]
[ROW][C]7[/C][C]1404000[/C][C]1217488.19929486[/C][C]186511.80070514[/C][/ROW]
[ROW][C]8[/C][C]1450800[/C][C]1291892.26289006[/C][C]158907.737109935[/C][/ROW]
[ROW][C]9[/C][C]1614600[/C][C]1351064.51074092[/C][C]263535.489259082[/C][/ROW]
[ROW][C]10[/C][C]1404000[/C][C]1477692.15237829[/C][C]-73692.1523782909[/C][/ROW]
[ROW][C]11[/C][C]1333800[/C][C]1395613.23975262[/C][C]-61813.2397526167[/C][/ROW]
[ROW][C]12[/C][C]1661400[/C][C]1320162.83538597[/C][C]341237.164614031[/C][/ROW]
[ROW][C]13[/C][C]1404000[/C][C]1496998.62665114[/C][C]-92998.6266511371[/C][/ROW]
[ROW][C]14[/C][C]1053000[/C][C]1405111.81038839[/C][C]-352111.810388392[/C][/ROW]
[ROW][C]15[/C][C]1240200[/C][C]1149544.70653075[/C][C]90655.2934692535[/C][/ROW]
[ROW][C]16[/C][C]936000[/C][C]1167932.9019638[/C][C]-231932.901963796[/C][/ROW]
[ROW][C]17[/C][C]1310400[/C][C]984861.997587739[/C][C]325538.002412261[/C][/ROW]
[ROW][C]18[/C][C]1076400[/C][C]1149091.29011458[/C][C]-72691.2901145839[/C][/ROW]
[ROW][C]19[/C][C]1427400[/C][C]1067021.68247122[/C][C]360378.317528777[/C][/ROW]
[ROW][C]20[/C][C]1287000[/C][C]1255958.1016517[/C][C]31041.8983482986[/C][/ROW]
[ROW][C]21[/C][C]1357200[/C][C]1242228.41183085[/C][C]114971.588169152[/C][/ROW]
[ROW][C]22[/C][C]1521000[/C][C]1281526.93226601[/C][C]239473.067733989[/C][/ROW]
[ROW][C]23[/C][C]1497600[/C][C]1400261.53090352[/C][C]97338.4690964799[/C][/ROW]
[ROW][C]24[/C][C]1778400[/C][C]1432472.28834298[/C][C]345927.71165702[/C][/ROW]
[ROW][C]25[/C][C]1287000[/C][C]1621806.56356712[/C][C]-334806.563567122[/C][/ROW]
[ROW][C]26[/C][C]1076400[/C][C]1387752.6493557[/C][C]-311352.649355703[/C][/ROW]
[ROW][C]27[/C][C]1193400[/C][C]1164660.51034801[/C][C]28739.4896519913[/C][/ROW]
[ROW][C]28[/C][C]865800[/C][C]1151535.94860525[/C][C]-285735.948605249[/C][/ROW]
[ROW][C]29[/C][C]1240200[/C][C]941349.146487814[/C][C]298850.853512186[/C][/ROW]
[ROW][C]30[/C][C]959400[/C][C]1094878.08471338[/C][C]-135478.08471338[/C][/ROW]
[ROW][C]31[/C][C]1357200[/C][C]979150.011997511[/C][C]378049.988002489[/C][/ROW]
[ROW][C]32[/C][C]1287000[/C][C]1184223.84948489[/C][C]102776.150515108[/C][/ROW]
[ROW][C]33[/C][C]1146600[/C][C]1220763.14778242[/C][C]-74163.1477824233[/C][/ROW]
[ROW][C]34[/C][C]1638000[/C][C]1147398.03092834[/C][C]490601.969071656[/C][/ROW]
[ROW][C]35[/C][C]1474200[/C][C]1427682.95783412[/C][C]46517.0421658752[/C][/ROW]
[ROW][C]36[/C][C]1684800[/C][C]1434740.48411389[/C][C]250059.515886113[/C][/ROW]
[ROW][C]37[/C][C]1263600[/C][C]1570076.63551844[/C][C]-306476.635518442[/C][/ROW]
[ROW][C]38[/C][C]1170000[/C][C]1358902.83718014[/C][C]-188902.837180145[/C][/ROW]
[ROW][C]39[/C][C]1053000[/C][C]1218084.59188627[/C][C]-165084.591886274[/C][/ROW]
[ROW][C]40[/C][C]865800[/C][C]1090095.09212123[/C][C]-224295.092121225[/C][/ROW]
[ROW][C]41[/C][C]1146600[/C][C]923087.619953271[/C][C]223512.380046729[/C][/ROW]
[ROW][C]42[/C][C]1029600[/C][C]1034634.30656275[/C][C]-5034.30656274746[/C][/ROW]
[ROW][C]43[/C][C]1404000[/C][C]1005240.17020234[/C][C]398759.829797662[/C][/ROW]
[ROW][C]44[/C][C]1357200[/C][C]1229236.59057832[/C][C]127963.409421682[/C][/ROW]
[ROW][C]45[/C][C]1170000[/C][C]1287741.32803906[/C][C]-117741.32803906[/C][/ROW]
[ROW][C]46[/C][C]1567800[/C][C]1193462.86991905[/C][C]374337.130080945[/C][/ROW]
[ROW][C]47[/C][C]1450800[/C][C]1406722.3275983[/C][C]44077.672401696[/C][/ROW]
[ROW][C]48[/C][C]1872000[/C][C]1416893.05589419[/C][C]455106.944105811[/C][/ROW]
[ROW][C]49[/C][C]1497600[/C][C]1685547.03383217[/C][C]-187947.033832171[/C][/ROW]
[ROW][C]50[/C][C]912600[/C][C]1555689.32096045[/C][C]-643089.32096045[/C][/ROW]
[ROW][C]51[/C][C]912600[/C][C]1138044.75239854[/C][C]-225444.752398539[/C][/ROW]
[ROW][C]52[/C][C]912600[/C][C]975319.703028718[/C][C]-62719.7030287181[/C][/ROW]
[ROW][C]53[/C][C]1076400[/C][C]912199.899839937[/C][C]164200.100160063[/C][/ROW]
[ROW][C]54[/C][C]1076400[/C][C]990805.257966128[/C][C]85594.7420338717[/C][/ROW]
[ROW][C]55[/C][C]1450800[/C][C]1021916.58961643[/C][C]428883.41038357[/C][/ROW]
[ROW][C]56[/C][C]1333800[/C][C]1269459.0038409[/C][C]64340.9961590976[/C][/ROW]
[ROW][C]57[/C][C]1193400[/C][C]1293006.98516221[/C][C]-99606.9851622062[/C][/ROW]
[ROW][C]58[/C][C]1497600[/C][C]1214373.1621643[/C][C]283226.837835703[/C][/ROW]
[ROW][C]59[/C][C]1380600[/C][C]1374911.94197938[/C][C]5688.05802062084[/C][/ROW]
[ROW][C]60[/C][C]1989000[/C][C]1364429.82955293[/C][C]624570.170447073[/C][/ROW]
[ROW][C]61[/C][C]1567800[/C][C]1742461.67270011[/C][C]-174661.67270011[/C][/ROW]
[ROW][C]62[/C][C]912600[/C][C]1625857.41786487[/C][C]-713257.417864873[/C][/ROW]
[ROW][C]63[/C][C]959400[/C][C]1169234.74319885[/C][C]-209834.743198854[/C][/ROW]
[ROW][C]64[/C][C]795600[/C][C]1020583.53722719[/C][C]-224983.53722719[/C][/ROW]
[ROW][C]65[/C][C]1099800[/C][C]860067.829212215[/C][C]239732.170787785[/C][/ROW]
[ROW][C]66[/C][C]1263600[/C][C]988711.242415348[/C][C]274888.757584652[/C][/ROW]
[ROW][C]67[/C][C]1591200[/C][C]1142113.036874[/C][C]449086.963125995[/C][/ROW]
[ROW][C]68[/C][C]1567800[/C][C]1407939.40448399[/C][C]159860.595516012[/C][/ROW]
[ROW][C]69[/C][C]1263600[/C][C]1497271.37548581[/C][C]-233671.37548581[/C][/ROW]
[ROW][C]70[/C][C]1474200[/C][C]1341392.463137[/C][C]132807.536863001[/C][/ROW]
[ROW][C]71[/C][C]1310400[/C][C]1412915.40949928[/C][C]-102515.409499283[/C][/ROW]
[ROW][C]72[/C][C]1872000[/C][C]1338225.8306005[/C][C]533774.169399499[/C][/ROW]
[ROW][C]73[/C][C]1427400[/C][C]1661761.27700464[/C][C]-234361.277004637[/C][/ROW]
[ROW][C]74[/C][C]1146600[/C][C]1509159.20657511[/C][C]-362559.206575105[/C][/ROW]
[ROW][C]75[/C][C]1029600[/C][C]1273460.35137409[/C][C]-243860.351374087[/C][/ROW]
[ROW][C]76[/C][C]772200[/C][C]1108193.47895977[/C][C]-335993.478959768[/C][/ROW]
[ROW][C]77[/C][C]1146600[/C][C]882359.7422164[/C][C]264240.2577836[/C][/ROW]
[ROW][C]78[/C][C]1380600[/C][C]1029498.44393636[/C][C]351101.556063635[/C][/ROW]
[ROW][C]79[/C][C]1614600[/C][C]1234123.90953239[/C][C]380476.090467611[/C][/ROW]
[ROW][C]80[/C][C]1521000[/C][C]1461129.09055411[/C][C]59870.9094458928[/C][/ROW]
[ROW][C]81[/C][C]1123200[/C][C]1491174.11695751[/C][C]-367974.116957509[/C][/ROW]
[ROW][C]82[/C][C]1614600[/C][C]1253348.44387273[/C][C]361251.556127267[/C][/ROW]
[ROW][C]83[/C][C]1263600[/C][C]1469099.72002957[/C][C]-205499.720029565[/C][/ROW]
[ROW][C]84[/C][C]1942200[/C][C]1333177.90888804[/C][C]609022.091111961[/C][/ROW]
[ROW][C]85[/C][C]1614600[/C][C]1706194.7290846[/C][C]-91594.7290846023[/C][/ROW]
[ROW][C]86[/C][C]1170000[/C][C]1646297.97837007[/C][C]-476297.978370073[/C][/ROW]
[ROW][C]87[/C][C]1076400[/C][C]1343908.32785597[/C][C]-267508.327855974[/C][/ROW]
[ROW][C]88[/C][C]725400[/C][C]1167220.29269729[/C][C]-441820.292697287[/C][/ROW]
[ROW][C]89[/C][C]1146600[/C][C]878119.153560385[/C][C]268480.846439615[/C][/ROW]
[ROW][C]90[/C][C]1099800[/C][C]1029887.52475875[/C][C]69912.4752412521[/C][/ROW]
[ROW][C]91[/C][C]1661400[/C][C]1060036.31784296[/C][C]601363.682157042[/C][/ROW]
[ROW][C]92[/C][C]1661400[/C][C]1424542.97501117[/C][C]236857.024988827[/C][/ROW]
[ROW][C]93[/C][C]1263600[/C][C]1567014.35254924[/C][C]-303414.352549238[/C][/ROW]
[ROW][C]94[/C][C]1638000[/C][C]1373036.34973729[/C][C]264963.650262712[/C][/ROW]
[ROW][C]95[/C][C]1216800[/C][C]1532401.90226325[/C][C]-315601.902263251[/C][/ROW]
[ROW][C]96[/C][C]1895400[/C][C]1330342.46489593[/C][C]565057.535104071[/C][/ROW]
[ROW][C]97[/C][C]1614600[/C][C]1677497.58078164[/C][C]-62897.580781643[/C][/ROW]
[ROW][C]98[/C][C]1193400[/C][C]1636852.60943247[/C][C]-443452.609432467[/C][/ROW]
[ROW][C]99[/C][C]912600[/C][C]1356640.65591798[/C][C]-444040.65591798[/C][/ROW]
[ROW][C]100[/C][C]631800[/C][C]1071080.26023202[/C][C]-439280.260232017[/C][/ROW]
[ROW][C]101[/C][C]1240200[/C][C]783521.844607609[/C][C]456678.155392391[/C][/ROW]
[ROW][C]102[/C][C]1193400[/C][C]1053391.8684346[/C][C]140008.131565396[/C][/ROW]
[ROW][C]103[/C][C]1567800[/C][C]1129627.33612525[/C][C]438172.663874749[/C][/ROW]
[ROW][C]104[/C][C]1801800[/C][C]1394582.07147807[/C][C]407217.92852193[/C][/ROW]
[ROW][C]105[/C][C]1333800[/C][C]1645027.69076355[/C][C]-311227.690763552[/C][/ROW]
[ROW][C]106[/C][C]1497600[/C][C]1449103.26619735[/C][C]48496.7338026545[/C][/ROW]
[ROW][C]107[/C][C]1123200[/C][C]1475470.3029335[/C][C]-352270.302933505[/C][/ROW]
[ROW][C]108[/C][C]1942200[/C][C]1250834.80638178[/C][C]691365.19361822[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=307503&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=307503&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
312870001170000117000
410296001196636.70019404-167036.700194036
513338001046307.50415143287492.495848573
613104001179394.38255426131005.617445744
714040001217488.19929486186511.80070514
814508001291892.26289006158907.737109935
916146001351064.51074092263535.489259082
1014040001477692.15237829-73692.1523782909
1113338001395613.23975262-61813.2397526167
1216614001320162.83538597341237.164614031
1314040001496998.62665114-92998.6266511371
1410530001405111.81038839-352111.810388392
1512402001149544.7065307590655.2934692535
169360001167932.9019638-231932.901963796
171310400984861.997587739325538.002412261
1810764001149091.29011458-72691.2901145839
1914274001067021.68247122360378.317528777
2012870001255958.101651731041.8983482986
2113572001242228.41183085114971.588169152
2215210001281526.93226601239473.067733989
2314976001400261.5309035297338.4690964799
2417784001432472.28834298345927.71165702
2512870001621806.56356712-334806.563567122
2610764001387752.6493557-311352.649355703
2711934001164660.5103480128739.4896519913
288658001151535.94860525-285735.948605249
291240200941349.146487814298850.853512186
309594001094878.08471338-135478.08471338
311357200979150.011997511378049.988002489
3212870001184223.84948489102776.150515108
3311466001220763.14778242-74163.1477824233
3416380001147398.03092834490601.969071656
3514742001427682.9578341246517.0421658752
3616848001434740.48411389250059.515886113
3712636001570076.63551844-306476.635518442
3811700001358902.83718014-188902.837180145
3910530001218084.59188627-165084.591886274
408658001090095.09212123-224295.092121225
411146600923087.619953271223512.380046729
4210296001034634.30656275-5034.30656274746
4314040001005240.17020234398759.829797662
4413572001229236.59057832127963.409421682
4511700001287741.32803906-117741.32803906
4615678001193462.86991905374337.130080945
4714508001406722.327598344077.672401696
4818720001416893.05589419455106.944105811
4914976001685547.03383217-187947.033832171
509126001555689.32096045-643089.32096045
519126001138044.75239854-225444.752398539
52912600975319.703028718-62719.7030287181
531076400912199.899839937164200.100160063
541076400990805.25796612885594.7420338717
5514508001021916.58961643428883.41038357
5613338001269459.003840964340.9961590976
5711934001293006.98516221-99606.9851622062
5814976001214373.1621643283226.837835703
5913806001374911.941979385688.05802062084
6019890001364429.82955293624570.170447073
6115678001742461.67270011-174661.67270011
629126001625857.41786487-713257.417864873
639594001169234.74319885-209834.743198854
647956001020583.53722719-224983.53722719
651099800860067.829212215239732.170787785
661263600988711.242415348274888.757584652
6715912001142113.036874449086.963125995
6815678001407939.40448399159860.595516012
6912636001497271.37548581-233671.37548581
7014742001341392.463137132807.536863001
7113104001412915.40949928-102515.409499283
7218720001338225.8306005533774.169399499
7314274001661761.27700464-234361.277004637
7411466001509159.20657511-362559.206575105
7510296001273460.35137409-243860.351374087
767722001108193.47895977-335993.478959768
771146600882359.7422164264240.2577836
7813806001029498.44393636351101.556063635
7916146001234123.90953239380476.090467611
8015210001461129.0905541159870.9094458928
8111232001491174.11695751-367974.116957509
8216146001253348.44387273361251.556127267
8312636001469099.72002957-205499.720029565
8419422001333177.90888804609022.091111961
8516146001706194.7290846-91594.7290846023
8611700001646297.97837007-476297.978370073
8710764001343908.32785597-267508.327855974
887254001167220.29269729-441820.292697287
891146600878119.153560385268480.846439615
9010998001029887.5247587569912.4752412521
9116614001060036.31784296601363.682157042
9216614001424542.97501117236857.024988827
9312636001567014.35254924-303414.352549238
9416380001373036.34973729264963.650262712
9512168001532401.90226325-315601.902263251
9618954001330342.46489593565057.535104071
9716146001677497.58078164-62897.580781643
9811934001636852.60943247-443452.609432467
999126001356640.65591798-444040.65591798
1006318001071080.26023202-439280.260232017
1011240200783521.844607609456678.155392391
10211934001053391.8684346140008.131565396
10315678001129627.33612525438172.663874749
10418018001394582.07147807407217.92852193
10513338001645027.69076355-311227.690763552
10614976001449103.2661973548496.7338026545
10711232001475470.3029335-352270.302933505
10819422001250834.80638178691365.19361822







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
1091677296.350929281074572.684870332280020.01698823
1101677575.83521979965963.0416161822389188.6288234
1111677855.31951031868734.7489076562486975.89011296
1121678134.80380082779125.6762766172577143.93132502
1131678414.28809134694997.6351374782661830.94104519
1141678693.77238185615001.8959129222742385.64885078
1151678973.25667236538225.5632111382819720.95013359
1161679252.74096288464018.3627425512894487.11918321
1171679532.22525339391898.7781231472967165.67238364
1181679811.70954391321499.2252070953038124.19388072
1191680091.19383442252532.1122875533107650.2753813
1201680370.67812494184767.8306878833175973.52556199

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
109 & 1677296.35092928 & 1074572.68487033 & 2280020.01698823 \tabularnewline
110 & 1677575.83521979 & 965963.041616182 & 2389188.6288234 \tabularnewline
111 & 1677855.31951031 & 868734.748907656 & 2486975.89011296 \tabularnewline
112 & 1678134.80380082 & 779125.676276617 & 2577143.93132502 \tabularnewline
113 & 1678414.28809134 & 694997.635137478 & 2661830.94104519 \tabularnewline
114 & 1678693.77238185 & 615001.895912922 & 2742385.64885078 \tabularnewline
115 & 1678973.25667236 & 538225.563211138 & 2819720.95013359 \tabularnewline
116 & 1679252.74096288 & 464018.362742551 & 2894487.11918321 \tabularnewline
117 & 1679532.22525339 & 391898.778123147 & 2967165.67238364 \tabularnewline
118 & 1679811.70954391 & 321499.225207095 & 3038124.19388072 \tabularnewline
119 & 1680091.19383442 & 252532.112287553 & 3107650.2753813 \tabularnewline
120 & 1680370.67812494 & 184767.830687883 & 3175973.52556199 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=307503&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]109[/C][C]1677296.35092928[/C][C]1074572.68487033[/C][C]2280020.01698823[/C][/ROW]
[ROW][C]110[/C][C]1677575.83521979[/C][C]965963.041616182[/C][C]2389188.6288234[/C][/ROW]
[ROW][C]111[/C][C]1677855.31951031[/C][C]868734.748907656[/C][C]2486975.89011296[/C][/ROW]
[ROW][C]112[/C][C]1678134.80380082[/C][C]779125.676276617[/C][C]2577143.93132502[/C][/ROW]
[ROW][C]113[/C][C]1678414.28809134[/C][C]694997.635137478[/C][C]2661830.94104519[/C][/ROW]
[ROW][C]114[/C][C]1678693.77238185[/C][C]615001.895912922[/C][C]2742385.64885078[/C][/ROW]
[ROW][C]115[/C][C]1678973.25667236[/C][C]538225.563211138[/C][C]2819720.95013359[/C][/ROW]
[ROW][C]116[/C][C]1679252.74096288[/C][C]464018.362742551[/C][C]2894487.11918321[/C][/ROW]
[ROW][C]117[/C][C]1679532.22525339[/C][C]391898.778123147[/C][C]2967165.67238364[/C][/ROW]
[ROW][C]118[/C][C]1679811.70954391[/C][C]321499.225207095[/C][C]3038124.19388072[/C][/ROW]
[ROW][C]119[/C][C]1680091.19383442[/C][C]252532.112287553[/C][C]3107650.2753813[/C][/ROW]
[ROW][C]120[/C][C]1680370.67812494[/C][C]184767.830687883[/C][C]3175973.52556199[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=307503&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=307503&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
1091677296.350929281074572.684870332280020.01698823
1101677575.83521979965963.0416161822389188.6288234
1111677855.31951031868734.7489076562486975.89011296
1121678134.80380082779125.6762766172577143.93132502
1131678414.28809134694997.6351374782661830.94104519
1141678693.77238185615001.8959129222742385.64885078
1151678973.25667236538225.5632111382819720.95013359
1161679252.74096288464018.3627425512894487.11918321
1171679532.22525339391898.7781231472967165.67238364
1181679811.70954391321499.2252070953038124.19388072
1191680091.19383442252532.1122875533107650.2753813
1201680370.67812494184767.8306878833175973.52556199



Parameters (Session):
Parameters (R input):
par1 = 12 ; par2 = Double ; 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')