Free Statistics

of Irreproducible Research!

Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationMon, 15 Aug 2016 20:49:06 +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/2016/Aug/15/t14712905806irohhqtlr3g02g.htm/, Retrieved Sun, 28 Apr 2024 06:12:31 +0200
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=, Retrieved Sun, 28 Apr 2024 06:12:31 +0200
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact0
Dataseries X:
1943
1932
1922
1901
2108
2098
1943
1839
1850
1850
1860
1881
1839
1819
1757
1664
1922
1839
1633
1674
1633
1736
1591
1684
1602
1581
1416
1354
1664
1602
1405
1529
1426
1509
1426
1571
1447
1426
1230
1168
1612
1509
1333
1498
1374
1333
1312
1416
1240
1240
1095
1044
1560
1426
1302
1405
1261
1199
1250
1405
1199
1281
1178
1137
1591
1498
1250
1374
1312
1354
1426
1622
1488
1540
1457
1395
1860
1746
1467
1426
1343
1374
1354
1529
1343
1405
1364
1323
1829
1726
1447
1343
1188
1199
1178
1323
1064
1054
1013
899
1467
1405
1095
1002
847
816
713
858
486
444
403
331
940
889
568
506
351
362
300
403




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'Herman Ole Andreas Wold' @ wold.wessa.net

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input & view raw input (R code)  \tabularnewline
Raw Output & view raw output of R engine  \tabularnewline
Computing time & 2 seconds \tabularnewline
R Server & 'Herman Ole Andreas Wold' @ wold.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=&T=0

[TABLE]
[ROW][C]Summary of computational transaction[/C][/ROW]
[ROW][C]Raw Input[/C][C]view raw input (R code) [/C][/ROW]
[ROW][C]Raw Output[/C][C]view raw output of R engine [/C][/ROW]
[ROW][C]Computing time[/C][C]2 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Herman Ole Andreas Wold' @ wold.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=&T=0

As an alternative you can also use a QR Code:  

The GUIDs for individual cells are displayed in the table below:

Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'Herman Ole Andreas Wold' @ wold.wessa.net







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.441686427472862
beta0
gammaFALSE

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.441686427472862 \tabularnewline
beta & 0 \tabularnewline
gamma & FALSE \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=&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]0.441686427472862[/C][/ROW]
[ROW][C]beta[/C][C]0[/C][/ROW]
[ROW][C]gamma[/C][C]FALSE[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=&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
alpha0.441686427472862
beta0
gammaFALSE







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
3192219211
419011910.44168642747-9.44168642747286
521081895.27142168212.728578319997
620981978.23074745954119.769252540456
719432020.13120073523-77.1312007352328
818391975.0633962358-136.063396235796
918501903.96604084258-53.9660408425825
1018501869.12997305797-19.1299730579676
1118601849.6805236003410.319476399658
1218811843.238496264737.7615037353025
1318391848.91723994555-9.9172399455465
1418191833.53692966361-14.5369296636072
1517571816.11616513406-59.1161651340644
1616641779.0053573501-115.005357350104
1719221717.2090519219204.790948078103
1818391796.6624341572942.3375658427053
1916331804.36236236226-171.362362362256
2016741717.67393272716-43.6739327271616
2116331687.38374940721-54.3837494072118
2217361652.3631854189683.6368145810388
2315911678.30443125647-87.3044312564705
2416841628.7432489122555.2567510877498
2516021642.14940589396-40.1494058939556
2615811613.4159582395-32.4159582394966
2714161588.09826945158-172.098269451584
2813541501.08479964325-147.084799643252
2916641425.11943995326238.880560046738
3016021519.6297411130282.3702588869776
3114051545.01156649083-140.011566490826
3215291472.1703578826156.8296421173859
3314261486.271239484-60.2712394840037
3415091448.6502510369560.3497489630472
3514261464.30591605533-38.3059160553253
3615711436.38671284177134.613287158227
3714471484.84357473707-37.843574737069
3814261457.12858140865-31.1285814086509
3912301432.37950949397-202.379509493966
4011681331.99122695187-163.991226951866
4116121248.55852778261363.441472217395
4215091398.08569324178110.914306758216
4313331436.07503714945-103.075037149449
4414981379.54819222928118.451807770723
4513741420.86674803123-46.8667480312297
4613331389.16634152605-56.1663415260452
4713121353.35843079319-41.3584307931858
4814161324.0909732502691.90902674974
4912401353.68594292786-113.68594292786
5012401292.47240494217-52.4724049421702
5110951258.29605586235-163.296055862354
5210441175.1704043281-131.170404328102
5315601106.23421705025453.765782949748
5414261295.65640463075130.343595369248
5513021342.22740161336-40.2274016133638
5614051313.4595043082491.5404956917587
5712611342.89169881943-81.8916988194292
5811991295.72124692819-96.7212469281919
5912501242.000784911767.99921508824173
6014051234.53392964667170.466070353329
6111991298.82647926637-99.8264792663704
6212811243.7344782720137.2655217279864
6311781249.19415343196-71.1941534319603
6411371206.74866214564-69.7486621456433
6515911164.94162474152426.058375258478
6614981342.12582640433155.874173595669
6712501399.97333327509-149.973333275087
6813741322.7321474846251.2678525153829
6913121334.37646210634-22.3764621063424
7013541313.4930824991140.5069175008898
7114261320.38443817802105.615561821984
7216221356.03339836471265.966601635292
7314881462.507236468125.4927635319023
7415401462.7670441189177.2329558810857
7514571485.8797924852-28.8797924852004
7613951462.12398011625-67.1239801162546
7718601421.47622914095438.523770859053
7817461604.16622685361141.83377314639
7914671655.81227940964-188.812279409635
8014261561.41645825419-135.416458254186
8113431490.60484658687-147.604846586867
8213741414.40978922023-40.4097892202337
8313541385.56133378462-31.5613337846175
8415291360.62112101901168.378878980989
8513431423.99178653801-80.9917865380098
8614051377.2188136873927.7811863126083
8713641378.48938662077-14.4893866207658
8813231361.08962120797-38.0896212079667
8918291333.26595249283495.734047507175
9017261541.22495291293184.775047087069
9114471611.83758334695-164.837583346949
9213431528.03106004517-185.031060045175
9311881435.30535216231-247.305352162305
9411991315.07393467082-116.073934670819
9511781252.80565314335-74.8056531433465
9613231208.76501145169114.234988548312
9710641248.221055436-184.221055435995
9810541155.85311559519-101.853115595191
9910131099.86597684097-86.8659768409705
1008991050.49845386114-151.498453861142
1011467972.583643007552494.416356992448
10214051179.96063741169225.039362588307
10310951268.35746951409-173.357469514093
10410021180.78782812868-178.787828128678
1058471090.81967104689-243.81967104689
106816972.127831594581-156.127831594581
107713892.168287428486-179.168287428486
108858802.03208663776755.9679133622328
109486815.752354343842-329.752354343842
110444659.105215002945-215.105215002945
111403553.096161057513-150.096161057513
112331475.800723902629-144.800723902629
113940400.844209466592539.155790533408
114889627.9820044386261.0179955614
115568732.270110404242-164.270110404242
116506648.71423219922-142.71423219922
117351574.679292829614-223.679292829614
118362464.883185080046-102.883185080046
119300408.441078615011-108.441078615011
120403349.54412601024353.4558739897569

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
3 & 1922 & 1921 & 1 \tabularnewline
4 & 1901 & 1910.44168642747 & -9.44168642747286 \tabularnewline
5 & 2108 & 1895.27142168 & 212.728578319997 \tabularnewline
6 & 2098 & 1978.23074745954 & 119.769252540456 \tabularnewline
7 & 1943 & 2020.13120073523 & -77.1312007352328 \tabularnewline
8 & 1839 & 1975.0633962358 & -136.063396235796 \tabularnewline
9 & 1850 & 1903.96604084258 & -53.9660408425825 \tabularnewline
10 & 1850 & 1869.12997305797 & -19.1299730579676 \tabularnewline
11 & 1860 & 1849.68052360034 & 10.319476399658 \tabularnewline
12 & 1881 & 1843.2384962647 & 37.7615037353025 \tabularnewline
13 & 1839 & 1848.91723994555 & -9.9172399455465 \tabularnewline
14 & 1819 & 1833.53692966361 & -14.5369296636072 \tabularnewline
15 & 1757 & 1816.11616513406 & -59.1161651340644 \tabularnewline
16 & 1664 & 1779.0053573501 & -115.005357350104 \tabularnewline
17 & 1922 & 1717.2090519219 & 204.790948078103 \tabularnewline
18 & 1839 & 1796.66243415729 & 42.3375658427053 \tabularnewline
19 & 1633 & 1804.36236236226 & -171.362362362256 \tabularnewline
20 & 1674 & 1717.67393272716 & -43.6739327271616 \tabularnewline
21 & 1633 & 1687.38374940721 & -54.3837494072118 \tabularnewline
22 & 1736 & 1652.36318541896 & 83.6368145810388 \tabularnewline
23 & 1591 & 1678.30443125647 & -87.3044312564705 \tabularnewline
24 & 1684 & 1628.74324891225 & 55.2567510877498 \tabularnewline
25 & 1602 & 1642.14940589396 & -40.1494058939556 \tabularnewline
26 & 1581 & 1613.4159582395 & -32.4159582394966 \tabularnewline
27 & 1416 & 1588.09826945158 & -172.098269451584 \tabularnewline
28 & 1354 & 1501.08479964325 & -147.084799643252 \tabularnewline
29 & 1664 & 1425.11943995326 & 238.880560046738 \tabularnewline
30 & 1602 & 1519.62974111302 & 82.3702588869776 \tabularnewline
31 & 1405 & 1545.01156649083 & -140.011566490826 \tabularnewline
32 & 1529 & 1472.17035788261 & 56.8296421173859 \tabularnewline
33 & 1426 & 1486.271239484 & -60.2712394840037 \tabularnewline
34 & 1509 & 1448.65025103695 & 60.3497489630472 \tabularnewline
35 & 1426 & 1464.30591605533 & -38.3059160553253 \tabularnewline
36 & 1571 & 1436.38671284177 & 134.613287158227 \tabularnewline
37 & 1447 & 1484.84357473707 & -37.843574737069 \tabularnewline
38 & 1426 & 1457.12858140865 & -31.1285814086509 \tabularnewline
39 & 1230 & 1432.37950949397 & -202.379509493966 \tabularnewline
40 & 1168 & 1331.99122695187 & -163.991226951866 \tabularnewline
41 & 1612 & 1248.55852778261 & 363.441472217395 \tabularnewline
42 & 1509 & 1398.08569324178 & 110.914306758216 \tabularnewline
43 & 1333 & 1436.07503714945 & -103.075037149449 \tabularnewline
44 & 1498 & 1379.54819222928 & 118.451807770723 \tabularnewline
45 & 1374 & 1420.86674803123 & -46.8667480312297 \tabularnewline
46 & 1333 & 1389.16634152605 & -56.1663415260452 \tabularnewline
47 & 1312 & 1353.35843079319 & -41.3584307931858 \tabularnewline
48 & 1416 & 1324.09097325026 & 91.90902674974 \tabularnewline
49 & 1240 & 1353.68594292786 & -113.68594292786 \tabularnewline
50 & 1240 & 1292.47240494217 & -52.4724049421702 \tabularnewline
51 & 1095 & 1258.29605586235 & -163.296055862354 \tabularnewline
52 & 1044 & 1175.1704043281 & -131.170404328102 \tabularnewline
53 & 1560 & 1106.23421705025 & 453.765782949748 \tabularnewline
54 & 1426 & 1295.65640463075 & 130.343595369248 \tabularnewline
55 & 1302 & 1342.22740161336 & -40.2274016133638 \tabularnewline
56 & 1405 & 1313.45950430824 & 91.5404956917587 \tabularnewline
57 & 1261 & 1342.89169881943 & -81.8916988194292 \tabularnewline
58 & 1199 & 1295.72124692819 & -96.7212469281919 \tabularnewline
59 & 1250 & 1242.00078491176 & 7.99921508824173 \tabularnewline
60 & 1405 & 1234.53392964667 & 170.466070353329 \tabularnewline
61 & 1199 & 1298.82647926637 & -99.8264792663704 \tabularnewline
62 & 1281 & 1243.73447827201 & 37.2655217279864 \tabularnewline
63 & 1178 & 1249.19415343196 & -71.1941534319603 \tabularnewline
64 & 1137 & 1206.74866214564 & -69.7486621456433 \tabularnewline
65 & 1591 & 1164.94162474152 & 426.058375258478 \tabularnewline
66 & 1498 & 1342.12582640433 & 155.874173595669 \tabularnewline
67 & 1250 & 1399.97333327509 & -149.973333275087 \tabularnewline
68 & 1374 & 1322.73214748462 & 51.2678525153829 \tabularnewline
69 & 1312 & 1334.37646210634 & -22.3764621063424 \tabularnewline
70 & 1354 & 1313.49308249911 & 40.5069175008898 \tabularnewline
71 & 1426 & 1320.38443817802 & 105.615561821984 \tabularnewline
72 & 1622 & 1356.03339836471 & 265.966601635292 \tabularnewline
73 & 1488 & 1462.5072364681 & 25.4927635319023 \tabularnewline
74 & 1540 & 1462.76704411891 & 77.2329558810857 \tabularnewline
75 & 1457 & 1485.8797924852 & -28.8797924852004 \tabularnewline
76 & 1395 & 1462.12398011625 & -67.1239801162546 \tabularnewline
77 & 1860 & 1421.47622914095 & 438.523770859053 \tabularnewline
78 & 1746 & 1604.16622685361 & 141.83377314639 \tabularnewline
79 & 1467 & 1655.81227940964 & -188.812279409635 \tabularnewline
80 & 1426 & 1561.41645825419 & -135.416458254186 \tabularnewline
81 & 1343 & 1490.60484658687 & -147.604846586867 \tabularnewline
82 & 1374 & 1414.40978922023 & -40.4097892202337 \tabularnewline
83 & 1354 & 1385.56133378462 & -31.5613337846175 \tabularnewline
84 & 1529 & 1360.62112101901 & 168.378878980989 \tabularnewline
85 & 1343 & 1423.99178653801 & -80.9917865380098 \tabularnewline
86 & 1405 & 1377.21881368739 & 27.7811863126083 \tabularnewline
87 & 1364 & 1378.48938662077 & -14.4893866207658 \tabularnewline
88 & 1323 & 1361.08962120797 & -38.0896212079667 \tabularnewline
89 & 1829 & 1333.26595249283 & 495.734047507175 \tabularnewline
90 & 1726 & 1541.22495291293 & 184.775047087069 \tabularnewline
91 & 1447 & 1611.83758334695 & -164.837583346949 \tabularnewline
92 & 1343 & 1528.03106004517 & -185.031060045175 \tabularnewline
93 & 1188 & 1435.30535216231 & -247.305352162305 \tabularnewline
94 & 1199 & 1315.07393467082 & -116.073934670819 \tabularnewline
95 & 1178 & 1252.80565314335 & -74.8056531433465 \tabularnewline
96 & 1323 & 1208.76501145169 & 114.234988548312 \tabularnewline
97 & 1064 & 1248.221055436 & -184.221055435995 \tabularnewline
98 & 1054 & 1155.85311559519 & -101.853115595191 \tabularnewline
99 & 1013 & 1099.86597684097 & -86.8659768409705 \tabularnewline
100 & 899 & 1050.49845386114 & -151.498453861142 \tabularnewline
101 & 1467 & 972.583643007552 & 494.416356992448 \tabularnewline
102 & 1405 & 1179.96063741169 & 225.039362588307 \tabularnewline
103 & 1095 & 1268.35746951409 & -173.357469514093 \tabularnewline
104 & 1002 & 1180.78782812868 & -178.787828128678 \tabularnewline
105 & 847 & 1090.81967104689 & -243.81967104689 \tabularnewline
106 & 816 & 972.127831594581 & -156.127831594581 \tabularnewline
107 & 713 & 892.168287428486 & -179.168287428486 \tabularnewline
108 & 858 & 802.032086637767 & 55.9679133622328 \tabularnewline
109 & 486 & 815.752354343842 & -329.752354343842 \tabularnewline
110 & 444 & 659.105215002945 & -215.105215002945 \tabularnewline
111 & 403 & 553.096161057513 & -150.096161057513 \tabularnewline
112 & 331 & 475.800723902629 & -144.800723902629 \tabularnewline
113 & 940 & 400.844209466592 & 539.155790533408 \tabularnewline
114 & 889 & 627.9820044386 & 261.0179955614 \tabularnewline
115 & 568 & 732.270110404242 & -164.270110404242 \tabularnewline
116 & 506 & 648.71423219922 & -142.71423219922 \tabularnewline
117 & 351 & 574.679292829614 & -223.679292829614 \tabularnewline
118 & 362 & 464.883185080046 & -102.883185080046 \tabularnewline
119 & 300 & 408.441078615011 & -108.441078615011 \tabularnewline
120 & 403 & 349.544126010243 & 53.4558739897569 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=&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]1922[/C][C]1921[/C][C]1[/C][/ROW]
[ROW][C]4[/C][C]1901[/C][C]1910.44168642747[/C][C]-9.44168642747286[/C][/ROW]
[ROW][C]5[/C][C]2108[/C][C]1895.27142168[/C][C]212.728578319997[/C][/ROW]
[ROW][C]6[/C][C]2098[/C][C]1978.23074745954[/C][C]119.769252540456[/C][/ROW]
[ROW][C]7[/C][C]1943[/C][C]2020.13120073523[/C][C]-77.1312007352328[/C][/ROW]
[ROW][C]8[/C][C]1839[/C][C]1975.0633962358[/C][C]-136.063396235796[/C][/ROW]
[ROW][C]9[/C][C]1850[/C][C]1903.96604084258[/C][C]-53.9660408425825[/C][/ROW]
[ROW][C]10[/C][C]1850[/C][C]1869.12997305797[/C][C]-19.1299730579676[/C][/ROW]
[ROW][C]11[/C][C]1860[/C][C]1849.68052360034[/C][C]10.319476399658[/C][/ROW]
[ROW][C]12[/C][C]1881[/C][C]1843.2384962647[/C][C]37.7615037353025[/C][/ROW]
[ROW][C]13[/C][C]1839[/C][C]1848.91723994555[/C][C]-9.9172399455465[/C][/ROW]
[ROW][C]14[/C][C]1819[/C][C]1833.53692966361[/C][C]-14.5369296636072[/C][/ROW]
[ROW][C]15[/C][C]1757[/C][C]1816.11616513406[/C][C]-59.1161651340644[/C][/ROW]
[ROW][C]16[/C][C]1664[/C][C]1779.0053573501[/C][C]-115.005357350104[/C][/ROW]
[ROW][C]17[/C][C]1922[/C][C]1717.2090519219[/C][C]204.790948078103[/C][/ROW]
[ROW][C]18[/C][C]1839[/C][C]1796.66243415729[/C][C]42.3375658427053[/C][/ROW]
[ROW][C]19[/C][C]1633[/C][C]1804.36236236226[/C][C]-171.362362362256[/C][/ROW]
[ROW][C]20[/C][C]1674[/C][C]1717.67393272716[/C][C]-43.6739327271616[/C][/ROW]
[ROW][C]21[/C][C]1633[/C][C]1687.38374940721[/C][C]-54.3837494072118[/C][/ROW]
[ROW][C]22[/C][C]1736[/C][C]1652.36318541896[/C][C]83.6368145810388[/C][/ROW]
[ROW][C]23[/C][C]1591[/C][C]1678.30443125647[/C][C]-87.3044312564705[/C][/ROW]
[ROW][C]24[/C][C]1684[/C][C]1628.74324891225[/C][C]55.2567510877498[/C][/ROW]
[ROW][C]25[/C][C]1602[/C][C]1642.14940589396[/C][C]-40.1494058939556[/C][/ROW]
[ROW][C]26[/C][C]1581[/C][C]1613.4159582395[/C][C]-32.4159582394966[/C][/ROW]
[ROW][C]27[/C][C]1416[/C][C]1588.09826945158[/C][C]-172.098269451584[/C][/ROW]
[ROW][C]28[/C][C]1354[/C][C]1501.08479964325[/C][C]-147.084799643252[/C][/ROW]
[ROW][C]29[/C][C]1664[/C][C]1425.11943995326[/C][C]238.880560046738[/C][/ROW]
[ROW][C]30[/C][C]1602[/C][C]1519.62974111302[/C][C]82.3702588869776[/C][/ROW]
[ROW][C]31[/C][C]1405[/C][C]1545.01156649083[/C][C]-140.011566490826[/C][/ROW]
[ROW][C]32[/C][C]1529[/C][C]1472.17035788261[/C][C]56.8296421173859[/C][/ROW]
[ROW][C]33[/C][C]1426[/C][C]1486.271239484[/C][C]-60.2712394840037[/C][/ROW]
[ROW][C]34[/C][C]1509[/C][C]1448.65025103695[/C][C]60.3497489630472[/C][/ROW]
[ROW][C]35[/C][C]1426[/C][C]1464.30591605533[/C][C]-38.3059160553253[/C][/ROW]
[ROW][C]36[/C][C]1571[/C][C]1436.38671284177[/C][C]134.613287158227[/C][/ROW]
[ROW][C]37[/C][C]1447[/C][C]1484.84357473707[/C][C]-37.843574737069[/C][/ROW]
[ROW][C]38[/C][C]1426[/C][C]1457.12858140865[/C][C]-31.1285814086509[/C][/ROW]
[ROW][C]39[/C][C]1230[/C][C]1432.37950949397[/C][C]-202.379509493966[/C][/ROW]
[ROW][C]40[/C][C]1168[/C][C]1331.99122695187[/C][C]-163.991226951866[/C][/ROW]
[ROW][C]41[/C][C]1612[/C][C]1248.55852778261[/C][C]363.441472217395[/C][/ROW]
[ROW][C]42[/C][C]1509[/C][C]1398.08569324178[/C][C]110.914306758216[/C][/ROW]
[ROW][C]43[/C][C]1333[/C][C]1436.07503714945[/C][C]-103.075037149449[/C][/ROW]
[ROW][C]44[/C][C]1498[/C][C]1379.54819222928[/C][C]118.451807770723[/C][/ROW]
[ROW][C]45[/C][C]1374[/C][C]1420.86674803123[/C][C]-46.8667480312297[/C][/ROW]
[ROW][C]46[/C][C]1333[/C][C]1389.16634152605[/C][C]-56.1663415260452[/C][/ROW]
[ROW][C]47[/C][C]1312[/C][C]1353.35843079319[/C][C]-41.3584307931858[/C][/ROW]
[ROW][C]48[/C][C]1416[/C][C]1324.09097325026[/C][C]91.90902674974[/C][/ROW]
[ROW][C]49[/C][C]1240[/C][C]1353.68594292786[/C][C]-113.68594292786[/C][/ROW]
[ROW][C]50[/C][C]1240[/C][C]1292.47240494217[/C][C]-52.4724049421702[/C][/ROW]
[ROW][C]51[/C][C]1095[/C][C]1258.29605586235[/C][C]-163.296055862354[/C][/ROW]
[ROW][C]52[/C][C]1044[/C][C]1175.1704043281[/C][C]-131.170404328102[/C][/ROW]
[ROW][C]53[/C][C]1560[/C][C]1106.23421705025[/C][C]453.765782949748[/C][/ROW]
[ROW][C]54[/C][C]1426[/C][C]1295.65640463075[/C][C]130.343595369248[/C][/ROW]
[ROW][C]55[/C][C]1302[/C][C]1342.22740161336[/C][C]-40.2274016133638[/C][/ROW]
[ROW][C]56[/C][C]1405[/C][C]1313.45950430824[/C][C]91.5404956917587[/C][/ROW]
[ROW][C]57[/C][C]1261[/C][C]1342.89169881943[/C][C]-81.8916988194292[/C][/ROW]
[ROW][C]58[/C][C]1199[/C][C]1295.72124692819[/C][C]-96.7212469281919[/C][/ROW]
[ROW][C]59[/C][C]1250[/C][C]1242.00078491176[/C][C]7.99921508824173[/C][/ROW]
[ROW][C]60[/C][C]1405[/C][C]1234.53392964667[/C][C]170.466070353329[/C][/ROW]
[ROW][C]61[/C][C]1199[/C][C]1298.82647926637[/C][C]-99.8264792663704[/C][/ROW]
[ROW][C]62[/C][C]1281[/C][C]1243.73447827201[/C][C]37.2655217279864[/C][/ROW]
[ROW][C]63[/C][C]1178[/C][C]1249.19415343196[/C][C]-71.1941534319603[/C][/ROW]
[ROW][C]64[/C][C]1137[/C][C]1206.74866214564[/C][C]-69.7486621456433[/C][/ROW]
[ROW][C]65[/C][C]1591[/C][C]1164.94162474152[/C][C]426.058375258478[/C][/ROW]
[ROW][C]66[/C][C]1498[/C][C]1342.12582640433[/C][C]155.874173595669[/C][/ROW]
[ROW][C]67[/C][C]1250[/C][C]1399.97333327509[/C][C]-149.973333275087[/C][/ROW]
[ROW][C]68[/C][C]1374[/C][C]1322.73214748462[/C][C]51.2678525153829[/C][/ROW]
[ROW][C]69[/C][C]1312[/C][C]1334.37646210634[/C][C]-22.3764621063424[/C][/ROW]
[ROW][C]70[/C][C]1354[/C][C]1313.49308249911[/C][C]40.5069175008898[/C][/ROW]
[ROW][C]71[/C][C]1426[/C][C]1320.38443817802[/C][C]105.615561821984[/C][/ROW]
[ROW][C]72[/C][C]1622[/C][C]1356.03339836471[/C][C]265.966601635292[/C][/ROW]
[ROW][C]73[/C][C]1488[/C][C]1462.5072364681[/C][C]25.4927635319023[/C][/ROW]
[ROW][C]74[/C][C]1540[/C][C]1462.76704411891[/C][C]77.2329558810857[/C][/ROW]
[ROW][C]75[/C][C]1457[/C][C]1485.8797924852[/C][C]-28.8797924852004[/C][/ROW]
[ROW][C]76[/C][C]1395[/C][C]1462.12398011625[/C][C]-67.1239801162546[/C][/ROW]
[ROW][C]77[/C][C]1860[/C][C]1421.47622914095[/C][C]438.523770859053[/C][/ROW]
[ROW][C]78[/C][C]1746[/C][C]1604.16622685361[/C][C]141.83377314639[/C][/ROW]
[ROW][C]79[/C][C]1467[/C][C]1655.81227940964[/C][C]-188.812279409635[/C][/ROW]
[ROW][C]80[/C][C]1426[/C][C]1561.41645825419[/C][C]-135.416458254186[/C][/ROW]
[ROW][C]81[/C][C]1343[/C][C]1490.60484658687[/C][C]-147.604846586867[/C][/ROW]
[ROW][C]82[/C][C]1374[/C][C]1414.40978922023[/C][C]-40.4097892202337[/C][/ROW]
[ROW][C]83[/C][C]1354[/C][C]1385.56133378462[/C][C]-31.5613337846175[/C][/ROW]
[ROW][C]84[/C][C]1529[/C][C]1360.62112101901[/C][C]168.378878980989[/C][/ROW]
[ROW][C]85[/C][C]1343[/C][C]1423.99178653801[/C][C]-80.9917865380098[/C][/ROW]
[ROW][C]86[/C][C]1405[/C][C]1377.21881368739[/C][C]27.7811863126083[/C][/ROW]
[ROW][C]87[/C][C]1364[/C][C]1378.48938662077[/C][C]-14.4893866207658[/C][/ROW]
[ROW][C]88[/C][C]1323[/C][C]1361.08962120797[/C][C]-38.0896212079667[/C][/ROW]
[ROW][C]89[/C][C]1829[/C][C]1333.26595249283[/C][C]495.734047507175[/C][/ROW]
[ROW][C]90[/C][C]1726[/C][C]1541.22495291293[/C][C]184.775047087069[/C][/ROW]
[ROW][C]91[/C][C]1447[/C][C]1611.83758334695[/C][C]-164.837583346949[/C][/ROW]
[ROW][C]92[/C][C]1343[/C][C]1528.03106004517[/C][C]-185.031060045175[/C][/ROW]
[ROW][C]93[/C][C]1188[/C][C]1435.30535216231[/C][C]-247.305352162305[/C][/ROW]
[ROW][C]94[/C][C]1199[/C][C]1315.07393467082[/C][C]-116.073934670819[/C][/ROW]
[ROW][C]95[/C][C]1178[/C][C]1252.80565314335[/C][C]-74.8056531433465[/C][/ROW]
[ROW][C]96[/C][C]1323[/C][C]1208.76501145169[/C][C]114.234988548312[/C][/ROW]
[ROW][C]97[/C][C]1064[/C][C]1248.221055436[/C][C]-184.221055435995[/C][/ROW]
[ROW][C]98[/C][C]1054[/C][C]1155.85311559519[/C][C]-101.853115595191[/C][/ROW]
[ROW][C]99[/C][C]1013[/C][C]1099.86597684097[/C][C]-86.8659768409705[/C][/ROW]
[ROW][C]100[/C][C]899[/C][C]1050.49845386114[/C][C]-151.498453861142[/C][/ROW]
[ROW][C]101[/C][C]1467[/C][C]972.583643007552[/C][C]494.416356992448[/C][/ROW]
[ROW][C]102[/C][C]1405[/C][C]1179.96063741169[/C][C]225.039362588307[/C][/ROW]
[ROW][C]103[/C][C]1095[/C][C]1268.35746951409[/C][C]-173.357469514093[/C][/ROW]
[ROW][C]104[/C][C]1002[/C][C]1180.78782812868[/C][C]-178.787828128678[/C][/ROW]
[ROW][C]105[/C][C]847[/C][C]1090.81967104689[/C][C]-243.81967104689[/C][/ROW]
[ROW][C]106[/C][C]816[/C][C]972.127831594581[/C][C]-156.127831594581[/C][/ROW]
[ROW][C]107[/C][C]713[/C][C]892.168287428486[/C][C]-179.168287428486[/C][/ROW]
[ROW][C]108[/C][C]858[/C][C]802.032086637767[/C][C]55.9679133622328[/C][/ROW]
[ROW][C]109[/C][C]486[/C][C]815.752354343842[/C][C]-329.752354343842[/C][/ROW]
[ROW][C]110[/C][C]444[/C][C]659.105215002945[/C][C]-215.105215002945[/C][/ROW]
[ROW][C]111[/C][C]403[/C][C]553.096161057513[/C][C]-150.096161057513[/C][/ROW]
[ROW][C]112[/C][C]331[/C][C]475.800723902629[/C][C]-144.800723902629[/C][/ROW]
[ROW][C]113[/C][C]940[/C][C]400.844209466592[/C][C]539.155790533408[/C][/ROW]
[ROW][C]114[/C][C]889[/C][C]627.9820044386[/C][C]261.0179955614[/C][/ROW]
[ROW][C]115[/C][C]568[/C][C]732.270110404242[/C][C]-164.270110404242[/C][/ROW]
[ROW][C]116[/C][C]506[/C][C]648.71423219922[/C][C]-142.71423219922[/C][/ROW]
[ROW][C]117[/C][C]351[/C][C]574.679292829614[/C][C]-223.679292829614[/C][/ROW]
[ROW][C]118[/C][C]362[/C][C]464.883185080046[/C][C]-102.883185080046[/C][/ROW]
[ROW][C]119[/C][C]300[/C][C]408.441078615011[/C][C]-108.441078615011[/C][/ROW]
[ROW][C]120[/C][C]403[/C][C]349.544126010243[/C][C]53.4558739897569[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=&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
3192219211
419011910.44168642747-9.44168642747286
521081895.27142168212.728578319997
620981978.23074745954119.769252540456
719432020.13120073523-77.1312007352328
818391975.0633962358-136.063396235796
918501903.96604084258-53.9660408425825
1018501869.12997305797-19.1299730579676
1118601849.6805236003410.319476399658
1218811843.238496264737.7615037353025
1318391848.91723994555-9.9172399455465
1418191833.53692966361-14.5369296636072
1517571816.11616513406-59.1161651340644
1616641779.0053573501-115.005357350104
1719221717.2090519219204.790948078103
1818391796.6624341572942.3375658427053
1916331804.36236236226-171.362362362256
2016741717.67393272716-43.6739327271616
2116331687.38374940721-54.3837494072118
2217361652.3631854189683.6368145810388
2315911678.30443125647-87.3044312564705
2416841628.7432489122555.2567510877498
2516021642.14940589396-40.1494058939556
2615811613.4159582395-32.4159582394966
2714161588.09826945158-172.098269451584
2813541501.08479964325-147.084799643252
2916641425.11943995326238.880560046738
3016021519.6297411130282.3702588869776
3114051545.01156649083-140.011566490826
3215291472.1703578826156.8296421173859
3314261486.271239484-60.2712394840037
3415091448.6502510369560.3497489630472
3514261464.30591605533-38.3059160553253
3615711436.38671284177134.613287158227
3714471484.84357473707-37.843574737069
3814261457.12858140865-31.1285814086509
3912301432.37950949397-202.379509493966
4011681331.99122695187-163.991226951866
4116121248.55852778261363.441472217395
4215091398.08569324178110.914306758216
4313331436.07503714945-103.075037149449
4414981379.54819222928118.451807770723
4513741420.86674803123-46.8667480312297
4613331389.16634152605-56.1663415260452
4713121353.35843079319-41.3584307931858
4814161324.0909732502691.90902674974
4912401353.68594292786-113.68594292786
5012401292.47240494217-52.4724049421702
5110951258.29605586235-163.296055862354
5210441175.1704043281-131.170404328102
5315601106.23421705025453.765782949748
5414261295.65640463075130.343595369248
5513021342.22740161336-40.2274016133638
5614051313.4595043082491.5404956917587
5712611342.89169881943-81.8916988194292
5811991295.72124692819-96.7212469281919
5912501242.000784911767.99921508824173
6014051234.53392964667170.466070353329
6111991298.82647926637-99.8264792663704
6212811243.7344782720137.2655217279864
6311781249.19415343196-71.1941534319603
6411371206.74866214564-69.7486621456433
6515911164.94162474152426.058375258478
6614981342.12582640433155.874173595669
6712501399.97333327509-149.973333275087
6813741322.7321474846251.2678525153829
6913121334.37646210634-22.3764621063424
7013541313.4930824991140.5069175008898
7114261320.38443817802105.615561821984
7216221356.03339836471265.966601635292
7314881462.507236468125.4927635319023
7415401462.7670441189177.2329558810857
7514571485.8797924852-28.8797924852004
7613951462.12398011625-67.1239801162546
7718601421.47622914095438.523770859053
7817461604.16622685361141.83377314639
7914671655.81227940964-188.812279409635
8014261561.41645825419-135.416458254186
8113431490.60484658687-147.604846586867
8213741414.40978922023-40.4097892202337
8313541385.56133378462-31.5613337846175
8415291360.62112101901168.378878980989
8513431423.99178653801-80.9917865380098
8614051377.2188136873927.7811863126083
8713641378.48938662077-14.4893866207658
8813231361.08962120797-38.0896212079667
8918291333.26595249283495.734047507175
9017261541.22495291293184.775047087069
9114471611.83758334695-164.837583346949
9213431528.03106004517-185.031060045175
9311881435.30535216231-247.305352162305
9411991315.07393467082-116.073934670819
9511781252.80565314335-74.8056531433465
9613231208.76501145169114.234988548312
9710641248.221055436-184.221055435995
9810541155.85311559519-101.853115595191
9910131099.86597684097-86.8659768409705
1008991050.49845386114-151.498453861142
1011467972.583643007552494.416356992448
10214051179.96063741169225.039362588307
10310951268.35746951409-173.357469514093
10410021180.78782812868-178.787828128678
1058471090.81967104689-243.81967104689
106816972.127831594581-156.127831594581
107713892.168287428486-179.168287428486
108858802.03208663776755.9679133622328
109486815.752354343842-329.752354343842
110444659.105215002945-215.105215002945
111403553.096161057513-150.096161057513
112331475.800723902629-144.800723902629
113940400.844209466592539.155790533408
114889627.9820044386261.0179955614
115568732.270110404242-164.270110404242
116506648.71423219922-142.71423219922
117351574.679292829614-223.679292829614
118362464.883185080046-102.883185080046
119300408.441078615011-108.441078615011
120403349.54412601024353.4558739897569







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
121362.15486002021832.9705651341515691.339154906285
122351.154860020218-8.70951055096998711.019230591407
123340.154860020218-47.9719625694579728.281682609894
124329.154860020218-85.3116592796143743.621379320051
125318.154860020218-121.074648127264757.3843681677
126307.154860020218-155.514164266517769.823884306953
127296.154860020218-188.822140714249781.131860754686
128285.154860020218-221.148168262608791.457888303045
129274.154860020218-252.61152240687800.921242447306
130263.154860020218-283.309124943367809.618844983803
131252.154860020218-313.321003363217817.630723403654
132241.154860020218-342.714146929288825.023866969724

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
121 & 362.154860020218 & 32.9705651341515 & 691.339154906285 \tabularnewline
122 & 351.154860020218 & -8.70951055096998 & 711.019230591407 \tabularnewline
123 & 340.154860020218 & -47.9719625694579 & 728.281682609894 \tabularnewline
124 & 329.154860020218 & -85.3116592796143 & 743.621379320051 \tabularnewline
125 & 318.154860020218 & -121.074648127264 & 757.3843681677 \tabularnewline
126 & 307.154860020218 & -155.514164266517 & 769.823884306953 \tabularnewline
127 & 296.154860020218 & -188.822140714249 & 781.131860754686 \tabularnewline
128 & 285.154860020218 & -221.148168262608 & 791.457888303045 \tabularnewline
129 & 274.154860020218 & -252.61152240687 & 800.921242447306 \tabularnewline
130 & 263.154860020218 & -283.309124943367 & 809.618844983803 \tabularnewline
131 & 252.154860020218 & -313.321003363217 & 817.630723403654 \tabularnewline
132 & 241.154860020218 & -342.714146929288 & 825.023866969724 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=&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]121[/C][C]362.154860020218[/C][C]32.9705651341515[/C][C]691.339154906285[/C][/ROW]
[ROW][C]122[/C][C]351.154860020218[/C][C]-8.70951055096998[/C][C]711.019230591407[/C][/ROW]
[ROW][C]123[/C][C]340.154860020218[/C][C]-47.9719625694579[/C][C]728.281682609894[/C][/ROW]
[ROW][C]124[/C][C]329.154860020218[/C][C]-85.3116592796143[/C][C]743.621379320051[/C][/ROW]
[ROW][C]125[/C][C]318.154860020218[/C][C]-121.074648127264[/C][C]757.3843681677[/C][/ROW]
[ROW][C]126[/C][C]307.154860020218[/C][C]-155.514164266517[/C][C]769.823884306953[/C][/ROW]
[ROW][C]127[/C][C]296.154860020218[/C][C]-188.822140714249[/C][C]781.131860754686[/C][/ROW]
[ROW][C]128[/C][C]285.154860020218[/C][C]-221.148168262608[/C][C]791.457888303045[/C][/ROW]
[ROW][C]129[/C][C]274.154860020218[/C][C]-252.61152240687[/C][C]800.921242447306[/C][/ROW]
[ROW][C]130[/C][C]263.154860020218[/C][C]-283.309124943367[/C][C]809.618844983803[/C][/ROW]
[ROW][C]131[/C][C]252.154860020218[/C][C]-313.321003363217[/C][C]817.630723403654[/C][/ROW]
[ROW][C]132[/C][C]241.154860020218[/C][C]-342.714146929288[/C][C]825.023866969724[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=&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
121362.15486002021832.9705651341515691.339154906285
122351.154860020218-8.70951055096998711.019230591407
123340.154860020218-47.9719625694579728.281682609894
124329.154860020218-85.3116592796143743.621379320051
125318.154860020218-121.074648127264757.3843681677
126307.154860020218-155.514164266517769.823884306953
127296.154860020218-188.822140714249781.131860754686
128285.154860020218-221.148168262608791.457888303045
129274.154860020218-252.61152240687800.921242447306
130263.154860020218-283.309124943367809.618844983803
131252.154860020218-313.321003363217817.630723403654
132241.154860020218-342.714146929288825.023866969724



Parameters (Session):
par1 = 12 ; par2 = Double ; par3 = additive ;
Parameters (R input):
par1 = 12 ; par2 = Double ; 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')