Free Statistics

of Irreproducible Research!

Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationTue, 26 May 2015 18:41:41 +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/2015/May/26/t1432662127ttg98ue9mggjos4.htm/, Retrieved Tue, 30 Apr 2024 16:00:18 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=279417, Retrieved Tue, 30 Apr 2024 16:00:18 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact121
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [] [2015-05-26 17:41:41] [f51cc71db71177f4a98625dd32633bf7] [Current]
Feedback Forum

Post a new message
Dataseries X:
950
775
805
680
705
755
715
860
900
1010
925
650
1060
1050
1025
1085
1160
1310
1445
1445
1615
1650
1255
1175
1300
1280
1390
1340
1110
1325
1265
1150
1430
1655
1570
1345
1430
1260
1495
1125
895
1085
870
1185
1455
1540
1615
1200
1260
1095
1160
1095
1300
1215
1245
1350
1300
1280
1270
1065
1340
1265
1155
930
880
925
980
1015
1040
1365
1160
1115
1630
1225
1200
1265
1140
1270
1445
1305
1665
1830
1690
1520




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time1 seconds
R Server'Sir Maurice George Kendall' @ kendall.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 & 1 seconds \tabularnewline
R Server & 'Sir Maurice George Kendall' @ kendall.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=279417&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]1 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Sir Maurice George Kendall' @ kendall.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=279417&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=279417&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 time1 seconds
R Server'Sir Maurice George Kendall' @ kendall.wessa.net







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.612673299501252
beta0.0228364348582505
gamma0.714213918449514

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.612673299501252 \tabularnewline
beta & 0.0228364348582505 \tabularnewline
gamma & 0.714213918449514 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=279417&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]0.612673299501252[/C][/ROW]
[ROW][C]beta[/C][C]0.0228364348582505[/C][/ROW]
[ROW][C]gamma[/C][C]0.714213918449514[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=279417&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=279417&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
alpha0.612673299501252
beta0.0228364348582505
gamma0.714213918449514







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
131060832.081095255667227.918904744333
141050959.25931241757590.7406875824253
151025986.86225353100338.1377464689967
1610851063.0045482934821.9954517065198
1711601159.473849975420.526150024575827
1813101323.8856135203-13.8856135203007
1914451144.37255626151300.627443738488
2014451622.71067478406-177.710674784061
2116151600.0875737974714.9124262025264
2216501811.58999921163-161.589999211627
2312551557.10226459804-302.102264598037
241175952.519114823413222.480885176587
2513001846.39663847693-546.396638476927
2612801410.31380628556-130.31380628556
2713901256.90513422205133.094865777949
2813401382.54474887927-42.5447488792695
2911101435.04296754111-325.042967541112
3013251391.41371346778-66.4137134677799
3112651239.891288657625.1087113424001
3211501385.65031163712-235.650311637118
3314301349.5752855690580.4247144309452
3416551519.09723953416135.902760465844
3515701394.60664749209175.393352507912
3613451163.55901939971181.440980600286
3714301828.95805703691-398.958057036911
3812601585.49575307031-325.495753070306
3914951372.04825396369122.951746036308
4011251432.30661034297-307.306610342968
418951222.56374464492-327.563744644921
4210851214.53738468247-129.537384682473
438701054.23938245267-184.239382452665
441185971.89501213854213.10498786146
4514551275.98515032718179.014849672822
4615401506.1509291289433.8490708710649
4716151332.36591767632282.634082323677
4812001168.1604399830331.8395600169708
4912601518.03275682094-258.032756820942
5010951360.62007871469-265.620078714689
5111601290.68664309092-130.686643090921
5210951084.2606287971610.739371202844
5313001042.95622332429257.043776675713
5412151509.90003711416-294.900037114156
5512451200.0730385778744.926961422133
5613501405.90122734404-55.9012273440383
5713001553.89597030669-253.895970306688
5812801468.59549804057-188.595498040575
5912701227.1052776575842.8947223424188
601065925.828781857287139.171218142713
6113401209.3841944163130.615805583704
6212651273.0263406333-8.02634063329788
6311551407.68748838062-252.687488380616
649301155.41342500522-225.41342500522
658801022.2932432149-142.293243214899
669251035.18629250847-110.186292508471
67980933.92553278350946.0744672164913
6810151071.79191029444-56.7919102944441
6910401121.28772576483-81.2877257648317
7013651132.25418627926232.745813720743
7111601209.5755892489-49.5755892489042
721115892.100770582902222.899229417098
7316301214.86262378904415.137376210961
7412251406.51656226379-181.516562263795
7512001357.04987115159-157.049871151589
7612651153.78129640278111.218703597225
7711401253.19632303185-113.19632303185
7812701325.73615486788-55.7361548678798
7914451305.53611416032139.46388583968
8013051508.20374330256-203.203743302555
8116651488.46944720465176.530552795346
8218301814.5043240343815.4956759656197
8316901629.3604853402960.6395146597145
8415201353.78967654241166.210323457594

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 1060 & 832.081095255667 & 227.918904744333 \tabularnewline
14 & 1050 & 959.259312417575 & 90.7406875824253 \tabularnewline
15 & 1025 & 986.862253531003 & 38.1377464689967 \tabularnewline
16 & 1085 & 1063.00454829348 & 21.9954517065198 \tabularnewline
17 & 1160 & 1159.47384997542 & 0.526150024575827 \tabularnewline
18 & 1310 & 1323.8856135203 & -13.8856135203007 \tabularnewline
19 & 1445 & 1144.37255626151 & 300.627443738488 \tabularnewline
20 & 1445 & 1622.71067478406 & -177.710674784061 \tabularnewline
21 & 1615 & 1600.08757379747 & 14.9124262025264 \tabularnewline
22 & 1650 & 1811.58999921163 & -161.589999211627 \tabularnewline
23 & 1255 & 1557.10226459804 & -302.102264598037 \tabularnewline
24 & 1175 & 952.519114823413 & 222.480885176587 \tabularnewline
25 & 1300 & 1846.39663847693 & -546.396638476927 \tabularnewline
26 & 1280 & 1410.31380628556 & -130.31380628556 \tabularnewline
27 & 1390 & 1256.90513422205 & 133.094865777949 \tabularnewline
28 & 1340 & 1382.54474887927 & -42.5447488792695 \tabularnewline
29 & 1110 & 1435.04296754111 & -325.042967541112 \tabularnewline
30 & 1325 & 1391.41371346778 & -66.4137134677799 \tabularnewline
31 & 1265 & 1239.8912886576 & 25.1087113424001 \tabularnewline
32 & 1150 & 1385.65031163712 & -235.650311637118 \tabularnewline
33 & 1430 & 1349.57528556905 & 80.4247144309452 \tabularnewline
34 & 1655 & 1519.09723953416 & 135.902760465844 \tabularnewline
35 & 1570 & 1394.60664749209 & 175.393352507912 \tabularnewline
36 & 1345 & 1163.55901939971 & 181.440980600286 \tabularnewline
37 & 1430 & 1828.95805703691 & -398.958057036911 \tabularnewline
38 & 1260 & 1585.49575307031 & -325.495753070306 \tabularnewline
39 & 1495 & 1372.04825396369 & 122.951746036308 \tabularnewline
40 & 1125 & 1432.30661034297 & -307.306610342968 \tabularnewline
41 & 895 & 1222.56374464492 & -327.563744644921 \tabularnewline
42 & 1085 & 1214.53738468247 & -129.537384682473 \tabularnewline
43 & 870 & 1054.23938245267 & -184.239382452665 \tabularnewline
44 & 1185 & 971.89501213854 & 213.10498786146 \tabularnewline
45 & 1455 & 1275.98515032718 & 179.014849672822 \tabularnewline
46 & 1540 & 1506.15092912894 & 33.8490708710649 \tabularnewline
47 & 1615 & 1332.36591767632 & 282.634082323677 \tabularnewline
48 & 1200 & 1168.16043998303 & 31.8395600169708 \tabularnewline
49 & 1260 & 1518.03275682094 & -258.032756820942 \tabularnewline
50 & 1095 & 1360.62007871469 & -265.620078714689 \tabularnewline
51 & 1160 & 1290.68664309092 & -130.686643090921 \tabularnewline
52 & 1095 & 1084.26062879716 & 10.739371202844 \tabularnewline
53 & 1300 & 1042.95622332429 & 257.043776675713 \tabularnewline
54 & 1215 & 1509.90003711416 & -294.900037114156 \tabularnewline
55 & 1245 & 1200.07303857787 & 44.926961422133 \tabularnewline
56 & 1350 & 1405.90122734404 & -55.9012273440383 \tabularnewline
57 & 1300 & 1553.89597030669 & -253.895970306688 \tabularnewline
58 & 1280 & 1468.59549804057 & -188.595498040575 \tabularnewline
59 & 1270 & 1227.10527765758 & 42.8947223424188 \tabularnewline
60 & 1065 & 925.828781857287 & 139.171218142713 \tabularnewline
61 & 1340 & 1209.3841944163 & 130.615805583704 \tabularnewline
62 & 1265 & 1273.0263406333 & -8.02634063329788 \tabularnewline
63 & 1155 & 1407.68748838062 & -252.687488380616 \tabularnewline
64 & 930 & 1155.41342500522 & -225.41342500522 \tabularnewline
65 & 880 & 1022.2932432149 & -142.293243214899 \tabularnewline
66 & 925 & 1035.18629250847 & -110.186292508471 \tabularnewline
67 & 980 & 933.925532783509 & 46.0744672164913 \tabularnewline
68 & 1015 & 1071.79191029444 & -56.7919102944441 \tabularnewline
69 & 1040 & 1121.28772576483 & -81.2877257648317 \tabularnewline
70 & 1365 & 1132.25418627926 & 232.745813720743 \tabularnewline
71 & 1160 & 1209.5755892489 & -49.5755892489042 \tabularnewline
72 & 1115 & 892.100770582902 & 222.899229417098 \tabularnewline
73 & 1630 & 1214.86262378904 & 415.137376210961 \tabularnewline
74 & 1225 & 1406.51656226379 & -181.516562263795 \tabularnewline
75 & 1200 & 1357.04987115159 & -157.049871151589 \tabularnewline
76 & 1265 & 1153.78129640278 & 111.218703597225 \tabularnewline
77 & 1140 & 1253.19632303185 & -113.19632303185 \tabularnewline
78 & 1270 & 1325.73615486788 & -55.7361548678798 \tabularnewline
79 & 1445 & 1305.53611416032 & 139.46388583968 \tabularnewline
80 & 1305 & 1508.20374330256 & -203.203743302555 \tabularnewline
81 & 1665 & 1488.46944720465 & 176.530552795346 \tabularnewline
82 & 1830 & 1814.50432403438 & 15.4956759656197 \tabularnewline
83 & 1690 & 1629.36048534029 & 60.6395146597145 \tabularnewline
84 & 1520 & 1353.78967654241 & 166.210323457594 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=279417&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]1060[/C][C]832.081095255667[/C][C]227.918904744333[/C][/ROW]
[ROW][C]14[/C][C]1050[/C][C]959.259312417575[/C][C]90.7406875824253[/C][/ROW]
[ROW][C]15[/C][C]1025[/C][C]986.862253531003[/C][C]38.1377464689967[/C][/ROW]
[ROW][C]16[/C][C]1085[/C][C]1063.00454829348[/C][C]21.9954517065198[/C][/ROW]
[ROW][C]17[/C][C]1160[/C][C]1159.47384997542[/C][C]0.526150024575827[/C][/ROW]
[ROW][C]18[/C][C]1310[/C][C]1323.8856135203[/C][C]-13.8856135203007[/C][/ROW]
[ROW][C]19[/C][C]1445[/C][C]1144.37255626151[/C][C]300.627443738488[/C][/ROW]
[ROW][C]20[/C][C]1445[/C][C]1622.71067478406[/C][C]-177.710674784061[/C][/ROW]
[ROW][C]21[/C][C]1615[/C][C]1600.08757379747[/C][C]14.9124262025264[/C][/ROW]
[ROW][C]22[/C][C]1650[/C][C]1811.58999921163[/C][C]-161.589999211627[/C][/ROW]
[ROW][C]23[/C][C]1255[/C][C]1557.10226459804[/C][C]-302.102264598037[/C][/ROW]
[ROW][C]24[/C][C]1175[/C][C]952.519114823413[/C][C]222.480885176587[/C][/ROW]
[ROW][C]25[/C][C]1300[/C][C]1846.39663847693[/C][C]-546.396638476927[/C][/ROW]
[ROW][C]26[/C][C]1280[/C][C]1410.31380628556[/C][C]-130.31380628556[/C][/ROW]
[ROW][C]27[/C][C]1390[/C][C]1256.90513422205[/C][C]133.094865777949[/C][/ROW]
[ROW][C]28[/C][C]1340[/C][C]1382.54474887927[/C][C]-42.5447488792695[/C][/ROW]
[ROW][C]29[/C][C]1110[/C][C]1435.04296754111[/C][C]-325.042967541112[/C][/ROW]
[ROW][C]30[/C][C]1325[/C][C]1391.41371346778[/C][C]-66.4137134677799[/C][/ROW]
[ROW][C]31[/C][C]1265[/C][C]1239.8912886576[/C][C]25.1087113424001[/C][/ROW]
[ROW][C]32[/C][C]1150[/C][C]1385.65031163712[/C][C]-235.650311637118[/C][/ROW]
[ROW][C]33[/C][C]1430[/C][C]1349.57528556905[/C][C]80.4247144309452[/C][/ROW]
[ROW][C]34[/C][C]1655[/C][C]1519.09723953416[/C][C]135.902760465844[/C][/ROW]
[ROW][C]35[/C][C]1570[/C][C]1394.60664749209[/C][C]175.393352507912[/C][/ROW]
[ROW][C]36[/C][C]1345[/C][C]1163.55901939971[/C][C]181.440980600286[/C][/ROW]
[ROW][C]37[/C][C]1430[/C][C]1828.95805703691[/C][C]-398.958057036911[/C][/ROW]
[ROW][C]38[/C][C]1260[/C][C]1585.49575307031[/C][C]-325.495753070306[/C][/ROW]
[ROW][C]39[/C][C]1495[/C][C]1372.04825396369[/C][C]122.951746036308[/C][/ROW]
[ROW][C]40[/C][C]1125[/C][C]1432.30661034297[/C][C]-307.306610342968[/C][/ROW]
[ROW][C]41[/C][C]895[/C][C]1222.56374464492[/C][C]-327.563744644921[/C][/ROW]
[ROW][C]42[/C][C]1085[/C][C]1214.53738468247[/C][C]-129.537384682473[/C][/ROW]
[ROW][C]43[/C][C]870[/C][C]1054.23938245267[/C][C]-184.239382452665[/C][/ROW]
[ROW][C]44[/C][C]1185[/C][C]971.89501213854[/C][C]213.10498786146[/C][/ROW]
[ROW][C]45[/C][C]1455[/C][C]1275.98515032718[/C][C]179.014849672822[/C][/ROW]
[ROW][C]46[/C][C]1540[/C][C]1506.15092912894[/C][C]33.8490708710649[/C][/ROW]
[ROW][C]47[/C][C]1615[/C][C]1332.36591767632[/C][C]282.634082323677[/C][/ROW]
[ROW][C]48[/C][C]1200[/C][C]1168.16043998303[/C][C]31.8395600169708[/C][/ROW]
[ROW][C]49[/C][C]1260[/C][C]1518.03275682094[/C][C]-258.032756820942[/C][/ROW]
[ROW][C]50[/C][C]1095[/C][C]1360.62007871469[/C][C]-265.620078714689[/C][/ROW]
[ROW][C]51[/C][C]1160[/C][C]1290.68664309092[/C][C]-130.686643090921[/C][/ROW]
[ROW][C]52[/C][C]1095[/C][C]1084.26062879716[/C][C]10.739371202844[/C][/ROW]
[ROW][C]53[/C][C]1300[/C][C]1042.95622332429[/C][C]257.043776675713[/C][/ROW]
[ROW][C]54[/C][C]1215[/C][C]1509.90003711416[/C][C]-294.900037114156[/C][/ROW]
[ROW][C]55[/C][C]1245[/C][C]1200.07303857787[/C][C]44.926961422133[/C][/ROW]
[ROW][C]56[/C][C]1350[/C][C]1405.90122734404[/C][C]-55.9012273440383[/C][/ROW]
[ROW][C]57[/C][C]1300[/C][C]1553.89597030669[/C][C]-253.895970306688[/C][/ROW]
[ROW][C]58[/C][C]1280[/C][C]1468.59549804057[/C][C]-188.595498040575[/C][/ROW]
[ROW][C]59[/C][C]1270[/C][C]1227.10527765758[/C][C]42.8947223424188[/C][/ROW]
[ROW][C]60[/C][C]1065[/C][C]925.828781857287[/C][C]139.171218142713[/C][/ROW]
[ROW][C]61[/C][C]1340[/C][C]1209.3841944163[/C][C]130.615805583704[/C][/ROW]
[ROW][C]62[/C][C]1265[/C][C]1273.0263406333[/C][C]-8.02634063329788[/C][/ROW]
[ROW][C]63[/C][C]1155[/C][C]1407.68748838062[/C][C]-252.687488380616[/C][/ROW]
[ROW][C]64[/C][C]930[/C][C]1155.41342500522[/C][C]-225.41342500522[/C][/ROW]
[ROW][C]65[/C][C]880[/C][C]1022.2932432149[/C][C]-142.293243214899[/C][/ROW]
[ROW][C]66[/C][C]925[/C][C]1035.18629250847[/C][C]-110.186292508471[/C][/ROW]
[ROW][C]67[/C][C]980[/C][C]933.925532783509[/C][C]46.0744672164913[/C][/ROW]
[ROW][C]68[/C][C]1015[/C][C]1071.79191029444[/C][C]-56.7919102944441[/C][/ROW]
[ROW][C]69[/C][C]1040[/C][C]1121.28772576483[/C][C]-81.2877257648317[/C][/ROW]
[ROW][C]70[/C][C]1365[/C][C]1132.25418627926[/C][C]232.745813720743[/C][/ROW]
[ROW][C]71[/C][C]1160[/C][C]1209.5755892489[/C][C]-49.5755892489042[/C][/ROW]
[ROW][C]72[/C][C]1115[/C][C]892.100770582902[/C][C]222.899229417098[/C][/ROW]
[ROW][C]73[/C][C]1630[/C][C]1214.86262378904[/C][C]415.137376210961[/C][/ROW]
[ROW][C]74[/C][C]1225[/C][C]1406.51656226379[/C][C]-181.516562263795[/C][/ROW]
[ROW][C]75[/C][C]1200[/C][C]1357.04987115159[/C][C]-157.049871151589[/C][/ROW]
[ROW][C]76[/C][C]1265[/C][C]1153.78129640278[/C][C]111.218703597225[/C][/ROW]
[ROW][C]77[/C][C]1140[/C][C]1253.19632303185[/C][C]-113.19632303185[/C][/ROW]
[ROW][C]78[/C][C]1270[/C][C]1325.73615486788[/C][C]-55.7361548678798[/C][/ROW]
[ROW][C]79[/C][C]1445[/C][C]1305.53611416032[/C][C]139.46388583968[/C][/ROW]
[ROW][C]80[/C][C]1305[/C][C]1508.20374330256[/C][C]-203.203743302555[/C][/ROW]
[ROW][C]81[/C][C]1665[/C][C]1488.46944720465[/C][C]176.530552795346[/C][/ROW]
[ROW][C]82[/C][C]1830[/C][C]1814.50432403438[/C][C]15.4956759656197[/C][/ROW]
[ROW][C]83[/C][C]1690[/C][C]1629.36048534029[/C][C]60.6395146597145[/C][/ROW]
[ROW][C]84[/C][C]1520[/C][C]1353.78967654241[/C][C]166.210323457594[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=279417&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=279417&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
131060832.081095255667227.918904744333
141050959.25931241757590.7406875824253
151025986.86225353100338.1377464689967
1610851063.0045482934821.9954517065198
1711601159.473849975420.526150024575827
1813101323.8856135203-13.8856135203007
1914451144.37255626151300.627443738488
2014451622.71067478406-177.710674784061
2116151600.0875737974714.9124262025264
2216501811.58999921163-161.589999211627
2312551557.10226459804-302.102264598037
241175952.519114823413222.480885176587
2513001846.39663847693-546.396638476927
2612801410.31380628556-130.31380628556
2713901256.90513422205133.094865777949
2813401382.54474887927-42.5447488792695
2911101435.04296754111-325.042967541112
3013251391.41371346778-66.4137134677799
3112651239.891288657625.1087113424001
3211501385.65031163712-235.650311637118
3314301349.5752855690580.4247144309452
3416551519.09723953416135.902760465844
3515701394.60664749209175.393352507912
3613451163.55901939971181.440980600286
3714301828.95805703691-398.958057036911
3812601585.49575307031-325.495753070306
3914951372.04825396369122.951746036308
4011251432.30661034297-307.306610342968
418951222.56374464492-327.563744644921
4210851214.53738468247-129.537384682473
438701054.23938245267-184.239382452665
441185971.89501213854213.10498786146
4514551275.98515032718179.014849672822
4615401506.1509291289433.8490708710649
4716151332.36591767632282.634082323677
4812001168.1604399830331.8395600169708
4912601518.03275682094-258.032756820942
5010951360.62007871469-265.620078714689
5111601290.68664309092-130.686643090921
5210951084.2606287971610.739371202844
5313001042.95622332429257.043776675713
5412151509.90003711416-294.900037114156
5512451200.0730385778744.926961422133
5613501405.90122734404-55.9012273440383
5713001553.89597030669-253.895970306688
5812801468.59549804057-188.595498040575
5912701227.1052776575842.8947223424188
601065925.828781857287139.171218142713
6113401209.3841944163130.615805583704
6212651273.0263406333-8.02634063329788
6311551407.68748838062-252.687488380616
649301155.41342500522-225.41342500522
658801022.2932432149-142.293243214899
669251035.18629250847-110.186292508471
67980933.92553278350946.0744672164913
6810151071.79191029444-56.7919102944441
6910401121.28772576483-81.2877257648317
7013651132.25418627926232.745813720743
7111601209.5755892489-49.5755892489042
721115892.100770582902222.899229417098
7316301214.86262378904415.137376210961
7412251406.51656226379-181.516562263795
7512001357.04987115159-157.049871151589
7612651153.78129640278111.218703597225
7711401253.19632303185-113.19632303185
7812701325.73615486788-55.7361548678798
7914451305.53611416032139.46388583968
8013051508.20374330256-203.203743302555
8116651488.46944720465176.530552795346
8218301814.5043240343815.4956759656197
8316901629.3604853402960.6395146597145
8415201353.78967654241166.210323457594







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
851749.22916134131410.980862061382087.47746062122
861490.450262399071097.088401780851883.81212301728
871567.219969436171096.690527408782037.74941146356
881522.781090400181003.08680315182042.47537764856
891482.17386324046918.498858495322045.8488679856
901684.64045426091010.472359951412358.80854857039
911771.843194463081023.44441450012520.24197442606
921792.63810282955994.4636449594062590.8125606997
932072.858684743971123.108107485943022.609262002
942290.65464063141211.901625168643369.40765609416
952061.374612185591048.361646910123074.38757746107
961709.28564659868886.0621737609712532.5091194364

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
85 & 1749.2291613413 & 1410.98086206138 & 2087.47746062122 \tabularnewline
86 & 1490.45026239907 & 1097.08840178085 & 1883.81212301728 \tabularnewline
87 & 1567.21996943617 & 1096.69052740878 & 2037.74941146356 \tabularnewline
88 & 1522.78109040018 & 1003.0868031518 & 2042.47537764856 \tabularnewline
89 & 1482.17386324046 & 918.49885849532 & 2045.8488679856 \tabularnewline
90 & 1684.6404542609 & 1010.47235995141 & 2358.80854857039 \tabularnewline
91 & 1771.84319446308 & 1023.4444145001 & 2520.24197442606 \tabularnewline
92 & 1792.63810282955 & 994.463644959406 & 2590.8125606997 \tabularnewline
93 & 2072.85868474397 & 1123.10810748594 & 3022.609262002 \tabularnewline
94 & 2290.6546406314 & 1211.90162516864 & 3369.40765609416 \tabularnewline
95 & 2061.37461218559 & 1048.36164691012 & 3074.38757746107 \tabularnewline
96 & 1709.28564659868 & 886.062173760971 & 2532.5091194364 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=279417&T=3

[TABLE]
[ROW][C]Extrapolation Forecasts of Exponential Smoothing[/C][/ROW]
[ROW][C]t[/C][C]Forecast[/C][C]95% Lower Bound[/C][C]95% Upper Bound[/C][/ROW]
[ROW][C]85[/C][C]1749.2291613413[/C][C]1410.98086206138[/C][C]2087.47746062122[/C][/ROW]
[ROW][C]86[/C][C]1490.45026239907[/C][C]1097.08840178085[/C][C]1883.81212301728[/C][/ROW]
[ROW][C]87[/C][C]1567.21996943617[/C][C]1096.69052740878[/C][C]2037.74941146356[/C][/ROW]
[ROW][C]88[/C][C]1522.78109040018[/C][C]1003.0868031518[/C][C]2042.47537764856[/C][/ROW]
[ROW][C]89[/C][C]1482.17386324046[/C][C]918.49885849532[/C][C]2045.8488679856[/C][/ROW]
[ROW][C]90[/C][C]1684.6404542609[/C][C]1010.47235995141[/C][C]2358.80854857039[/C][/ROW]
[ROW][C]91[/C][C]1771.84319446308[/C][C]1023.4444145001[/C][C]2520.24197442606[/C][/ROW]
[ROW][C]92[/C][C]1792.63810282955[/C][C]994.463644959406[/C][C]2590.8125606997[/C][/ROW]
[ROW][C]93[/C][C]2072.85868474397[/C][C]1123.10810748594[/C][C]3022.609262002[/C][/ROW]
[ROW][C]94[/C][C]2290.6546406314[/C][C]1211.90162516864[/C][C]3369.40765609416[/C][/ROW]
[ROW][C]95[/C][C]2061.37461218559[/C][C]1048.36164691012[/C][C]3074.38757746107[/C][/ROW]
[ROW][C]96[/C][C]1709.28564659868[/C][C]886.062173760971[/C][C]2532.5091194364[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=279417&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=279417&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
851749.22916134131410.980862061382087.47746062122
861490.450262399071097.088401780851883.81212301728
871567.219969436171096.690527408782037.74941146356
881522.781090400181003.08680315182042.47537764856
891482.17386324046918.498858495322045.8488679856
901684.64045426091010.472359951412358.80854857039
911771.843194463081023.44441450012520.24197442606
921792.63810282955994.4636449594062590.8125606997
932072.858684743971123.108107485943022.609262002
942290.65464063141211.901625168643369.40765609416
952061.374612185591048.361646910123074.38757746107
961709.28564659868886.0621737609712532.5091194364



Parameters (Session):
par1 = 12 ; par2 = Triple ; par3 = multiplicative ;
Parameters (R input):
par1 = 12 ; par2 = Triple ; par3 = multiplicative ;
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')