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Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationFri, 28 Nov 2014 19:39:20 +0000
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2014/Nov/28/t1417203608e8j7k6ubj2zok59.htm/, Retrieved Sun, 19 May 2024 14:06:30 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=261014, Retrieved Sun, 19 May 2024 14:06:30 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact63
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [] [2014-11-28 19:39:20] [76c30f62b7052b57088120e90a652e05] [Current]
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Dataseries X:
1143
1162
1169
1184
1169
1189
1192
1198
1168
1179
1173
1172
1125
1127
1123
1132
1114
1127
1129
1139
1117
1131
1132
1140
1105
1126
1129
1139
1123
1101
1110
1128
1101
1134
1139
1137
1141
1165
1146
1134
1141
1159
1166
1192
1171
1179
1181
1195
1167
1176
1181
1197
1194
1173
1179
1184
1193
1193
1193
1191
1222
1198
1218
1219
1260
1235
1256
1258
1295
1294
1318
1262





Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'George Udny Yule' @ yule.wessa.net
R Framework error message
Warning: there are blank lines in the 'Data' field.
Please, use NA for missing data - blank lines are simply
 deleted and are NOT treated as missing values.

\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 & 'George Udny Yule' @ yule.wessa.net \tabularnewline
R Framework error message & 
Warning: there are blank lines in the 'Data' field.
Please, use NA for missing data - blank lines are simply
 deleted and are NOT treated as missing values.
\tabularnewline \hline \end{tabular} %Source: https://freestatistics.org/blog/index.php?pk=261014&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]'George Udny Yule' @ yule.wessa.net[/C][/ROW]
[ROW][C]R Framework error message[/C][C]
Warning: there are blank lines in the 'Data' field.
Please, use NA for missing data - blank lines are simply
 deleted and are NOT treated as missing values.
[/C][/ROW] [/TABLE] Source: https://freestatistics.org/blog/index.php?pk=261014&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=261014&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'George Udny Yule' @ yule.wessa.net
R Framework error message
Warning: there are blank lines in the 'Data' field.
Please, use NA for missing data - blank lines are simply
 deleted and are NOT treated as missing values.







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.480102926361699
beta0.390935883848184
gammaFALSE

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.480102926361699 \tabularnewline
beta & 0.390935883848184 \tabularnewline
gamma & FALSE \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=261014&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]0.480102926361699[/C][/ROW]
[ROW][C]beta[/C][C]0.390935883848184[/C][/ROW]
[ROW][C]gamma[/C][C]FALSE[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=261014&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=261014&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
alpha0.480102926361699
beta0.390935883848184
gammaFALSE







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
311691181-12
411841191.9864913414-7.98649134139578
511691203.40089967279-34.4008996727869
611891195.67698691924-6.67698691924056
711921200.01020572718-8.01020572718085
811981202.19991108166-4.19991108166369
911681205.430670995-37.4306709950019
1011791185.68190333279-6.68190333278835
1111731179.44158616652-6.44158616651953
1211721172.10762813394-0.107628133942399
1311251167.79442122172-42.7944212217176
1411271134.95509814154-7.95509814154184
1511231117.349147935435.65085206457275
1611321107.3360596222224.6639403777767
1711141111.08037234412.91962765590188
1811271104.9331602400322.0668397599691
1911291112.1202939781916.8797060218092
2011391119.9852125687419.0147874312604
2111171132.44406521225-15.4440652122528
2211311125.4604335745.53956642599724
2311321129.590823132382.40917686762032
2411401132.670480612937.32951938707424
2511051139.48808248518-34.4880824851816
2611261119.755881683076.24411831692646
2711291120.751284889878.2487151101252
2811391124.2572977832814.7427022167167
2911231133.64814273567-10.64814273567
3011011128.8502245438-27.8502245438033
3111101110.56634287916-0.566342879162448
3211281105.2752360540122.7247639459938
3311011115.43145648962-14.4314564896231
3411341105.0402344592328.9597655407661
3511391120.9167079138518.0832920861526
3611371134.965397994632.03460200537188
3711411141.69093835883-0.690938358831772
3811651146.9782569695218.0217430304797
3911461164.63207992638-18.6320799263767
4011341161.19125016468-27.1912501646757
4111411148.53762661376-7.53762661375845
4211591143.9050321604515.0949678395548
4311661152.9715789258513.0284210741452
4411921163.4912678819628.5087321180415
4511711186.79388806064-15.7938880606382
4611791185.86234429534-6.86234429533897
4711811187.93087112083-6.93087112082935
4811951188.665646546016.33435345398925
4911671196.95798649939-29.9579864993882
5011761182.2034694723-6.20346947229677
5111811177.689239737333.31076026267056
5211971178.3642143522318.63578564777
5311941189.894519080564.10548091943542
5411731195.21933749233-22.2193374923252
5511791183.73519805194-4.73519805194292
5611841179.756498347664.24350165234341
5711931180.8849591878312.1150408121687
5811931188.0664345044.9335654959998
5911931192.726040758250.273959241745615
6011911195.1999756768-4.19997567680093
6112221194.7376701740227.2623298259825
6211981214.49736162717-16.4973616271668
6312181210.151516231147.84848376886112
6412191218.967260149450.0327398505487508
6512601224.0367874658235.9632125341811
6612351253.10655587029-18.1065558702862
6712561252.818860508723.18113949127792
6812581263.34851634495-5.34851634494612
6912951268.7791992988326.2208007011664
7012941294.28777172282-0.287771722817297
7113181307.0154892325810.9845107674178
7212621327.21673946737-65.2167394673654

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
3 & 1169 & 1181 & -12 \tabularnewline
4 & 1184 & 1191.9864913414 & -7.98649134139578 \tabularnewline
5 & 1169 & 1203.40089967279 & -34.4008996727869 \tabularnewline
6 & 1189 & 1195.67698691924 & -6.67698691924056 \tabularnewline
7 & 1192 & 1200.01020572718 & -8.01020572718085 \tabularnewline
8 & 1198 & 1202.19991108166 & -4.19991108166369 \tabularnewline
9 & 1168 & 1205.430670995 & -37.4306709950019 \tabularnewline
10 & 1179 & 1185.68190333279 & -6.68190333278835 \tabularnewline
11 & 1173 & 1179.44158616652 & -6.44158616651953 \tabularnewline
12 & 1172 & 1172.10762813394 & -0.107628133942399 \tabularnewline
13 & 1125 & 1167.79442122172 & -42.7944212217176 \tabularnewline
14 & 1127 & 1134.95509814154 & -7.95509814154184 \tabularnewline
15 & 1123 & 1117.34914793543 & 5.65085206457275 \tabularnewline
16 & 1132 & 1107.33605962222 & 24.6639403777767 \tabularnewline
17 & 1114 & 1111.0803723441 & 2.91962765590188 \tabularnewline
18 & 1127 & 1104.93316024003 & 22.0668397599691 \tabularnewline
19 & 1129 & 1112.12029397819 & 16.8797060218092 \tabularnewline
20 & 1139 & 1119.98521256874 & 19.0147874312604 \tabularnewline
21 & 1117 & 1132.44406521225 & -15.4440652122528 \tabularnewline
22 & 1131 & 1125.460433574 & 5.53956642599724 \tabularnewline
23 & 1132 & 1129.59082313238 & 2.40917686762032 \tabularnewline
24 & 1140 & 1132.67048061293 & 7.32951938707424 \tabularnewline
25 & 1105 & 1139.48808248518 & -34.4880824851816 \tabularnewline
26 & 1126 & 1119.75588168307 & 6.24411831692646 \tabularnewline
27 & 1129 & 1120.75128488987 & 8.2487151101252 \tabularnewline
28 & 1139 & 1124.25729778328 & 14.7427022167167 \tabularnewline
29 & 1123 & 1133.64814273567 & -10.64814273567 \tabularnewline
30 & 1101 & 1128.8502245438 & -27.8502245438033 \tabularnewline
31 & 1110 & 1110.56634287916 & -0.566342879162448 \tabularnewline
32 & 1128 & 1105.27523605401 & 22.7247639459938 \tabularnewline
33 & 1101 & 1115.43145648962 & -14.4314564896231 \tabularnewline
34 & 1134 & 1105.04023445923 & 28.9597655407661 \tabularnewline
35 & 1139 & 1120.91670791385 & 18.0832920861526 \tabularnewline
36 & 1137 & 1134.96539799463 & 2.03460200537188 \tabularnewline
37 & 1141 & 1141.69093835883 & -0.690938358831772 \tabularnewline
38 & 1165 & 1146.97825696952 & 18.0217430304797 \tabularnewline
39 & 1146 & 1164.63207992638 & -18.6320799263767 \tabularnewline
40 & 1134 & 1161.19125016468 & -27.1912501646757 \tabularnewline
41 & 1141 & 1148.53762661376 & -7.53762661375845 \tabularnewline
42 & 1159 & 1143.90503216045 & 15.0949678395548 \tabularnewline
43 & 1166 & 1152.97157892585 & 13.0284210741452 \tabularnewline
44 & 1192 & 1163.49126788196 & 28.5087321180415 \tabularnewline
45 & 1171 & 1186.79388806064 & -15.7938880606382 \tabularnewline
46 & 1179 & 1185.86234429534 & -6.86234429533897 \tabularnewline
47 & 1181 & 1187.93087112083 & -6.93087112082935 \tabularnewline
48 & 1195 & 1188.66564654601 & 6.33435345398925 \tabularnewline
49 & 1167 & 1196.95798649939 & -29.9579864993882 \tabularnewline
50 & 1176 & 1182.2034694723 & -6.20346947229677 \tabularnewline
51 & 1181 & 1177.68923973733 & 3.31076026267056 \tabularnewline
52 & 1197 & 1178.36421435223 & 18.63578564777 \tabularnewline
53 & 1194 & 1189.89451908056 & 4.10548091943542 \tabularnewline
54 & 1173 & 1195.21933749233 & -22.2193374923252 \tabularnewline
55 & 1179 & 1183.73519805194 & -4.73519805194292 \tabularnewline
56 & 1184 & 1179.75649834766 & 4.24350165234341 \tabularnewline
57 & 1193 & 1180.88495918783 & 12.1150408121687 \tabularnewline
58 & 1193 & 1188.066434504 & 4.9335654959998 \tabularnewline
59 & 1193 & 1192.72604075825 & 0.273959241745615 \tabularnewline
60 & 1191 & 1195.1999756768 & -4.19997567680093 \tabularnewline
61 & 1222 & 1194.73767017402 & 27.2623298259825 \tabularnewline
62 & 1198 & 1214.49736162717 & -16.4973616271668 \tabularnewline
63 & 1218 & 1210.15151623114 & 7.84848376886112 \tabularnewline
64 & 1219 & 1218.96726014945 & 0.0327398505487508 \tabularnewline
65 & 1260 & 1224.03678746582 & 35.9632125341811 \tabularnewline
66 & 1235 & 1253.10655587029 & -18.1065558702862 \tabularnewline
67 & 1256 & 1252.81886050872 & 3.18113949127792 \tabularnewline
68 & 1258 & 1263.34851634495 & -5.34851634494612 \tabularnewline
69 & 1295 & 1268.77919929883 & 26.2208007011664 \tabularnewline
70 & 1294 & 1294.28777172282 & -0.287771722817297 \tabularnewline
71 & 1318 & 1307.01548923258 & 10.9845107674178 \tabularnewline
72 & 1262 & 1327.21673946737 & -65.2167394673654 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=261014&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]1169[/C][C]1181[/C][C]-12[/C][/ROW]
[ROW][C]4[/C][C]1184[/C][C]1191.9864913414[/C][C]-7.98649134139578[/C][/ROW]
[ROW][C]5[/C][C]1169[/C][C]1203.40089967279[/C][C]-34.4008996727869[/C][/ROW]
[ROW][C]6[/C][C]1189[/C][C]1195.67698691924[/C][C]-6.67698691924056[/C][/ROW]
[ROW][C]7[/C][C]1192[/C][C]1200.01020572718[/C][C]-8.01020572718085[/C][/ROW]
[ROW][C]8[/C][C]1198[/C][C]1202.19991108166[/C][C]-4.19991108166369[/C][/ROW]
[ROW][C]9[/C][C]1168[/C][C]1205.430670995[/C][C]-37.4306709950019[/C][/ROW]
[ROW][C]10[/C][C]1179[/C][C]1185.68190333279[/C][C]-6.68190333278835[/C][/ROW]
[ROW][C]11[/C][C]1173[/C][C]1179.44158616652[/C][C]-6.44158616651953[/C][/ROW]
[ROW][C]12[/C][C]1172[/C][C]1172.10762813394[/C][C]-0.107628133942399[/C][/ROW]
[ROW][C]13[/C][C]1125[/C][C]1167.79442122172[/C][C]-42.7944212217176[/C][/ROW]
[ROW][C]14[/C][C]1127[/C][C]1134.95509814154[/C][C]-7.95509814154184[/C][/ROW]
[ROW][C]15[/C][C]1123[/C][C]1117.34914793543[/C][C]5.65085206457275[/C][/ROW]
[ROW][C]16[/C][C]1132[/C][C]1107.33605962222[/C][C]24.6639403777767[/C][/ROW]
[ROW][C]17[/C][C]1114[/C][C]1111.0803723441[/C][C]2.91962765590188[/C][/ROW]
[ROW][C]18[/C][C]1127[/C][C]1104.93316024003[/C][C]22.0668397599691[/C][/ROW]
[ROW][C]19[/C][C]1129[/C][C]1112.12029397819[/C][C]16.8797060218092[/C][/ROW]
[ROW][C]20[/C][C]1139[/C][C]1119.98521256874[/C][C]19.0147874312604[/C][/ROW]
[ROW][C]21[/C][C]1117[/C][C]1132.44406521225[/C][C]-15.4440652122528[/C][/ROW]
[ROW][C]22[/C][C]1131[/C][C]1125.460433574[/C][C]5.53956642599724[/C][/ROW]
[ROW][C]23[/C][C]1132[/C][C]1129.59082313238[/C][C]2.40917686762032[/C][/ROW]
[ROW][C]24[/C][C]1140[/C][C]1132.67048061293[/C][C]7.32951938707424[/C][/ROW]
[ROW][C]25[/C][C]1105[/C][C]1139.48808248518[/C][C]-34.4880824851816[/C][/ROW]
[ROW][C]26[/C][C]1126[/C][C]1119.75588168307[/C][C]6.24411831692646[/C][/ROW]
[ROW][C]27[/C][C]1129[/C][C]1120.75128488987[/C][C]8.2487151101252[/C][/ROW]
[ROW][C]28[/C][C]1139[/C][C]1124.25729778328[/C][C]14.7427022167167[/C][/ROW]
[ROW][C]29[/C][C]1123[/C][C]1133.64814273567[/C][C]-10.64814273567[/C][/ROW]
[ROW][C]30[/C][C]1101[/C][C]1128.8502245438[/C][C]-27.8502245438033[/C][/ROW]
[ROW][C]31[/C][C]1110[/C][C]1110.56634287916[/C][C]-0.566342879162448[/C][/ROW]
[ROW][C]32[/C][C]1128[/C][C]1105.27523605401[/C][C]22.7247639459938[/C][/ROW]
[ROW][C]33[/C][C]1101[/C][C]1115.43145648962[/C][C]-14.4314564896231[/C][/ROW]
[ROW][C]34[/C][C]1134[/C][C]1105.04023445923[/C][C]28.9597655407661[/C][/ROW]
[ROW][C]35[/C][C]1139[/C][C]1120.91670791385[/C][C]18.0832920861526[/C][/ROW]
[ROW][C]36[/C][C]1137[/C][C]1134.96539799463[/C][C]2.03460200537188[/C][/ROW]
[ROW][C]37[/C][C]1141[/C][C]1141.69093835883[/C][C]-0.690938358831772[/C][/ROW]
[ROW][C]38[/C][C]1165[/C][C]1146.97825696952[/C][C]18.0217430304797[/C][/ROW]
[ROW][C]39[/C][C]1146[/C][C]1164.63207992638[/C][C]-18.6320799263767[/C][/ROW]
[ROW][C]40[/C][C]1134[/C][C]1161.19125016468[/C][C]-27.1912501646757[/C][/ROW]
[ROW][C]41[/C][C]1141[/C][C]1148.53762661376[/C][C]-7.53762661375845[/C][/ROW]
[ROW][C]42[/C][C]1159[/C][C]1143.90503216045[/C][C]15.0949678395548[/C][/ROW]
[ROW][C]43[/C][C]1166[/C][C]1152.97157892585[/C][C]13.0284210741452[/C][/ROW]
[ROW][C]44[/C][C]1192[/C][C]1163.49126788196[/C][C]28.5087321180415[/C][/ROW]
[ROW][C]45[/C][C]1171[/C][C]1186.79388806064[/C][C]-15.7938880606382[/C][/ROW]
[ROW][C]46[/C][C]1179[/C][C]1185.86234429534[/C][C]-6.86234429533897[/C][/ROW]
[ROW][C]47[/C][C]1181[/C][C]1187.93087112083[/C][C]-6.93087112082935[/C][/ROW]
[ROW][C]48[/C][C]1195[/C][C]1188.66564654601[/C][C]6.33435345398925[/C][/ROW]
[ROW][C]49[/C][C]1167[/C][C]1196.95798649939[/C][C]-29.9579864993882[/C][/ROW]
[ROW][C]50[/C][C]1176[/C][C]1182.2034694723[/C][C]-6.20346947229677[/C][/ROW]
[ROW][C]51[/C][C]1181[/C][C]1177.68923973733[/C][C]3.31076026267056[/C][/ROW]
[ROW][C]52[/C][C]1197[/C][C]1178.36421435223[/C][C]18.63578564777[/C][/ROW]
[ROW][C]53[/C][C]1194[/C][C]1189.89451908056[/C][C]4.10548091943542[/C][/ROW]
[ROW][C]54[/C][C]1173[/C][C]1195.21933749233[/C][C]-22.2193374923252[/C][/ROW]
[ROW][C]55[/C][C]1179[/C][C]1183.73519805194[/C][C]-4.73519805194292[/C][/ROW]
[ROW][C]56[/C][C]1184[/C][C]1179.75649834766[/C][C]4.24350165234341[/C][/ROW]
[ROW][C]57[/C][C]1193[/C][C]1180.88495918783[/C][C]12.1150408121687[/C][/ROW]
[ROW][C]58[/C][C]1193[/C][C]1188.066434504[/C][C]4.9335654959998[/C][/ROW]
[ROW][C]59[/C][C]1193[/C][C]1192.72604075825[/C][C]0.273959241745615[/C][/ROW]
[ROW][C]60[/C][C]1191[/C][C]1195.1999756768[/C][C]-4.19997567680093[/C][/ROW]
[ROW][C]61[/C][C]1222[/C][C]1194.73767017402[/C][C]27.2623298259825[/C][/ROW]
[ROW][C]62[/C][C]1198[/C][C]1214.49736162717[/C][C]-16.4973616271668[/C][/ROW]
[ROW][C]63[/C][C]1218[/C][C]1210.15151623114[/C][C]7.84848376886112[/C][/ROW]
[ROW][C]64[/C][C]1219[/C][C]1218.96726014945[/C][C]0.0327398505487508[/C][/ROW]
[ROW][C]65[/C][C]1260[/C][C]1224.03678746582[/C][C]35.9632125341811[/C][/ROW]
[ROW][C]66[/C][C]1235[/C][C]1253.10655587029[/C][C]-18.1065558702862[/C][/ROW]
[ROW][C]67[/C][C]1256[/C][C]1252.81886050872[/C][C]3.18113949127792[/C][/ROW]
[ROW][C]68[/C][C]1258[/C][C]1263.34851634495[/C][C]-5.34851634494612[/C][/ROW]
[ROW][C]69[/C][C]1295[/C][C]1268.77919929883[/C][C]26.2208007011664[/C][/ROW]
[ROW][C]70[/C][C]1294[/C][C]1294.28777172282[/C][C]-0.287771722817297[/C][/ROW]
[ROW][C]71[/C][C]1318[/C][C]1307.01548923258[/C][C]10.9845107674178[/C][/ROW]
[ROW][C]72[/C][C]1262[/C][C]1327.21673946737[/C][C]-65.2167394673654[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=261014&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=261014&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
311691181-12
411841191.9864913414-7.98649134139578
511691203.40089967279-34.4008996727869
611891195.67698691924-6.67698691924056
711921200.01020572718-8.01020572718085
811981202.19991108166-4.19991108166369
911681205.430670995-37.4306709950019
1011791185.68190333279-6.68190333278835
1111731179.44158616652-6.44158616651953
1211721172.10762813394-0.107628133942399
1311251167.79442122172-42.7944212217176
1411271134.95509814154-7.95509814154184
1511231117.349147935435.65085206457275
1611321107.3360596222224.6639403777767
1711141111.08037234412.91962765590188
1811271104.9331602400322.0668397599691
1911291112.1202939781916.8797060218092
2011391119.9852125687419.0147874312604
2111171132.44406521225-15.4440652122528
2211311125.4604335745.53956642599724
2311321129.590823132382.40917686762032
2411401132.670480612937.32951938707424
2511051139.48808248518-34.4880824851816
2611261119.755881683076.24411831692646
2711291120.751284889878.2487151101252
2811391124.2572977832814.7427022167167
2911231133.64814273567-10.64814273567
3011011128.8502245438-27.8502245438033
3111101110.56634287916-0.566342879162448
3211281105.2752360540122.7247639459938
3311011115.43145648962-14.4314564896231
3411341105.0402344592328.9597655407661
3511391120.9167079138518.0832920861526
3611371134.965397994632.03460200537188
3711411141.69093835883-0.690938358831772
3811651146.9782569695218.0217430304797
3911461164.63207992638-18.6320799263767
4011341161.19125016468-27.1912501646757
4111411148.53762661376-7.53762661375845
4211591143.9050321604515.0949678395548
4311661152.9715789258513.0284210741452
4411921163.4912678819628.5087321180415
4511711186.79388806064-15.7938880606382
4611791185.86234429534-6.86234429533897
4711811187.93087112083-6.93087112082935
4811951188.665646546016.33435345398925
4911671196.95798649939-29.9579864993882
5011761182.2034694723-6.20346947229677
5111811177.689239737333.31076026267056
5211971178.3642143522318.63578564777
5311941189.894519080564.10548091943542
5411731195.21933749233-22.2193374923252
5511791183.73519805194-4.73519805194292
5611841179.756498347664.24350165234341
5711931180.8849591878312.1150408121687
5811931188.0664345044.9335654959998
5911931192.726040758250.273959241745615
6011911195.1999756768-4.19997567680093
6112221194.7376701740227.2623298259825
6211981214.49736162717-16.4973616271668
6312181210.151516231147.84848376886112
6412191218.967260149450.0327398505487508
6512601224.0367874658235.9632125341811
6612351253.10655587029-18.1065558702862
6712561252.818860508723.18113949127792
6812581263.34851634495-5.34851634494612
6912951268.7791992988326.2208007011664
7012941294.28777172282-0.287771722817297
7113181307.0154892325810.9845107674178
7212621327.21673946737-65.2167394673654







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
731298.593051737421261.966357819841335.21974565501
741301.280111473531257.237419357031345.32280359002
751303.967171209631249.915851257321358.01849116195
761306.654230945741240.462161480751372.84630041073

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
73 & 1298.59305173742 & 1261.96635781984 & 1335.21974565501 \tabularnewline
74 & 1301.28011147353 & 1257.23741935703 & 1345.32280359002 \tabularnewline
75 & 1303.96717120963 & 1249.91585125732 & 1358.01849116195 \tabularnewline
76 & 1306.65423094574 & 1240.46216148075 & 1372.84630041073 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=261014&T=3

[TABLE]
[ROW][C]Extrapolation Forecasts of Exponential Smoothing[/C][/ROW]
[ROW][C]t[/C][C]Forecast[/C][C]95% Lower Bound[/C][C]95% Upper Bound[/C][/ROW]
[ROW][C]73[/C][C]1298.59305173742[/C][C]1261.96635781984[/C][C]1335.21974565501[/C][/ROW]
[ROW][C]74[/C][C]1301.28011147353[/C][C]1257.23741935703[/C][C]1345.32280359002[/C][/ROW]
[ROW][C]75[/C][C]1303.96717120963[/C][C]1249.91585125732[/C][C]1358.01849116195[/C][/ROW]
[ROW][C]76[/C][C]1306.65423094574[/C][C]1240.46216148075[/C][C]1372.84630041073[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=261014&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=261014&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
731298.593051737421261.966357819841335.21974565501
741301.280111473531257.237419357031345.32280359002
751303.967171209631249.915851257321358.01849116195
761306.654230945741240.462161480751372.84630041073



Parameters (Session):
par1 = 4 ; par2 = Double ; par3 = additive ;
Parameters (R input):
par1 = 4 ; 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')