Free Statistics

of Irreproducible Research!

Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationMon, 13 Aug 2012 09:28:09 -0400
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2012/Aug/13/t13448647139q9z7ayb0qczksw.htm/, Retrieved Sun, 28 Apr 2024 12:25:55 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=169286, Retrieved Sun, 28 Apr 2024 12:25:55 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywordsVan Puyenbroeck Willem
Estimated Impact150
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [Tijdsreeks 1 stap 32] [2012-08-13 13:28:09] [d94b10b2615af2e11b32dea0ad6a3c7b] [Current]
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Dataseries X:
181896
181580
181234
180598
187123
186807
181896
178638
178954
178954
179269
179936
181580
179616
181580
179936
185158
187469
177656
175025
177305
176989
175025
175345
179269
178638
179269
179269
183545
184176
172398
172398
176989
174709
170785
172398
176327
174363
174047
169803
176007
177305
164545
164229
170785
167176
160967
163598
166509
167176
165212
161287
169456
169456
155078
154101
158025
150838
143616
145932
150838
146910
144283
138710
146247
146563
132190
131839
134470
126301
117465
121043
125950
120728
120412
115154
123670
125319
109266
105688
107968
99132
89981
92928
98470
91946
92928
89004
97172
98150
78524
77221
80799
71333
62817
65764
72950
64462
63799
57244
64462
66742
46448
46448
49391
41542
32706
37297
45466
36631
40244
35333
43186
45813
24853
23240
26502
18649
12444
15040




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'Gertrude Mary Cox' @ cox.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 & 'Gertrude Mary Cox' @ cox.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=169286&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]'Gertrude Mary Cox' @ cox.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=169286&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=169286&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'Gertrude Mary Cox' @ cox.wessa.net







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.481814648069058
beta0.104130420221486
gamma1

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.481814648069058 \tabularnewline
beta & 0.104130420221486 \tabularnewline
gamma & 1 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=169286&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]0.481814648069058[/C][/ROW]
[ROW][C]beta[/C][C]0.104130420221486[/C][/ROW]
[ROW][C]gamma[/C][C]1[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=169286&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=169286&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
alpha0.481814648069058
beta0.104130420221486
gamma1







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
13181580181944.496527778-364.496527777723
14179616179955.489022677-339.489022677008
15181580181781.53947204-201.539472039934
16179936179987.277818857-51.2778188566735
17185158185236.966742964-78.9667429638503
18187469187667.769519691-198.769519690977
19177656179966.460319809-2310.46031980938
20175025175354.079824247-329.079824246932
21177305175226.2636927812078.7363072187
22176989175992.612090359996.387909641257
23175025176698.751179894-1673.75117989368
24175345176331.236766329-986.236766328715
25179269177128.4107342772140.58926572348
26178638176311.4922773612326.50772263925
27179269179579.443162534-310.443162534299
28179269177891.0103512111377.98964878908
29183545183967.13871093-422.138710929779
30184176186305.444117649-2129.44411764873
31172398176617.723370519-4219.72337051903
32172398172054.426605553343.573394446983
33176989173474.420045953514.57995405031
34174709174419.780726376289.219273624389
35170785173414.147756481-2629.14775648067
36172398172907.214549466-509.214549465833
37176327175543.078579932783.921420067549
38174363174089.350081954273.649918045994
39174047174819.291780372-772.291780371772
40169803173577.60012023-3774.60012023032
41176007175774.167060159232.832939841464
42177305177112.039653906192.960346093983
43164545167145.34686953-2600.34686953016
44164229165493.381175415-1264.38117541478
45170785167467.5923204733317.40767952689
46167176166322.510030386853.489969613933
47160967163780.698421653-2813.69842165272
48163598163978.307661613-380.307661612751
49166509167047.775822057-538.775822056574
50167176164327.3861993232848.61380067709
51165212165520.230506362-308.23050636219
52161287162733.899799635-1446.8997996354
53169456168032.8859590261423.11404097354
54169456169887.6162885-431.616288499703
55155078158105.230724855-3027.23072485547
56154101156851.134834576-2750.1348345759
57158025160320.432236993-2295.43223699331
58150838154749.358711124-3911.35871112419
59143616147327.553324036-3711.55332403601
60145932147624.527003849-1692.52700384933
61150838149184.8133267321653.18667326786
62146910148590.993750282-1680.99375028154
63144283145053.473550218-770.473550217517
64138710140519.091409284-1809.09140928395
65146247146177.30154282369.6984571771463
66146563145397.4734220591165.52657794143
67132190132098.36754980391.6324501969211
68131839131705.813133915133.186866085045
69134470136159.858625077-1689.8586250775
70126301129433.493713818-3132.49371381837
71117465121919.853796048-4454.85379604793
72121043122296.992419188-1253.99241918766
73125950125216.341047261733.65895273925
74120728121819.692047122-1091.69204712214
75120412118435.4264144321976.57358556821
76115154114221.741051047932.258948952673
77123670121847.1989490821822.80105091831
78125319122240.702931293078.29706870986
79109266109163.507889519102.492110480598
80105688108655.049748927-2967.04974892717
81107968110372.467686511-2404.46768651067
8299132102220.175567412-3088.1755674124
838998193710.8189445554-3729.81894455543
849292895800.4633767834-2872.46337678342
859847098593.3135182929-123.313518292896
869194693418.2295336932-1472.22953369324
879292891001.79056784751926.20943215251
888900485781.4085171953222.59148280502
899717294645.47565879272526.52434120735
909815095737.5579800942412.44201990597
917852480473.0531988656-1949.05319886561
927722176958.1371322571262.862867742864
938079980257.9441087931541.055891206852
947133373052.9905491746-1719.99054917465
956281764821.4288517184-2004.4288517184
966576468224.2996580926-2460.29965809263
977295072698.6234582436251.376541756414
986446267082.1988530301-2620.19885303012
996379965893.1940716429-2094.19407164287
1005724459225.3003146439-1981.30031464393
1016446264778.0883895319-316.088389531877
1026674263855.54817535182886.45182464819
1034644845997.2528434805450.747156519479
1044644844343.06749471482104.93250528523
1054939148325.27491451881065.72508548116
1064154239878.505744911663.49425508998
1073270632976.5517748831-270.55177488309
1083729736912.3826505795384.617349420514
1094546644239.09222279991226.90777720005
1103663137730.1406749356-1099.14067493564
1114024437748.34196642882495.65803357121
1123533333782.45611516511550.54388483491
1134318642509.0750647089676.924935291056
1144581344383.56185067681429.43814932324
1152485325147.0780618908-294.078061890767
1162324024539.7991402458-1299.79914024578
1172650226720.8337243493-218.83372434933
1181864918278.2310161287370.768983871312
119124449999.701190751212444.29880924879
1201504015967.766621181-927.766621180956

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 181580 & 181944.496527778 & -364.496527777723 \tabularnewline
14 & 179616 & 179955.489022677 & -339.489022677008 \tabularnewline
15 & 181580 & 181781.53947204 & -201.539472039934 \tabularnewline
16 & 179936 & 179987.277818857 & -51.2778188566735 \tabularnewline
17 & 185158 & 185236.966742964 & -78.9667429638503 \tabularnewline
18 & 187469 & 187667.769519691 & -198.769519690977 \tabularnewline
19 & 177656 & 179966.460319809 & -2310.46031980938 \tabularnewline
20 & 175025 & 175354.079824247 & -329.079824246932 \tabularnewline
21 & 177305 & 175226.263692781 & 2078.7363072187 \tabularnewline
22 & 176989 & 175992.612090359 & 996.387909641257 \tabularnewline
23 & 175025 & 176698.751179894 & -1673.75117989368 \tabularnewline
24 & 175345 & 176331.236766329 & -986.236766328715 \tabularnewline
25 & 179269 & 177128.410734277 & 2140.58926572348 \tabularnewline
26 & 178638 & 176311.492277361 & 2326.50772263925 \tabularnewline
27 & 179269 & 179579.443162534 & -310.443162534299 \tabularnewline
28 & 179269 & 177891.010351211 & 1377.98964878908 \tabularnewline
29 & 183545 & 183967.13871093 & -422.138710929779 \tabularnewline
30 & 184176 & 186305.444117649 & -2129.44411764873 \tabularnewline
31 & 172398 & 176617.723370519 & -4219.72337051903 \tabularnewline
32 & 172398 & 172054.426605553 & 343.573394446983 \tabularnewline
33 & 176989 & 173474.42004595 & 3514.57995405031 \tabularnewline
34 & 174709 & 174419.780726376 & 289.219273624389 \tabularnewline
35 & 170785 & 173414.147756481 & -2629.14775648067 \tabularnewline
36 & 172398 & 172907.214549466 & -509.214549465833 \tabularnewline
37 & 176327 & 175543.078579932 & 783.921420067549 \tabularnewline
38 & 174363 & 174089.350081954 & 273.649918045994 \tabularnewline
39 & 174047 & 174819.291780372 & -772.291780371772 \tabularnewline
40 & 169803 & 173577.60012023 & -3774.60012023032 \tabularnewline
41 & 176007 & 175774.167060159 & 232.832939841464 \tabularnewline
42 & 177305 & 177112.039653906 & 192.960346093983 \tabularnewline
43 & 164545 & 167145.34686953 & -2600.34686953016 \tabularnewline
44 & 164229 & 165493.381175415 & -1264.38117541478 \tabularnewline
45 & 170785 & 167467.592320473 & 3317.40767952689 \tabularnewline
46 & 167176 & 166322.510030386 & 853.489969613933 \tabularnewline
47 & 160967 & 163780.698421653 & -2813.69842165272 \tabularnewline
48 & 163598 & 163978.307661613 & -380.307661612751 \tabularnewline
49 & 166509 & 167047.775822057 & -538.775822056574 \tabularnewline
50 & 167176 & 164327.386199323 & 2848.61380067709 \tabularnewline
51 & 165212 & 165520.230506362 & -308.23050636219 \tabularnewline
52 & 161287 & 162733.899799635 & -1446.8997996354 \tabularnewline
53 & 169456 & 168032.885959026 & 1423.11404097354 \tabularnewline
54 & 169456 & 169887.6162885 & -431.616288499703 \tabularnewline
55 & 155078 & 158105.230724855 & -3027.23072485547 \tabularnewline
56 & 154101 & 156851.134834576 & -2750.1348345759 \tabularnewline
57 & 158025 & 160320.432236993 & -2295.43223699331 \tabularnewline
58 & 150838 & 154749.358711124 & -3911.35871112419 \tabularnewline
59 & 143616 & 147327.553324036 & -3711.55332403601 \tabularnewline
60 & 145932 & 147624.527003849 & -1692.52700384933 \tabularnewline
61 & 150838 & 149184.813326732 & 1653.18667326786 \tabularnewline
62 & 146910 & 148590.993750282 & -1680.99375028154 \tabularnewline
63 & 144283 & 145053.473550218 & -770.473550217517 \tabularnewline
64 & 138710 & 140519.091409284 & -1809.09140928395 \tabularnewline
65 & 146247 & 146177.301542823 & 69.6984571771463 \tabularnewline
66 & 146563 & 145397.473422059 & 1165.52657794143 \tabularnewline
67 & 132190 & 132098.367549803 & 91.6324501969211 \tabularnewline
68 & 131839 & 131705.813133915 & 133.186866085045 \tabularnewline
69 & 134470 & 136159.858625077 & -1689.8586250775 \tabularnewline
70 & 126301 & 129433.493713818 & -3132.49371381837 \tabularnewline
71 & 117465 & 121919.853796048 & -4454.85379604793 \tabularnewline
72 & 121043 & 122296.992419188 & -1253.99241918766 \tabularnewline
73 & 125950 & 125216.341047261 & 733.65895273925 \tabularnewline
74 & 120728 & 121819.692047122 & -1091.69204712214 \tabularnewline
75 & 120412 & 118435.426414432 & 1976.57358556821 \tabularnewline
76 & 115154 & 114221.741051047 & 932.258948952673 \tabularnewline
77 & 123670 & 121847.198949082 & 1822.80105091831 \tabularnewline
78 & 125319 & 122240.70293129 & 3078.29706870986 \tabularnewline
79 & 109266 & 109163.507889519 & 102.492110480598 \tabularnewline
80 & 105688 & 108655.049748927 & -2967.04974892717 \tabularnewline
81 & 107968 & 110372.467686511 & -2404.46768651067 \tabularnewline
82 & 99132 & 102220.175567412 & -3088.1755674124 \tabularnewline
83 & 89981 & 93710.8189445554 & -3729.81894455543 \tabularnewline
84 & 92928 & 95800.4633767834 & -2872.46337678342 \tabularnewline
85 & 98470 & 98593.3135182929 & -123.313518292896 \tabularnewline
86 & 91946 & 93418.2295336932 & -1472.22953369324 \tabularnewline
87 & 92928 & 91001.7905678475 & 1926.20943215251 \tabularnewline
88 & 89004 & 85781.408517195 & 3222.59148280502 \tabularnewline
89 & 97172 & 94645.4756587927 & 2526.52434120735 \tabularnewline
90 & 98150 & 95737.557980094 & 2412.44201990597 \tabularnewline
91 & 78524 & 80473.0531988656 & -1949.05319886561 \tabularnewline
92 & 77221 & 76958.1371322571 & 262.862867742864 \tabularnewline
93 & 80799 & 80257.9441087931 & 541.055891206852 \tabularnewline
94 & 71333 & 73052.9905491746 & -1719.99054917465 \tabularnewline
95 & 62817 & 64821.4288517184 & -2004.4288517184 \tabularnewline
96 & 65764 & 68224.2996580926 & -2460.29965809263 \tabularnewline
97 & 72950 & 72698.6234582436 & 251.376541756414 \tabularnewline
98 & 64462 & 67082.1988530301 & -2620.19885303012 \tabularnewline
99 & 63799 & 65893.1940716429 & -2094.19407164287 \tabularnewline
100 & 57244 & 59225.3003146439 & -1981.30031464393 \tabularnewline
101 & 64462 & 64778.0883895319 & -316.088389531877 \tabularnewline
102 & 66742 & 63855.5481753518 & 2886.45182464819 \tabularnewline
103 & 46448 & 45997.2528434805 & 450.747156519479 \tabularnewline
104 & 46448 & 44343.0674947148 & 2104.93250528523 \tabularnewline
105 & 49391 & 48325.2749145188 & 1065.72508548116 \tabularnewline
106 & 41542 & 39878.50574491 & 1663.49425508998 \tabularnewline
107 & 32706 & 32976.5517748831 & -270.55177488309 \tabularnewline
108 & 37297 & 36912.3826505795 & 384.617349420514 \tabularnewline
109 & 45466 & 44239.0922227999 & 1226.90777720005 \tabularnewline
110 & 36631 & 37730.1406749356 & -1099.14067493564 \tabularnewline
111 & 40244 & 37748.3419664288 & 2495.65803357121 \tabularnewline
112 & 35333 & 33782.4561151651 & 1550.54388483491 \tabularnewline
113 & 43186 & 42509.0750647089 & 676.924935291056 \tabularnewline
114 & 45813 & 44383.5618506768 & 1429.43814932324 \tabularnewline
115 & 24853 & 25147.0780618908 & -294.078061890767 \tabularnewline
116 & 23240 & 24539.7991402458 & -1299.79914024578 \tabularnewline
117 & 26502 & 26720.8337243493 & -218.83372434933 \tabularnewline
118 & 18649 & 18278.2310161287 & 370.768983871312 \tabularnewline
119 & 12444 & 9999.70119075121 & 2444.29880924879 \tabularnewline
120 & 15040 & 15967.766621181 & -927.766621180956 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=169286&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]181580[/C][C]181944.496527778[/C][C]-364.496527777723[/C][/ROW]
[ROW][C]14[/C][C]179616[/C][C]179955.489022677[/C][C]-339.489022677008[/C][/ROW]
[ROW][C]15[/C][C]181580[/C][C]181781.53947204[/C][C]-201.539472039934[/C][/ROW]
[ROW][C]16[/C][C]179936[/C][C]179987.277818857[/C][C]-51.2778188566735[/C][/ROW]
[ROW][C]17[/C][C]185158[/C][C]185236.966742964[/C][C]-78.9667429638503[/C][/ROW]
[ROW][C]18[/C][C]187469[/C][C]187667.769519691[/C][C]-198.769519690977[/C][/ROW]
[ROW][C]19[/C][C]177656[/C][C]179966.460319809[/C][C]-2310.46031980938[/C][/ROW]
[ROW][C]20[/C][C]175025[/C][C]175354.079824247[/C][C]-329.079824246932[/C][/ROW]
[ROW][C]21[/C][C]177305[/C][C]175226.263692781[/C][C]2078.7363072187[/C][/ROW]
[ROW][C]22[/C][C]176989[/C][C]175992.612090359[/C][C]996.387909641257[/C][/ROW]
[ROW][C]23[/C][C]175025[/C][C]176698.751179894[/C][C]-1673.75117989368[/C][/ROW]
[ROW][C]24[/C][C]175345[/C][C]176331.236766329[/C][C]-986.236766328715[/C][/ROW]
[ROW][C]25[/C][C]179269[/C][C]177128.410734277[/C][C]2140.58926572348[/C][/ROW]
[ROW][C]26[/C][C]178638[/C][C]176311.492277361[/C][C]2326.50772263925[/C][/ROW]
[ROW][C]27[/C][C]179269[/C][C]179579.443162534[/C][C]-310.443162534299[/C][/ROW]
[ROW][C]28[/C][C]179269[/C][C]177891.010351211[/C][C]1377.98964878908[/C][/ROW]
[ROW][C]29[/C][C]183545[/C][C]183967.13871093[/C][C]-422.138710929779[/C][/ROW]
[ROW][C]30[/C][C]184176[/C][C]186305.444117649[/C][C]-2129.44411764873[/C][/ROW]
[ROW][C]31[/C][C]172398[/C][C]176617.723370519[/C][C]-4219.72337051903[/C][/ROW]
[ROW][C]32[/C][C]172398[/C][C]172054.426605553[/C][C]343.573394446983[/C][/ROW]
[ROW][C]33[/C][C]176989[/C][C]173474.42004595[/C][C]3514.57995405031[/C][/ROW]
[ROW][C]34[/C][C]174709[/C][C]174419.780726376[/C][C]289.219273624389[/C][/ROW]
[ROW][C]35[/C][C]170785[/C][C]173414.147756481[/C][C]-2629.14775648067[/C][/ROW]
[ROW][C]36[/C][C]172398[/C][C]172907.214549466[/C][C]-509.214549465833[/C][/ROW]
[ROW][C]37[/C][C]176327[/C][C]175543.078579932[/C][C]783.921420067549[/C][/ROW]
[ROW][C]38[/C][C]174363[/C][C]174089.350081954[/C][C]273.649918045994[/C][/ROW]
[ROW][C]39[/C][C]174047[/C][C]174819.291780372[/C][C]-772.291780371772[/C][/ROW]
[ROW][C]40[/C][C]169803[/C][C]173577.60012023[/C][C]-3774.60012023032[/C][/ROW]
[ROW][C]41[/C][C]176007[/C][C]175774.167060159[/C][C]232.832939841464[/C][/ROW]
[ROW][C]42[/C][C]177305[/C][C]177112.039653906[/C][C]192.960346093983[/C][/ROW]
[ROW][C]43[/C][C]164545[/C][C]167145.34686953[/C][C]-2600.34686953016[/C][/ROW]
[ROW][C]44[/C][C]164229[/C][C]165493.381175415[/C][C]-1264.38117541478[/C][/ROW]
[ROW][C]45[/C][C]170785[/C][C]167467.592320473[/C][C]3317.40767952689[/C][/ROW]
[ROW][C]46[/C][C]167176[/C][C]166322.510030386[/C][C]853.489969613933[/C][/ROW]
[ROW][C]47[/C][C]160967[/C][C]163780.698421653[/C][C]-2813.69842165272[/C][/ROW]
[ROW][C]48[/C][C]163598[/C][C]163978.307661613[/C][C]-380.307661612751[/C][/ROW]
[ROW][C]49[/C][C]166509[/C][C]167047.775822057[/C][C]-538.775822056574[/C][/ROW]
[ROW][C]50[/C][C]167176[/C][C]164327.386199323[/C][C]2848.61380067709[/C][/ROW]
[ROW][C]51[/C][C]165212[/C][C]165520.230506362[/C][C]-308.23050636219[/C][/ROW]
[ROW][C]52[/C][C]161287[/C][C]162733.899799635[/C][C]-1446.8997996354[/C][/ROW]
[ROW][C]53[/C][C]169456[/C][C]168032.885959026[/C][C]1423.11404097354[/C][/ROW]
[ROW][C]54[/C][C]169456[/C][C]169887.6162885[/C][C]-431.616288499703[/C][/ROW]
[ROW][C]55[/C][C]155078[/C][C]158105.230724855[/C][C]-3027.23072485547[/C][/ROW]
[ROW][C]56[/C][C]154101[/C][C]156851.134834576[/C][C]-2750.1348345759[/C][/ROW]
[ROW][C]57[/C][C]158025[/C][C]160320.432236993[/C][C]-2295.43223699331[/C][/ROW]
[ROW][C]58[/C][C]150838[/C][C]154749.358711124[/C][C]-3911.35871112419[/C][/ROW]
[ROW][C]59[/C][C]143616[/C][C]147327.553324036[/C][C]-3711.55332403601[/C][/ROW]
[ROW][C]60[/C][C]145932[/C][C]147624.527003849[/C][C]-1692.52700384933[/C][/ROW]
[ROW][C]61[/C][C]150838[/C][C]149184.813326732[/C][C]1653.18667326786[/C][/ROW]
[ROW][C]62[/C][C]146910[/C][C]148590.993750282[/C][C]-1680.99375028154[/C][/ROW]
[ROW][C]63[/C][C]144283[/C][C]145053.473550218[/C][C]-770.473550217517[/C][/ROW]
[ROW][C]64[/C][C]138710[/C][C]140519.091409284[/C][C]-1809.09140928395[/C][/ROW]
[ROW][C]65[/C][C]146247[/C][C]146177.301542823[/C][C]69.6984571771463[/C][/ROW]
[ROW][C]66[/C][C]146563[/C][C]145397.473422059[/C][C]1165.52657794143[/C][/ROW]
[ROW][C]67[/C][C]132190[/C][C]132098.367549803[/C][C]91.6324501969211[/C][/ROW]
[ROW][C]68[/C][C]131839[/C][C]131705.813133915[/C][C]133.186866085045[/C][/ROW]
[ROW][C]69[/C][C]134470[/C][C]136159.858625077[/C][C]-1689.8586250775[/C][/ROW]
[ROW][C]70[/C][C]126301[/C][C]129433.493713818[/C][C]-3132.49371381837[/C][/ROW]
[ROW][C]71[/C][C]117465[/C][C]121919.853796048[/C][C]-4454.85379604793[/C][/ROW]
[ROW][C]72[/C][C]121043[/C][C]122296.992419188[/C][C]-1253.99241918766[/C][/ROW]
[ROW][C]73[/C][C]125950[/C][C]125216.341047261[/C][C]733.65895273925[/C][/ROW]
[ROW][C]74[/C][C]120728[/C][C]121819.692047122[/C][C]-1091.69204712214[/C][/ROW]
[ROW][C]75[/C][C]120412[/C][C]118435.426414432[/C][C]1976.57358556821[/C][/ROW]
[ROW][C]76[/C][C]115154[/C][C]114221.741051047[/C][C]932.258948952673[/C][/ROW]
[ROW][C]77[/C][C]123670[/C][C]121847.198949082[/C][C]1822.80105091831[/C][/ROW]
[ROW][C]78[/C][C]125319[/C][C]122240.70293129[/C][C]3078.29706870986[/C][/ROW]
[ROW][C]79[/C][C]109266[/C][C]109163.507889519[/C][C]102.492110480598[/C][/ROW]
[ROW][C]80[/C][C]105688[/C][C]108655.049748927[/C][C]-2967.04974892717[/C][/ROW]
[ROW][C]81[/C][C]107968[/C][C]110372.467686511[/C][C]-2404.46768651067[/C][/ROW]
[ROW][C]82[/C][C]99132[/C][C]102220.175567412[/C][C]-3088.1755674124[/C][/ROW]
[ROW][C]83[/C][C]89981[/C][C]93710.8189445554[/C][C]-3729.81894455543[/C][/ROW]
[ROW][C]84[/C][C]92928[/C][C]95800.4633767834[/C][C]-2872.46337678342[/C][/ROW]
[ROW][C]85[/C][C]98470[/C][C]98593.3135182929[/C][C]-123.313518292896[/C][/ROW]
[ROW][C]86[/C][C]91946[/C][C]93418.2295336932[/C][C]-1472.22953369324[/C][/ROW]
[ROW][C]87[/C][C]92928[/C][C]91001.7905678475[/C][C]1926.20943215251[/C][/ROW]
[ROW][C]88[/C][C]89004[/C][C]85781.408517195[/C][C]3222.59148280502[/C][/ROW]
[ROW][C]89[/C][C]97172[/C][C]94645.4756587927[/C][C]2526.52434120735[/C][/ROW]
[ROW][C]90[/C][C]98150[/C][C]95737.557980094[/C][C]2412.44201990597[/C][/ROW]
[ROW][C]91[/C][C]78524[/C][C]80473.0531988656[/C][C]-1949.05319886561[/C][/ROW]
[ROW][C]92[/C][C]77221[/C][C]76958.1371322571[/C][C]262.862867742864[/C][/ROW]
[ROW][C]93[/C][C]80799[/C][C]80257.9441087931[/C][C]541.055891206852[/C][/ROW]
[ROW][C]94[/C][C]71333[/C][C]73052.9905491746[/C][C]-1719.99054917465[/C][/ROW]
[ROW][C]95[/C][C]62817[/C][C]64821.4288517184[/C][C]-2004.4288517184[/C][/ROW]
[ROW][C]96[/C][C]65764[/C][C]68224.2996580926[/C][C]-2460.29965809263[/C][/ROW]
[ROW][C]97[/C][C]72950[/C][C]72698.6234582436[/C][C]251.376541756414[/C][/ROW]
[ROW][C]98[/C][C]64462[/C][C]67082.1988530301[/C][C]-2620.19885303012[/C][/ROW]
[ROW][C]99[/C][C]63799[/C][C]65893.1940716429[/C][C]-2094.19407164287[/C][/ROW]
[ROW][C]100[/C][C]57244[/C][C]59225.3003146439[/C][C]-1981.30031464393[/C][/ROW]
[ROW][C]101[/C][C]64462[/C][C]64778.0883895319[/C][C]-316.088389531877[/C][/ROW]
[ROW][C]102[/C][C]66742[/C][C]63855.5481753518[/C][C]2886.45182464819[/C][/ROW]
[ROW][C]103[/C][C]46448[/C][C]45997.2528434805[/C][C]450.747156519479[/C][/ROW]
[ROW][C]104[/C][C]46448[/C][C]44343.0674947148[/C][C]2104.93250528523[/C][/ROW]
[ROW][C]105[/C][C]49391[/C][C]48325.2749145188[/C][C]1065.72508548116[/C][/ROW]
[ROW][C]106[/C][C]41542[/C][C]39878.50574491[/C][C]1663.49425508998[/C][/ROW]
[ROW][C]107[/C][C]32706[/C][C]32976.5517748831[/C][C]-270.55177488309[/C][/ROW]
[ROW][C]108[/C][C]37297[/C][C]36912.3826505795[/C][C]384.617349420514[/C][/ROW]
[ROW][C]109[/C][C]45466[/C][C]44239.0922227999[/C][C]1226.90777720005[/C][/ROW]
[ROW][C]110[/C][C]36631[/C][C]37730.1406749356[/C][C]-1099.14067493564[/C][/ROW]
[ROW][C]111[/C][C]40244[/C][C]37748.3419664288[/C][C]2495.65803357121[/C][/ROW]
[ROW][C]112[/C][C]35333[/C][C]33782.4561151651[/C][C]1550.54388483491[/C][/ROW]
[ROW][C]113[/C][C]43186[/C][C]42509.0750647089[/C][C]676.924935291056[/C][/ROW]
[ROW][C]114[/C][C]45813[/C][C]44383.5618506768[/C][C]1429.43814932324[/C][/ROW]
[ROW][C]115[/C][C]24853[/C][C]25147.0780618908[/C][C]-294.078061890767[/C][/ROW]
[ROW][C]116[/C][C]23240[/C][C]24539.7991402458[/C][C]-1299.79914024578[/C][/ROW]
[ROW][C]117[/C][C]26502[/C][C]26720.8337243493[/C][C]-218.83372434933[/C][/ROW]
[ROW][C]118[/C][C]18649[/C][C]18278.2310161287[/C][C]370.768983871312[/C][/ROW]
[ROW][C]119[/C][C]12444[/C][C]9999.70119075121[/C][C]2444.29880924879[/C][/ROW]
[ROW][C]120[/C][C]15040[/C][C]15967.766621181[/C][C]-927.766621180956[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=169286&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=169286&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
13181580181944.496527778-364.496527777723
14179616179955.489022677-339.489022677008
15181580181781.53947204-201.539472039934
16179936179987.277818857-51.2778188566735
17185158185236.966742964-78.9667429638503
18187469187667.769519691-198.769519690977
19177656179966.460319809-2310.46031980938
20175025175354.079824247-329.079824246932
21177305175226.2636927812078.7363072187
22176989175992.612090359996.387909641257
23175025176698.751179894-1673.75117989368
24175345176331.236766329-986.236766328715
25179269177128.4107342772140.58926572348
26178638176311.4922773612326.50772263925
27179269179579.443162534-310.443162534299
28179269177891.0103512111377.98964878908
29183545183967.13871093-422.138710929779
30184176186305.444117649-2129.44411764873
31172398176617.723370519-4219.72337051903
32172398172054.426605553343.573394446983
33176989173474.420045953514.57995405031
34174709174419.780726376289.219273624389
35170785173414.147756481-2629.14775648067
36172398172907.214549466-509.214549465833
37176327175543.078579932783.921420067549
38174363174089.350081954273.649918045994
39174047174819.291780372-772.291780371772
40169803173577.60012023-3774.60012023032
41176007175774.167060159232.832939841464
42177305177112.039653906192.960346093983
43164545167145.34686953-2600.34686953016
44164229165493.381175415-1264.38117541478
45170785167467.5923204733317.40767952689
46167176166322.510030386853.489969613933
47160967163780.698421653-2813.69842165272
48163598163978.307661613-380.307661612751
49166509167047.775822057-538.775822056574
50167176164327.3861993232848.61380067709
51165212165520.230506362-308.23050636219
52161287162733.899799635-1446.8997996354
53169456168032.8859590261423.11404097354
54169456169887.6162885-431.616288499703
55155078158105.230724855-3027.23072485547
56154101156851.134834576-2750.1348345759
57158025160320.432236993-2295.43223699331
58150838154749.358711124-3911.35871112419
59143616147327.553324036-3711.55332403601
60145932147624.527003849-1692.52700384933
61150838149184.8133267321653.18667326786
62146910148590.993750282-1680.99375028154
63144283145053.473550218-770.473550217517
64138710140519.091409284-1809.09140928395
65146247146177.30154282369.6984571771463
66146563145397.4734220591165.52657794143
67132190132098.36754980391.6324501969211
68131839131705.813133915133.186866085045
69134470136159.858625077-1689.8586250775
70126301129433.493713818-3132.49371381837
71117465121919.853796048-4454.85379604793
72121043122296.992419188-1253.99241918766
73125950125216.341047261733.65895273925
74120728121819.692047122-1091.69204712214
75120412118435.4264144321976.57358556821
76115154114221.741051047932.258948952673
77123670121847.1989490821822.80105091831
78125319122240.702931293078.29706870986
79109266109163.507889519102.492110480598
80105688108655.049748927-2967.04974892717
81107968110372.467686511-2404.46768651067
8299132102220.175567412-3088.1755674124
838998193710.8189445554-3729.81894455543
849292895800.4633767834-2872.46337678342
859847098593.3135182929-123.313518292896
869194693418.2295336932-1472.22953369324
879292891001.79056784751926.20943215251
888900485781.4085171953222.59148280502
899717294645.47565879272526.52434120735
909815095737.5579800942412.44201990597
917852480473.0531988656-1949.05319886561
927722176958.1371322571262.862867742864
938079980257.9441087931541.055891206852
947133373052.9905491746-1719.99054917465
956281764821.4288517184-2004.4288517184
966576468224.2996580926-2460.29965809263
977295072698.6234582436251.376541756414
986446267082.1988530301-2620.19885303012
996379965893.1940716429-2094.19407164287
1005724459225.3003146439-1981.30031464393
1016446264778.0883895319-316.088389531877
1026674263855.54817535182886.45182464819
1034644845997.2528434805450.747156519479
1044644844343.06749471482104.93250528523
1054939148325.27491451881065.72508548116
1064154239878.505744911663.49425508998
1073270632976.5517748831-270.55177488309
1083729736912.3826505795384.617349420514
1094546644239.09222279991226.90777720005
1103663137730.1406749356-1099.14067493564
1114024437748.34196642882495.65803357121
1123533333782.45611516511550.54388483491
1134318642509.0750647089676.924935291056
1144581344383.56185067681429.43814932324
1152485325147.0780618908-294.078061890767
1162324024539.7991402458-1299.79914024578
1172650226720.8337243493-218.83372434933
1181864918278.2310161287370.768983871312
119124449999.701190751212444.29880924879
1201504015967.766621181-927.766621180956







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
12123417.449313499819728.137922685327106.7607043143
12215369.311890917811190.428817534619548.194964301
12318092.293397986513393.78913232122790.7976636519
12412621.43368481987375.6565985512617867.2107710883
12520257.703170075314438.915377582726076.490962568
12622271.438384738515855.457737929728687.4190315472
1271456.87181174057-5579.195912303278492.93953578442
128488.63074181396-7189.333725765048166.59520939296
1293939.7776533088-4400.9656363788612280.5209429964
130-3997.17542683921-13020.77519159755026.42433791911
131-11303.7876090397-21029.6152630576-1577.95995502185
132-8307.32356131004-18754.12374451592139.47662189578

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
121 & 23417.4493134998 & 19728.1379226853 & 27106.7607043143 \tabularnewline
122 & 15369.3118909178 & 11190.4288175346 & 19548.194964301 \tabularnewline
123 & 18092.2933979865 & 13393.789132321 & 22790.7976636519 \tabularnewline
124 & 12621.4336848198 & 7375.65659855126 & 17867.2107710883 \tabularnewline
125 & 20257.7031700753 & 14438.9153775827 & 26076.490962568 \tabularnewline
126 & 22271.4383847385 & 15855.4577379297 & 28687.4190315472 \tabularnewline
127 & 1456.87181174057 & -5579.19591230327 & 8492.93953578442 \tabularnewline
128 & 488.63074181396 & -7189.33372576504 & 8166.59520939296 \tabularnewline
129 & 3939.7776533088 & -4400.96563637886 & 12280.5209429964 \tabularnewline
130 & -3997.17542683921 & -13020.7751915975 & 5026.42433791911 \tabularnewline
131 & -11303.7876090397 & -21029.6152630576 & -1577.95995502185 \tabularnewline
132 & -8307.32356131004 & -18754.1237445159 & 2139.47662189578 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=169286&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]23417.4493134998[/C][C]19728.1379226853[/C][C]27106.7607043143[/C][/ROW]
[ROW][C]122[/C][C]15369.3118909178[/C][C]11190.4288175346[/C][C]19548.194964301[/C][/ROW]
[ROW][C]123[/C][C]18092.2933979865[/C][C]13393.789132321[/C][C]22790.7976636519[/C][/ROW]
[ROW][C]124[/C][C]12621.4336848198[/C][C]7375.65659855126[/C][C]17867.2107710883[/C][/ROW]
[ROW][C]125[/C][C]20257.7031700753[/C][C]14438.9153775827[/C][C]26076.490962568[/C][/ROW]
[ROW][C]126[/C][C]22271.4383847385[/C][C]15855.4577379297[/C][C]28687.4190315472[/C][/ROW]
[ROW][C]127[/C][C]1456.87181174057[/C][C]-5579.19591230327[/C][C]8492.93953578442[/C][/ROW]
[ROW][C]128[/C][C]488.63074181396[/C][C]-7189.33372576504[/C][C]8166.59520939296[/C][/ROW]
[ROW][C]129[/C][C]3939.7776533088[/C][C]-4400.96563637886[/C][C]12280.5209429964[/C][/ROW]
[ROW][C]130[/C][C]-3997.17542683921[/C][C]-13020.7751915975[/C][C]5026.42433791911[/C][/ROW]
[ROW][C]131[/C][C]-11303.7876090397[/C][C]-21029.6152630576[/C][C]-1577.95995502185[/C][/ROW]
[ROW][C]132[/C][C]-8307.32356131004[/C][C]-18754.1237445159[/C][C]2139.47662189578[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=169286&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=169286&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
12123417.449313499819728.137922685327106.7607043143
12215369.311890917811190.428817534619548.194964301
12318092.293397986513393.78913232122790.7976636519
12412621.43368481987375.6565985512617867.2107710883
12520257.703170075314438.915377582726076.490962568
12622271.438384738515855.457737929728687.4190315472
1271456.87181174057-5579.195912303278492.93953578442
128488.63074181396-7189.333725765048166.59520939296
1293939.7776533088-4400.9656363788612280.5209429964
130-3997.17542683921-13020.77519159755026.42433791911
131-11303.7876090397-21029.6152630576-1577.95995502185
132-8307.32356131004-18754.12374451592139.47662189578



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