Free Statistics

of Irreproducible Research!

Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationThu, 19 May 2011 19:13:59 +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/2011/May/19/t13058322433iqt3t0k5uc877w.htm/, Retrieved Sun, 12 May 2024 08:22:37 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=122203, Retrieved Sun, 12 May 2024 08:22:37 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywordsKDGP2W102
Estimated Impact84
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [Opgave 10 oef2-st...] [2011-05-19 19:13:59] [439e035dc5bc96f212031d0688fc7c62] [Current]
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Dataseries X:
112
118
129
99
116
168
118
129
205
147
150
267
126
129
124
97
102
127
222
214
118
141
154
226
89
77
82
97
127
121
117
117
106
112
134
169
75
108
115
85
101
108
109
124
105
95
135
164
88
85
112
87
91
87
87
142
95
108
139
159
61
82
124
93
108
75
87
103
90
108
123
129
57
65
67
71
76
67
110
118
99
85
107
141
58
65
70
86
93
74
87
73
101
100
96
157
63
115
70
66
67
83
79
77
102
116
100
135
71
60
89
74
73
91
86
74
87
87
109
137
43
69
73
77
69
76
78
70
83
65
110
132
54
55
66
65
60
65
96
55
71
63
74
106
34
47
56
53
53
55
67
52
46
51
58
91
33
40
46
45
41
55
57
54
46
52
48
77
77
35
42
48
44
45
0
0
46
51
63
84
30
39
45
52
28
40
62




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'Sir Ronald Aylmer Fisher' @ 193.190.124.24

\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 & 'Sir Ronald Aylmer Fisher' @ 193.190.124.24 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=122203&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]'Sir Ronald Aylmer Fisher' @ 193.190.124.24[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=122203&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=122203&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'Sir Ronald Aylmer Fisher' @ 193.190.124.24







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.159423424226509
beta0.127725156122087
gammaFALSE

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.159423424226509 \tabularnewline
beta & 0.127725156122087 \tabularnewline
gamma & FALSE \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=122203&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]0.159423424226509[/C][/ROW]
[ROW][C]beta[/C][C]0.127725156122087[/C][/ROW]
[ROW][C]gamma[/C][C]FALSE[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=122203&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=122203&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
alpha0.159423424226509
beta0.127725156122087
gammaFALSE







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
31291245
499130.898929029877-31.8989290298768
5116131.265766273234-15.2657662732339
6168133.97347191842834.0265280815725
7118145.23238507203-27.2323850720304
8129146.170676305523-17.1706763055232
9205148.36340373832356.6365962616766
10147163.475995290642-16.4759952906417
11150166.597236637815-16.5972366378149
12267169.36119000586997.6388099941312
13126192.32520382069-66.3252038206905
14129187.798973983464-58.7989739834636
15124183.275314323711-59.2753143237111
1697177.468728277277-80.4687282772769
17102166.644880643289-64.6448806432889
18127157.027401245783-30.0274012457825
19222152.31732954482569.6826704551753
20214164.92228404139249.0777159586081
21118175.241665323796-57.2416653237957
22141167.445670139252-26.4456701392518
23154164.020781128511-10.0207811285115
24226163.01035719564362.9896428043567
2589174.922124203388-85.922124203388
2677161.344288313437-84.3442883134365
2782146.300545826955-64.3005458269554
2897133.142933141196-36.1429331411957
29127123.7383472856993.26165271430052
30121120.6821904552150.31780954478532
31117117.163187425534-0.163187425534304
32117113.5641793271483.43582067285233
33106110.608898915786-4.60889891578596
34112106.2772536014965.72274639850362
35134103.70924330792330.2907566920772
36169105.67474129300863.3252587069916
3775114.196165799066-39.1961657990656
38108105.5751464626962.42485353730424
39115103.63886834213911.3611316578606
4085103.358581979319-18.3585819793189
4110197.96645264679753.03354735320247
4210896.046500073222211.9534999267778
4310995.791998611608213.2080013883918
4412496.006440435111627.9935595648884
4510599.14806211858175.85193788141828
469598.8789500484571-3.87895004845711
4713596.97952184211638.020478157884
48164102.53403144408761.4659685559129
4988113.07789492428-25.07789492428
5085109.313993672763-24.3139936727632
51112105.176785353536.82321464646965
5287106.142514306789-19.1425143067895
5391102.578910653835-11.5789106538349
548799.9853483957574-12.9853483957574
558796.9031543957249-9.9031543957249
5614294.110682506984547.8893174930155
5795101.506824945746-6.50682494574593
58108100.0984536386897.90154636131112
59139101.14800852634537.8519914736549
60159107.7431226312651.25687736874
6161117.519001651171-56.5190016511712
6282108.962019501021-26.9620195010212
63124104.5681017212519.4318982787497
6493107.96614090807-14.9661409080702
65108105.5755806265722.42441937342751
6675106.00684996717-31.0068499671697
6787100.477018557389-13.4770185573894
6810397.46742870036785.53257129963218
699097.60106908035-7.60106908034997
7010895.486123668082412.5138763319176
7112396.832784058596126.1672159414039
72129100.88893344208528.1110665579149
7357105.827386415663-48.8273864156626
746597.5058058795078-32.5058058795078
756791.1243719728431-24.1243719728431
767185.5879052879448-14.5879052879448
777681.2747302805858-5.2747302805858
786778.3388874517252-11.3388874517252
7911074.205389166694635.7946108333054
8011878.314938104377139.6850618956229
819983.852798452245315.1472015477547
828585.7871821806066-0.787182180606607
8310785.16522298798621.834777012014
8414188.594342057484952.4056579425151
855897.9642796593702-39.9642796593702
866591.7945175944322-26.7945175944322
877087.1787238981009-17.1787238981009
888683.74611322552322.2538867744768
899383.4574103909499.54258960905096
907484.5250073729243-10.5250073729243
918782.17904510999854.82095489000153
927382.3777548229433-9.3777548229433
9310180.121904190200420.8780958097996
9410083.114672625283316.8853273747167
959685.814725726260110.1852742737399
9615787.654029862358369.3459701376417
9763100.33698382939-37.3369838293898
9811595.251906050313419.7480939496866
997099.6696450708296-29.6696450708296
1006695.604894279878-29.6048942798781
1016790.9476401227802-23.9476401227802
1028386.7046538049625-3.70465380496248
1037985.6134381074776-6.61343810747763
1047783.9238287047327-6.92382870473267
10510282.043750126876219.9562498731238
10611684.855342497571231.1446575024288
10710090.08480852967369.9151914703264
10813592.131697306269642.8683026937304
10971100.304984657393-29.3049846573926
1106096.3754401165778-36.3754401165778
1118990.5780087576825-1.57800875768251
1127490.2959710435823-16.2959710435823
1137387.3357206008697-14.3357206008697
1149184.39607058055616.6039294194439
1158684.92916300046681.07083699953323
1167484.6019556720088-10.6019556720088
1178782.19795069688974.80204930311027
1188782.3474861027934.65251389720696
11910982.567918326310926.4320816736891
12013786.798743960385350.2012560396147
1214395.8411499026628-52.8411499026628
1226987.3802109827183-18.3802109827183
1237384.0388880747974-11.0388880747974
1247781.643165950148-4.64316595014799
1256980.1725258294112-11.1725258294112
1267677.4334535626778-1.43345356267781
1277876.2178290168341.78217098316604
1287075.5511395930163-5.5511395930163
1298373.6023142626939.39768573730697
1306574.2280411192326-9.22804111923263
13111071.696485925531138.3035140744689
13213277.522524795527654.4774752044724
1335487.0363630790026-33.0363630790026
1345581.9257465595128-26.9257465595128
1356677.2410331193776-11.2410331193776
1366574.827936196252-9.82793619625205
1376072.4399998347437-12.4399998347437
1386569.3823313180988-4.38233131809885
1399667.520009204410628.4799907955894
1405571.4766314549045-16.4766314549045
1417167.93061158494723.06938841505283
1426367.5631851913006-4.56318519130062
1437465.88603045881248.11396954118763
14410666.395130888522939.6048691114771
1453472.7310678236632-38.7310678236632
1464765.7897646640455-18.7897646640455
1475661.6449679766126-5.64496797661265
1485359.4808147949518-6.48081479495183
1495357.0514432264841-4.05144322648414
1505554.92687335856860.073126641431358
1516753.461345575046613.5386544249534
1525254.4182175895574-2.4182175895574
1534652.7819497578604-6.78194975786042
1545150.31190415151410.688095848485872
1555849.04677006520648.95322993479357
1569149.281601042446641.7183989575534
1573355.58945342618-22.58945342618
1584051.185152704084-11.185152704084
1594648.3712083047337-2.3712083047337
1604546.9141296537628-1.91412965376283
1614145.4909438077439-4.49094380774388
1625543.56550711347611.434492886524
1635744.411791578570712.5882084214293
1645445.69833123023468.30166876976542
1654646.4705378011899-0.470537801189934
1665245.83466789224626.1653321077538
1674846.38225193289441.61774806710556
1687746.237785757540630.7622142424594
1697751.366022126960225.6339778730398
1703556.1986663373163-21.1986663373163
1714253.1334347055488-11.1334347055488
1724851.4461335185003-3.44613351850032
1734450.9141967234904-6.91419672349043
1744549.6885799037367-4.68857990373672
175048.7223078845444-48.7223078845444
176039.743925936363-39.743925936363
1774631.3876273902614.61237260974
1785131.994538795991119.0054612040089
1796333.688807884699929.3111921153001
1808437.622897567809446.3771024321906
1813045.2220413753098-15.2220413753098
1823942.6908817301164-3.6908817301164
1834541.92290389808383.07709610191616
1845242.29655727262819.70344272737187
1852843.9241907214072-15.9241907214072
1864041.1419246404493-1.14192464044927
1876240.693045730487821.3069542695122

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
3 & 129 & 124 & 5 \tabularnewline
4 & 99 & 130.898929029877 & -31.8989290298768 \tabularnewline
5 & 116 & 131.265766273234 & -15.2657662732339 \tabularnewline
6 & 168 & 133.973471918428 & 34.0265280815725 \tabularnewline
7 & 118 & 145.23238507203 & -27.2323850720304 \tabularnewline
8 & 129 & 146.170676305523 & -17.1706763055232 \tabularnewline
9 & 205 & 148.363403738323 & 56.6365962616766 \tabularnewline
10 & 147 & 163.475995290642 & -16.4759952906417 \tabularnewline
11 & 150 & 166.597236637815 & -16.5972366378149 \tabularnewline
12 & 267 & 169.361190005869 & 97.6388099941312 \tabularnewline
13 & 126 & 192.32520382069 & -66.3252038206905 \tabularnewline
14 & 129 & 187.798973983464 & -58.7989739834636 \tabularnewline
15 & 124 & 183.275314323711 & -59.2753143237111 \tabularnewline
16 & 97 & 177.468728277277 & -80.4687282772769 \tabularnewline
17 & 102 & 166.644880643289 & -64.6448806432889 \tabularnewline
18 & 127 & 157.027401245783 & -30.0274012457825 \tabularnewline
19 & 222 & 152.317329544825 & 69.6826704551753 \tabularnewline
20 & 214 & 164.922284041392 & 49.0777159586081 \tabularnewline
21 & 118 & 175.241665323796 & -57.2416653237957 \tabularnewline
22 & 141 & 167.445670139252 & -26.4456701392518 \tabularnewline
23 & 154 & 164.020781128511 & -10.0207811285115 \tabularnewline
24 & 226 & 163.010357195643 & 62.9896428043567 \tabularnewline
25 & 89 & 174.922124203388 & -85.922124203388 \tabularnewline
26 & 77 & 161.344288313437 & -84.3442883134365 \tabularnewline
27 & 82 & 146.300545826955 & -64.3005458269554 \tabularnewline
28 & 97 & 133.142933141196 & -36.1429331411957 \tabularnewline
29 & 127 & 123.738347285699 & 3.26165271430052 \tabularnewline
30 & 121 & 120.682190455215 & 0.31780954478532 \tabularnewline
31 & 117 & 117.163187425534 & -0.163187425534304 \tabularnewline
32 & 117 & 113.564179327148 & 3.43582067285233 \tabularnewline
33 & 106 & 110.608898915786 & -4.60889891578596 \tabularnewline
34 & 112 & 106.277253601496 & 5.72274639850362 \tabularnewline
35 & 134 & 103.709243307923 & 30.2907566920772 \tabularnewline
36 & 169 & 105.674741293008 & 63.3252587069916 \tabularnewline
37 & 75 & 114.196165799066 & -39.1961657990656 \tabularnewline
38 & 108 & 105.575146462696 & 2.42485353730424 \tabularnewline
39 & 115 & 103.638868342139 & 11.3611316578606 \tabularnewline
40 & 85 & 103.358581979319 & -18.3585819793189 \tabularnewline
41 & 101 & 97.9664526467975 & 3.03354735320247 \tabularnewline
42 & 108 & 96.0465000732222 & 11.9534999267778 \tabularnewline
43 & 109 & 95.7919986116082 & 13.2080013883918 \tabularnewline
44 & 124 & 96.0064404351116 & 27.9935595648884 \tabularnewline
45 & 105 & 99.1480621185817 & 5.85193788141828 \tabularnewline
46 & 95 & 98.8789500484571 & -3.87895004845711 \tabularnewline
47 & 135 & 96.979521842116 & 38.020478157884 \tabularnewline
48 & 164 & 102.534031444087 & 61.4659685559129 \tabularnewline
49 & 88 & 113.07789492428 & -25.07789492428 \tabularnewline
50 & 85 & 109.313993672763 & -24.3139936727632 \tabularnewline
51 & 112 & 105.17678535353 & 6.82321464646965 \tabularnewline
52 & 87 & 106.142514306789 & -19.1425143067895 \tabularnewline
53 & 91 & 102.578910653835 & -11.5789106538349 \tabularnewline
54 & 87 & 99.9853483957574 & -12.9853483957574 \tabularnewline
55 & 87 & 96.9031543957249 & -9.9031543957249 \tabularnewline
56 & 142 & 94.1106825069845 & 47.8893174930155 \tabularnewline
57 & 95 & 101.506824945746 & -6.50682494574593 \tabularnewline
58 & 108 & 100.098453638689 & 7.90154636131112 \tabularnewline
59 & 139 & 101.148008526345 & 37.8519914736549 \tabularnewline
60 & 159 & 107.74312263126 & 51.25687736874 \tabularnewline
61 & 61 & 117.519001651171 & -56.5190016511712 \tabularnewline
62 & 82 & 108.962019501021 & -26.9620195010212 \tabularnewline
63 & 124 & 104.56810172125 & 19.4318982787497 \tabularnewline
64 & 93 & 107.96614090807 & -14.9661409080702 \tabularnewline
65 & 108 & 105.575580626572 & 2.42441937342751 \tabularnewline
66 & 75 & 106.00684996717 & -31.0068499671697 \tabularnewline
67 & 87 & 100.477018557389 & -13.4770185573894 \tabularnewline
68 & 103 & 97.4674287003678 & 5.53257129963218 \tabularnewline
69 & 90 & 97.60106908035 & -7.60106908034997 \tabularnewline
70 & 108 & 95.4861236680824 & 12.5138763319176 \tabularnewline
71 & 123 & 96.8327840585961 & 26.1672159414039 \tabularnewline
72 & 129 & 100.888933442085 & 28.1110665579149 \tabularnewline
73 & 57 & 105.827386415663 & -48.8273864156626 \tabularnewline
74 & 65 & 97.5058058795078 & -32.5058058795078 \tabularnewline
75 & 67 & 91.1243719728431 & -24.1243719728431 \tabularnewline
76 & 71 & 85.5879052879448 & -14.5879052879448 \tabularnewline
77 & 76 & 81.2747302805858 & -5.2747302805858 \tabularnewline
78 & 67 & 78.3388874517252 & -11.3388874517252 \tabularnewline
79 & 110 & 74.2053891666946 & 35.7946108333054 \tabularnewline
80 & 118 & 78.3149381043771 & 39.6850618956229 \tabularnewline
81 & 99 & 83.8527984522453 & 15.1472015477547 \tabularnewline
82 & 85 & 85.7871821806066 & -0.787182180606607 \tabularnewline
83 & 107 & 85.165222987986 & 21.834777012014 \tabularnewline
84 & 141 & 88.5943420574849 & 52.4056579425151 \tabularnewline
85 & 58 & 97.9642796593702 & -39.9642796593702 \tabularnewline
86 & 65 & 91.7945175944322 & -26.7945175944322 \tabularnewline
87 & 70 & 87.1787238981009 & -17.1787238981009 \tabularnewline
88 & 86 & 83.7461132255232 & 2.2538867744768 \tabularnewline
89 & 93 & 83.457410390949 & 9.54258960905096 \tabularnewline
90 & 74 & 84.5250073729243 & -10.5250073729243 \tabularnewline
91 & 87 & 82.1790451099985 & 4.82095489000153 \tabularnewline
92 & 73 & 82.3777548229433 & -9.3777548229433 \tabularnewline
93 & 101 & 80.1219041902004 & 20.8780958097996 \tabularnewline
94 & 100 & 83.1146726252833 & 16.8853273747167 \tabularnewline
95 & 96 & 85.8147257262601 & 10.1852742737399 \tabularnewline
96 & 157 & 87.6540298623583 & 69.3459701376417 \tabularnewline
97 & 63 & 100.33698382939 & -37.3369838293898 \tabularnewline
98 & 115 & 95.2519060503134 & 19.7480939496866 \tabularnewline
99 & 70 & 99.6696450708296 & -29.6696450708296 \tabularnewline
100 & 66 & 95.604894279878 & -29.6048942798781 \tabularnewline
101 & 67 & 90.9476401227802 & -23.9476401227802 \tabularnewline
102 & 83 & 86.7046538049625 & -3.70465380496248 \tabularnewline
103 & 79 & 85.6134381074776 & -6.61343810747763 \tabularnewline
104 & 77 & 83.9238287047327 & -6.92382870473267 \tabularnewline
105 & 102 & 82.0437501268762 & 19.9562498731238 \tabularnewline
106 & 116 & 84.8553424975712 & 31.1446575024288 \tabularnewline
107 & 100 & 90.0848085296736 & 9.9151914703264 \tabularnewline
108 & 135 & 92.1316973062696 & 42.8683026937304 \tabularnewline
109 & 71 & 100.304984657393 & -29.3049846573926 \tabularnewline
110 & 60 & 96.3754401165778 & -36.3754401165778 \tabularnewline
111 & 89 & 90.5780087576825 & -1.57800875768251 \tabularnewline
112 & 74 & 90.2959710435823 & -16.2959710435823 \tabularnewline
113 & 73 & 87.3357206008697 & -14.3357206008697 \tabularnewline
114 & 91 & 84.3960705805561 & 6.6039294194439 \tabularnewline
115 & 86 & 84.9291630004668 & 1.07083699953323 \tabularnewline
116 & 74 & 84.6019556720088 & -10.6019556720088 \tabularnewline
117 & 87 & 82.1979506968897 & 4.80204930311027 \tabularnewline
118 & 87 & 82.347486102793 & 4.65251389720696 \tabularnewline
119 & 109 & 82.5679183263109 & 26.4320816736891 \tabularnewline
120 & 137 & 86.7987439603853 & 50.2012560396147 \tabularnewline
121 & 43 & 95.8411499026628 & -52.8411499026628 \tabularnewline
122 & 69 & 87.3802109827183 & -18.3802109827183 \tabularnewline
123 & 73 & 84.0388880747974 & -11.0388880747974 \tabularnewline
124 & 77 & 81.643165950148 & -4.64316595014799 \tabularnewline
125 & 69 & 80.1725258294112 & -11.1725258294112 \tabularnewline
126 & 76 & 77.4334535626778 & -1.43345356267781 \tabularnewline
127 & 78 & 76.217829016834 & 1.78217098316604 \tabularnewline
128 & 70 & 75.5511395930163 & -5.5511395930163 \tabularnewline
129 & 83 & 73.602314262693 & 9.39768573730697 \tabularnewline
130 & 65 & 74.2280411192326 & -9.22804111923263 \tabularnewline
131 & 110 & 71.6964859255311 & 38.3035140744689 \tabularnewline
132 & 132 & 77.5225247955276 & 54.4774752044724 \tabularnewline
133 & 54 & 87.0363630790026 & -33.0363630790026 \tabularnewline
134 & 55 & 81.9257465595128 & -26.9257465595128 \tabularnewline
135 & 66 & 77.2410331193776 & -11.2410331193776 \tabularnewline
136 & 65 & 74.827936196252 & -9.82793619625205 \tabularnewline
137 & 60 & 72.4399998347437 & -12.4399998347437 \tabularnewline
138 & 65 & 69.3823313180988 & -4.38233131809885 \tabularnewline
139 & 96 & 67.5200092044106 & 28.4799907955894 \tabularnewline
140 & 55 & 71.4766314549045 & -16.4766314549045 \tabularnewline
141 & 71 & 67.9306115849472 & 3.06938841505283 \tabularnewline
142 & 63 & 67.5631851913006 & -4.56318519130062 \tabularnewline
143 & 74 & 65.8860304588124 & 8.11396954118763 \tabularnewline
144 & 106 & 66.3951308885229 & 39.6048691114771 \tabularnewline
145 & 34 & 72.7310678236632 & -38.7310678236632 \tabularnewline
146 & 47 & 65.7897646640455 & -18.7897646640455 \tabularnewline
147 & 56 & 61.6449679766126 & -5.64496797661265 \tabularnewline
148 & 53 & 59.4808147949518 & -6.48081479495183 \tabularnewline
149 & 53 & 57.0514432264841 & -4.05144322648414 \tabularnewline
150 & 55 & 54.9268733585686 & 0.073126641431358 \tabularnewline
151 & 67 & 53.4613455750466 & 13.5386544249534 \tabularnewline
152 & 52 & 54.4182175895574 & -2.4182175895574 \tabularnewline
153 & 46 & 52.7819497578604 & -6.78194975786042 \tabularnewline
154 & 51 & 50.3119041515141 & 0.688095848485872 \tabularnewline
155 & 58 & 49.0467700652064 & 8.95322993479357 \tabularnewline
156 & 91 & 49.2816010424466 & 41.7183989575534 \tabularnewline
157 & 33 & 55.58945342618 & -22.58945342618 \tabularnewline
158 & 40 & 51.185152704084 & -11.185152704084 \tabularnewline
159 & 46 & 48.3712083047337 & -2.3712083047337 \tabularnewline
160 & 45 & 46.9141296537628 & -1.91412965376283 \tabularnewline
161 & 41 & 45.4909438077439 & -4.49094380774388 \tabularnewline
162 & 55 & 43.565507113476 & 11.434492886524 \tabularnewline
163 & 57 & 44.4117915785707 & 12.5882084214293 \tabularnewline
164 & 54 & 45.6983312302346 & 8.30166876976542 \tabularnewline
165 & 46 & 46.4705378011899 & -0.470537801189934 \tabularnewline
166 & 52 & 45.8346678922462 & 6.1653321077538 \tabularnewline
167 & 48 & 46.3822519328944 & 1.61774806710556 \tabularnewline
168 & 77 & 46.2377857575406 & 30.7622142424594 \tabularnewline
169 & 77 & 51.3660221269602 & 25.6339778730398 \tabularnewline
170 & 35 & 56.1986663373163 & -21.1986663373163 \tabularnewline
171 & 42 & 53.1334347055488 & -11.1334347055488 \tabularnewline
172 & 48 & 51.4461335185003 & -3.44613351850032 \tabularnewline
173 & 44 & 50.9141967234904 & -6.91419672349043 \tabularnewline
174 & 45 & 49.6885799037367 & -4.68857990373672 \tabularnewline
175 & 0 & 48.7223078845444 & -48.7223078845444 \tabularnewline
176 & 0 & 39.743925936363 & -39.743925936363 \tabularnewline
177 & 46 & 31.38762739026 & 14.61237260974 \tabularnewline
178 & 51 & 31.9945387959911 & 19.0054612040089 \tabularnewline
179 & 63 & 33.6888078846999 & 29.3111921153001 \tabularnewline
180 & 84 & 37.6228975678094 & 46.3771024321906 \tabularnewline
181 & 30 & 45.2220413753098 & -15.2220413753098 \tabularnewline
182 & 39 & 42.6908817301164 & -3.6908817301164 \tabularnewline
183 & 45 & 41.9229038980838 & 3.07709610191616 \tabularnewline
184 & 52 & 42.2965572726281 & 9.70344272737187 \tabularnewline
185 & 28 & 43.9241907214072 & -15.9241907214072 \tabularnewline
186 & 40 & 41.1419246404493 & -1.14192464044927 \tabularnewline
187 & 62 & 40.6930457304878 & 21.3069542695122 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=122203&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]129[/C][C]124[/C][C]5[/C][/ROW]
[ROW][C]4[/C][C]99[/C][C]130.898929029877[/C][C]-31.8989290298768[/C][/ROW]
[ROW][C]5[/C][C]116[/C][C]131.265766273234[/C][C]-15.2657662732339[/C][/ROW]
[ROW][C]6[/C][C]168[/C][C]133.973471918428[/C][C]34.0265280815725[/C][/ROW]
[ROW][C]7[/C][C]118[/C][C]145.23238507203[/C][C]-27.2323850720304[/C][/ROW]
[ROW][C]8[/C][C]129[/C][C]146.170676305523[/C][C]-17.1706763055232[/C][/ROW]
[ROW][C]9[/C][C]205[/C][C]148.363403738323[/C][C]56.6365962616766[/C][/ROW]
[ROW][C]10[/C][C]147[/C][C]163.475995290642[/C][C]-16.4759952906417[/C][/ROW]
[ROW][C]11[/C][C]150[/C][C]166.597236637815[/C][C]-16.5972366378149[/C][/ROW]
[ROW][C]12[/C][C]267[/C][C]169.361190005869[/C][C]97.6388099941312[/C][/ROW]
[ROW][C]13[/C][C]126[/C][C]192.32520382069[/C][C]-66.3252038206905[/C][/ROW]
[ROW][C]14[/C][C]129[/C][C]187.798973983464[/C][C]-58.7989739834636[/C][/ROW]
[ROW][C]15[/C][C]124[/C][C]183.275314323711[/C][C]-59.2753143237111[/C][/ROW]
[ROW][C]16[/C][C]97[/C][C]177.468728277277[/C][C]-80.4687282772769[/C][/ROW]
[ROW][C]17[/C][C]102[/C][C]166.644880643289[/C][C]-64.6448806432889[/C][/ROW]
[ROW][C]18[/C][C]127[/C][C]157.027401245783[/C][C]-30.0274012457825[/C][/ROW]
[ROW][C]19[/C][C]222[/C][C]152.317329544825[/C][C]69.6826704551753[/C][/ROW]
[ROW][C]20[/C][C]214[/C][C]164.922284041392[/C][C]49.0777159586081[/C][/ROW]
[ROW][C]21[/C][C]118[/C][C]175.241665323796[/C][C]-57.2416653237957[/C][/ROW]
[ROW][C]22[/C][C]141[/C][C]167.445670139252[/C][C]-26.4456701392518[/C][/ROW]
[ROW][C]23[/C][C]154[/C][C]164.020781128511[/C][C]-10.0207811285115[/C][/ROW]
[ROW][C]24[/C][C]226[/C][C]163.010357195643[/C][C]62.9896428043567[/C][/ROW]
[ROW][C]25[/C][C]89[/C][C]174.922124203388[/C][C]-85.922124203388[/C][/ROW]
[ROW][C]26[/C][C]77[/C][C]161.344288313437[/C][C]-84.3442883134365[/C][/ROW]
[ROW][C]27[/C][C]82[/C][C]146.300545826955[/C][C]-64.3005458269554[/C][/ROW]
[ROW][C]28[/C][C]97[/C][C]133.142933141196[/C][C]-36.1429331411957[/C][/ROW]
[ROW][C]29[/C][C]127[/C][C]123.738347285699[/C][C]3.26165271430052[/C][/ROW]
[ROW][C]30[/C][C]121[/C][C]120.682190455215[/C][C]0.31780954478532[/C][/ROW]
[ROW][C]31[/C][C]117[/C][C]117.163187425534[/C][C]-0.163187425534304[/C][/ROW]
[ROW][C]32[/C][C]117[/C][C]113.564179327148[/C][C]3.43582067285233[/C][/ROW]
[ROW][C]33[/C][C]106[/C][C]110.608898915786[/C][C]-4.60889891578596[/C][/ROW]
[ROW][C]34[/C][C]112[/C][C]106.277253601496[/C][C]5.72274639850362[/C][/ROW]
[ROW][C]35[/C][C]134[/C][C]103.709243307923[/C][C]30.2907566920772[/C][/ROW]
[ROW][C]36[/C][C]169[/C][C]105.674741293008[/C][C]63.3252587069916[/C][/ROW]
[ROW][C]37[/C][C]75[/C][C]114.196165799066[/C][C]-39.1961657990656[/C][/ROW]
[ROW][C]38[/C][C]108[/C][C]105.575146462696[/C][C]2.42485353730424[/C][/ROW]
[ROW][C]39[/C][C]115[/C][C]103.638868342139[/C][C]11.3611316578606[/C][/ROW]
[ROW][C]40[/C][C]85[/C][C]103.358581979319[/C][C]-18.3585819793189[/C][/ROW]
[ROW][C]41[/C][C]101[/C][C]97.9664526467975[/C][C]3.03354735320247[/C][/ROW]
[ROW][C]42[/C][C]108[/C][C]96.0465000732222[/C][C]11.9534999267778[/C][/ROW]
[ROW][C]43[/C][C]109[/C][C]95.7919986116082[/C][C]13.2080013883918[/C][/ROW]
[ROW][C]44[/C][C]124[/C][C]96.0064404351116[/C][C]27.9935595648884[/C][/ROW]
[ROW][C]45[/C][C]105[/C][C]99.1480621185817[/C][C]5.85193788141828[/C][/ROW]
[ROW][C]46[/C][C]95[/C][C]98.8789500484571[/C][C]-3.87895004845711[/C][/ROW]
[ROW][C]47[/C][C]135[/C][C]96.979521842116[/C][C]38.020478157884[/C][/ROW]
[ROW][C]48[/C][C]164[/C][C]102.534031444087[/C][C]61.4659685559129[/C][/ROW]
[ROW][C]49[/C][C]88[/C][C]113.07789492428[/C][C]-25.07789492428[/C][/ROW]
[ROW][C]50[/C][C]85[/C][C]109.313993672763[/C][C]-24.3139936727632[/C][/ROW]
[ROW][C]51[/C][C]112[/C][C]105.17678535353[/C][C]6.82321464646965[/C][/ROW]
[ROW][C]52[/C][C]87[/C][C]106.142514306789[/C][C]-19.1425143067895[/C][/ROW]
[ROW][C]53[/C][C]91[/C][C]102.578910653835[/C][C]-11.5789106538349[/C][/ROW]
[ROW][C]54[/C][C]87[/C][C]99.9853483957574[/C][C]-12.9853483957574[/C][/ROW]
[ROW][C]55[/C][C]87[/C][C]96.9031543957249[/C][C]-9.9031543957249[/C][/ROW]
[ROW][C]56[/C][C]142[/C][C]94.1106825069845[/C][C]47.8893174930155[/C][/ROW]
[ROW][C]57[/C][C]95[/C][C]101.506824945746[/C][C]-6.50682494574593[/C][/ROW]
[ROW][C]58[/C][C]108[/C][C]100.098453638689[/C][C]7.90154636131112[/C][/ROW]
[ROW][C]59[/C][C]139[/C][C]101.148008526345[/C][C]37.8519914736549[/C][/ROW]
[ROW][C]60[/C][C]159[/C][C]107.74312263126[/C][C]51.25687736874[/C][/ROW]
[ROW][C]61[/C][C]61[/C][C]117.519001651171[/C][C]-56.5190016511712[/C][/ROW]
[ROW][C]62[/C][C]82[/C][C]108.962019501021[/C][C]-26.9620195010212[/C][/ROW]
[ROW][C]63[/C][C]124[/C][C]104.56810172125[/C][C]19.4318982787497[/C][/ROW]
[ROW][C]64[/C][C]93[/C][C]107.96614090807[/C][C]-14.9661409080702[/C][/ROW]
[ROW][C]65[/C][C]108[/C][C]105.575580626572[/C][C]2.42441937342751[/C][/ROW]
[ROW][C]66[/C][C]75[/C][C]106.00684996717[/C][C]-31.0068499671697[/C][/ROW]
[ROW][C]67[/C][C]87[/C][C]100.477018557389[/C][C]-13.4770185573894[/C][/ROW]
[ROW][C]68[/C][C]103[/C][C]97.4674287003678[/C][C]5.53257129963218[/C][/ROW]
[ROW][C]69[/C][C]90[/C][C]97.60106908035[/C][C]-7.60106908034997[/C][/ROW]
[ROW][C]70[/C][C]108[/C][C]95.4861236680824[/C][C]12.5138763319176[/C][/ROW]
[ROW][C]71[/C][C]123[/C][C]96.8327840585961[/C][C]26.1672159414039[/C][/ROW]
[ROW][C]72[/C][C]129[/C][C]100.888933442085[/C][C]28.1110665579149[/C][/ROW]
[ROW][C]73[/C][C]57[/C][C]105.827386415663[/C][C]-48.8273864156626[/C][/ROW]
[ROW][C]74[/C][C]65[/C][C]97.5058058795078[/C][C]-32.5058058795078[/C][/ROW]
[ROW][C]75[/C][C]67[/C][C]91.1243719728431[/C][C]-24.1243719728431[/C][/ROW]
[ROW][C]76[/C][C]71[/C][C]85.5879052879448[/C][C]-14.5879052879448[/C][/ROW]
[ROW][C]77[/C][C]76[/C][C]81.2747302805858[/C][C]-5.2747302805858[/C][/ROW]
[ROW][C]78[/C][C]67[/C][C]78.3388874517252[/C][C]-11.3388874517252[/C][/ROW]
[ROW][C]79[/C][C]110[/C][C]74.2053891666946[/C][C]35.7946108333054[/C][/ROW]
[ROW][C]80[/C][C]118[/C][C]78.3149381043771[/C][C]39.6850618956229[/C][/ROW]
[ROW][C]81[/C][C]99[/C][C]83.8527984522453[/C][C]15.1472015477547[/C][/ROW]
[ROW][C]82[/C][C]85[/C][C]85.7871821806066[/C][C]-0.787182180606607[/C][/ROW]
[ROW][C]83[/C][C]107[/C][C]85.165222987986[/C][C]21.834777012014[/C][/ROW]
[ROW][C]84[/C][C]141[/C][C]88.5943420574849[/C][C]52.4056579425151[/C][/ROW]
[ROW][C]85[/C][C]58[/C][C]97.9642796593702[/C][C]-39.9642796593702[/C][/ROW]
[ROW][C]86[/C][C]65[/C][C]91.7945175944322[/C][C]-26.7945175944322[/C][/ROW]
[ROW][C]87[/C][C]70[/C][C]87.1787238981009[/C][C]-17.1787238981009[/C][/ROW]
[ROW][C]88[/C][C]86[/C][C]83.7461132255232[/C][C]2.2538867744768[/C][/ROW]
[ROW][C]89[/C][C]93[/C][C]83.457410390949[/C][C]9.54258960905096[/C][/ROW]
[ROW][C]90[/C][C]74[/C][C]84.5250073729243[/C][C]-10.5250073729243[/C][/ROW]
[ROW][C]91[/C][C]87[/C][C]82.1790451099985[/C][C]4.82095489000153[/C][/ROW]
[ROW][C]92[/C][C]73[/C][C]82.3777548229433[/C][C]-9.3777548229433[/C][/ROW]
[ROW][C]93[/C][C]101[/C][C]80.1219041902004[/C][C]20.8780958097996[/C][/ROW]
[ROW][C]94[/C][C]100[/C][C]83.1146726252833[/C][C]16.8853273747167[/C][/ROW]
[ROW][C]95[/C][C]96[/C][C]85.8147257262601[/C][C]10.1852742737399[/C][/ROW]
[ROW][C]96[/C][C]157[/C][C]87.6540298623583[/C][C]69.3459701376417[/C][/ROW]
[ROW][C]97[/C][C]63[/C][C]100.33698382939[/C][C]-37.3369838293898[/C][/ROW]
[ROW][C]98[/C][C]115[/C][C]95.2519060503134[/C][C]19.7480939496866[/C][/ROW]
[ROW][C]99[/C][C]70[/C][C]99.6696450708296[/C][C]-29.6696450708296[/C][/ROW]
[ROW][C]100[/C][C]66[/C][C]95.604894279878[/C][C]-29.6048942798781[/C][/ROW]
[ROW][C]101[/C][C]67[/C][C]90.9476401227802[/C][C]-23.9476401227802[/C][/ROW]
[ROW][C]102[/C][C]83[/C][C]86.7046538049625[/C][C]-3.70465380496248[/C][/ROW]
[ROW][C]103[/C][C]79[/C][C]85.6134381074776[/C][C]-6.61343810747763[/C][/ROW]
[ROW][C]104[/C][C]77[/C][C]83.9238287047327[/C][C]-6.92382870473267[/C][/ROW]
[ROW][C]105[/C][C]102[/C][C]82.0437501268762[/C][C]19.9562498731238[/C][/ROW]
[ROW][C]106[/C][C]116[/C][C]84.8553424975712[/C][C]31.1446575024288[/C][/ROW]
[ROW][C]107[/C][C]100[/C][C]90.0848085296736[/C][C]9.9151914703264[/C][/ROW]
[ROW][C]108[/C][C]135[/C][C]92.1316973062696[/C][C]42.8683026937304[/C][/ROW]
[ROW][C]109[/C][C]71[/C][C]100.304984657393[/C][C]-29.3049846573926[/C][/ROW]
[ROW][C]110[/C][C]60[/C][C]96.3754401165778[/C][C]-36.3754401165778[/C][/ROW]
[ROW][C]111[/C][C]89[/C][C]90.5780087576825[/C][C]-1.57800875768251[/C][/ROW]
[ROW][C]112[/C][C]74[/C][C]90.2959710435823[/C][C]-16.2959710435823[/C][/ROW]
[ROW][C]113[/C][C]73[/C][C]87.3357206008697[/C][C]-14.3357206008697[/C][/ROW]
[ROW][C]114[/C][C]91[/C][C]84.3960705805561[/C][C]6.6039294194439[/C][/ROW]
[ROW][C]115[/C][C]86[/C][C]84.9291630004668[/C][C]1.07083699953323[/C][/ROW]
[ROW][C]116[/C][C]74[/C][C]84.6019556720088[/C][C]-10.6019556720088[/C][/ROW]
[ROW][C]117[/C][C]87[/C][C]82.1979506968897[/C][C]4.80204930311027[/C][/ROW]
[ROW][C]118[/C][C]87[/C][C]82.347486102793[/C][C]4.65251389720696[/C][/ROW]
[ROW][C]119[/C][C]109[/C][C]82.5679183263109[/C][C]26.4320816736891[/C][/ROW]
[ROW][C]120[/C][C]137[/C][C]86.7987439603853[/C][C]50.2012560396147[/C][/ROW]
[ROW][C]121[/C][C]43[/C][C]95.8411499026628[/C][C]-52.8411499026628[/C][/ROW]
[ROW][C]122[/C][C]69[/C][C]87.3802109827183[/C][C]-18.3802109827183[/C][/ROW]
[ROW][C]123[/C][C]73[/C][C]84.0388880747974[/C][C]-11.0388880747974[/C][/ROW]
[ROW][C]124[/C][C]77[/C][C]81.643165950148[/C][C]-4.64316595014799[/C][/ROW]
[ROW][C]125[/C][C]69[/C][C]80.1725258294112[/C][C]-11.1725258294112[/C][/ROW]
[ROW][C]126[/C][C]76[/C][C]77.4334535626778[/C][C]-1.43345356267781[/C][/ROW]
[ROW][C]127[/C][C]78[/C][C]76.217829016834[/C][C]1.78217098316604[/C][/ROW]
[ROW][C]128[/C][C]70[/C][C]75.5511395930163[/C][C]-5.5511395930163[/C][/ROW]
[ROW][C]129[/C][C]83[/C][C]73.602314262693[/C][C]9.39768573730697[/C][/ROW]
[ROW][C]130[/C][C]65[/C][C]74.2280411192326[/C][C]-9.22804111923263[/C][/ROW]
[ROW][C]131[/C][C]110[/C][C]71.6964859255311[/C][C]38.3035140744689[/C][/ROW]
[ROW][C]132[/C][C]132[/C][C]77.5225247955276[/C][C]54.4774752044724[/C][/ROW]
[ROW][C]133[/C][C]54[/C][C]87.0363630790026[/C][C]-33.0363630790026[/C][/ROW]
[ROW][C]134[/C][C]55[/C][C]81.9257465595128[/C][C]-26.9257465595128[/C][/ROW]
[ROW][C]135[/C][C]66[/C][C]77.2410331193776[/C][C]-11.2410331193776[/C][/ROW]
[ROW][C]136[/C][C]65[/C][C]74.827936196252[/C][C]-9.82793619625205[/C][/ROW]
[ROW][C]137[/C][C]60[/C][C]72.4399998347437[/C][C]-12.4399998347437[/C][/ROW]
[ROW][C]138[/C][C]65[/C][C]69.3823313180988[/C][C]-4.38233131809885[/C][/ROW]
[ROW][C]139[/C][C]96[/C][C]67.5200092044106[/C][C]28.4799907955894[/C][/ROW]
[ROW][C]140[/C][C]55[/C][C]71.4766314549045[/C][C]-16.4766314549045[/C][/ROW]
[ROW][C]141[/C][C]71[/C][C]67.9306115849472[/C][C]3.06938841505283[/C][/ROW]
[ROW][C]142[/C][C]63[/C][C]67.5631851913006[/C][C]-4.56318519130062[/C][/ROW]
[ROW][C]143[/C][C]74[/C][C]65.8860304588124[/C][C]8.11396954118763[/C][/ROW]
[ROW][C]144[/C][C]106[/C][C]66.3951308885229[/C][C]39.6048691114771[/C][/ROW]
[ROW][C]145[/C][C]34[/C][C]72.7310678236632[/C][C]-38.7310678236632[/C][/ROW]
[ROW][C]146[/C][C]47[/C][C]65.7897646640455[/C][C]-18.7897646640455[/C][/ROW]
[ROW][C]147[/C][C]56[/C][C]61.6449679766126[/C][C]-5.64496797661265[/C][/ROW]
[ROW][C]148[/C][C]53[/C][C]59.4808147949518[/C][C]-6.48081479495183[/C][/ROW]
[ROW][C]149[/C][C]53[/C][C]57.0514432264841[/C][C]-4.05144322648414[/C][/ROW]
[ROW][C]150[/C][C]55[/C][C]54.9268733585686[/C][C]0.073126641431358[/C][/ROW]
[ROW][C]151[/C][C]67[/C][C]53.4613455750466[/C][C]13.5386544249534[/C][/ROW]
[ROW][C]152[/C][C]52[/C][C]54.4182175895574[/C][C]-2.4182175895574[/C][/ROW]
[ROW][C]153[/C][C]46[/C][C]52.7819497578604[/C][C]-6.78194975786042[/C][/ROW]
[ROW][C]154[/C][C]51[/C][C]50.3119041515141[/C][C]0.688095848485872[/C][/ROW]
[ROW][C]155[/C][C]58[/C][C]49.0467700652064[/C][C]8.95322993479357[/C][/ROW]
[ROW][C]156[/C][C]91[/C][C]49.2816010424466[/C][C]41.7183989575534[/C][/ROW]
[ROW][C]157[/C][C]33[/C][C]55.58945342618[/C][C]-22.58945342618[/C][/ROW]
[ROW][C]158[/C][C]40[/C][C]51.185152704084[/C][C]-11.185152704084[/C][/ROW]
[ROW][C]159[/C][C]46[/C][C]48.3712083047337[/C][C]-2.3712083047337[/C][/ROW]
[ROW][C]160[/C][C]45[/C][C]46.9141296537628[/C][C]-1.91412965376283[/C][/ROW]
[ROW][C]161[/C][C]41[/C][C]45.4909438077439[/C][C]-4.49094380774388[/C][/ROW]
[ROW][C]162[/C][C]55[/C][C]43.565507113476[/C][C]11.434492886524[/C][/ROW]
[ROW][C]163[/C][C]57[/C][C]44.4117915785707[/C][C]12.5882084214293[/C][/ROW]
[ROW][C]164[/C][C]54[/C][C]45.6983312302346[/C][C]8.30166876976542[/C][/ROW]
[ROW][C]165[/C][C]46[/C][C]46.4705378011899[/C][C]-0.470537801189934[/C][/ROW]
[ROW][C]166[/C][C]52[/C][C]45.8346678922462[/C][C]6.1653321077538[/C][/ROW]
[ROW][C]167[/C][C]48[/C][C]46.3822519328944[/C][C]1.61774806710556[/C][/ROW]
[ROW][C]168[/C][C]77[/C][C]46.2377857575406[/C][C]30.7622142424594[/C][/ROW]
[ROW][C]169[/C][C]77[/C][C]51.3660221269602[/C][C]25.6339778730398[/C][/ROW]
[ROW][C]170[/C][C]35[/C][C]56.1986663373163[/C][C]-21.1986663373163[/C][/ROW]
[ROW][C]171[/C][C]42[/C][C]53.1334347055488[/C][C]-11.1334347055488[/C][/ROW]
[ROW][C]172[/C][C]48[/C][C]51.4461335185003[/C][C]-3.44613351850032[/C][/ROW]
[ROW][C]173[/C][C]44[/C][C]50.9141967234904[/C][C]-6.91419672349043[/C][/ROW]
[ROW][C]174[/C][C]45[/C][C]49.6885799037367[/C][C]-4.68857990373672[/C][/ROW]
[ROW][C]175[/C][C]0[/C][C]48.7223078845444[/C][C]-48.7223078845444[/C][/ROW]
[ROW][C]176[/C][C]0[/C][C]39.743925936363[/C][C]-39.743925936363[/C][/ROW]
[ROW][C]177[/C][C]46[/C][C]31.38762739026[/C][C]14.61237260974[/C][/ROW]
[ROW][C]178[/C][C]51[/C][C]31.9945387959911[/C][C]19.0054612040089[/C][/ROW]
[ROW][C]179[/C][C]63[/C][C]33.6888078846999[/C][C]29.3111921153001[/C][/ROW]
[ROW][C]180[/C][C]84[/C][C]37.6228975678094[/C][C]46.3771024321906[/C][/ROW]
[ROW][C]181[/C][C]30[/C][C]45.2220413753098[/C][C]-15.2220413753098[/C][/ROW]
[ROW][C]182[/C][C]39[/C][C]42.6908817301164[/C][C]-3.6908817301164[/C][/ROW]
[ROW][C]183[/C][C]45[/C][C]41.9229038980838[/C][C]3.07709610191616[/C][/ROW]
[ROW][C]184[/C][C]52[/C][C]42.2965572726281[/C][C]9.70344272737187[/C][/ROW]
[ROW][C]185[/C][C]28[/C][C]43.9241907214072[/C][C]-15.9241907214072[/C][/ROW]
[ROW][C]186[/C][C]40[/C][C]41.1419246404493[/C][C]-1.14192464044927[/C][/ROW]
[ROW][C]187[/C][C]62[/C][C]40.6930457304878[/C][C]21.3069542695122[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=122203&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=122203&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
31291245
499130.898929029877-31.8989290298768
5116131.265766273234-15.2657662732339
6168133.97347191842834.0265280815725
7118145.23238507203-27.2323850720304
8129146.170676305523-17.1706763055232
9205148.36340373832356.6365962616766
10147163.475995290642-16.4759952906417
11150166.597236637815-16.5972366378149
12267169.36119000586997.6388099941312
13126192.32520382069-66.3252038206905
14129187.798973983464-58.7989739834636
15124183.275314323711-59.2753143237111
1697177.468728277277-80.4687282772769
17102166.644880643289-64.6448806432889
18127157.027401245783-30.0274012457825
19222152.31732954482569.6826704551753
20214164.92228404139249.0777159586081
21118175.241665323796-57.2416653237957
22141167.445670139252-26.4456701392518
23154164.020781128511-10.0207811285115
24226163.01035719564362.9896428043567
2589174.922124203388-85.922124203388
2677161.344288313437-84.3442883134365
2782146.300545826955-64.3005458269554
2897133.142933141196-36.1429331411957
29127123.7383472856993.26165271430052
30121120.6821904552150.31780954478532
31117117.163187425534-0.163187425534304
32117113.5641793271483.43582067285233
33106110.608898915786-4.60889891578596
34112106.2772536014965.72274639850362
35134103.70924330792330.2907566920772
36169105.67474129300863.3252587069916
3775114.196165799066-39.1961657990656
38108105.5751464626962.42485353730424
39115103.63886834213911.3611316578606
4085103.358581979319-18.3585819793189
4110197.96645264679753.03354735320247
4210896.046500073222211.9534999267778
4310995.791998611608213.2080013883918
4412496.006440435111627.9935595648884
4510599.14806211858175.85193788141828
469598.8789500484571-3.87895004845711
4713596.97952184211638.020478157884
48164102.53403144408761.4659685559129
4988113.07789492428-25.07789492428
5085109.313993672763-24.3139936727632
51112105.176785353536.82321464646965
5287106.142514306789-19.1425143067895
5391102.578910653835-11.5789106538349
548799.9853483957574-12.9853483957574
558796.9031543957249-9.9031543957249
5614294.110682506984547.8893174930155
5795101.506824945746-6.50682494574593
58108100.0984536386897.90154636131112
59139101.14800852634537.8519914736549
60159107.7431226312651.25687736874
6161117.519001651171-56.5190016511712
6282108.962019501021-26.9620195010212
63124104.5681017212519.4318982787497
6493107.96614090807-14.9661409080702
65108105.5755806265722.42441937342751
6675106.00684996717-31.0068499671697
6787100.477018557389-13.4770185573894
6810397.46742870036785.53257129963218
699097.60106908035-7.60106908034997
7010895.486123668082412.5138763319176
7112396.832784058596126.1672159414039
72129100.88893344208528.1110665579149
7357105.827386415663-48.8273864156626
746597.5058058795078-32.5058058795078
756791.1243719728431-24.1243719728431
767185.5879052879448-14.5879052879448
777681.2747302805858-5.2747302805858
786778.3388874517252-11.3388874517252
7911074.205389166694635.7946108333054
8011878.314938104377139.6850618956229
819983.852798452245315.1472015477547
828585.7871821806066-0.787182180606607
8310785.16522298798621.834777012014
8414188.594342057484952.4056579425151
855897.9642796593702-39.9642796593702
866591.7945175944322-26.7945175944322
877087.1787238981009-17.1787238981009
888683.74611322552322.2538867744768
899383.4574103909499.54258960905096
907484.5250073729243-10.5250073729243
918782.17904510999854.82095489000153
927382.3777548229433-9.3777548229433
9310180.121904190200420.8780958097996
9410083.114672625283316.8853273747167
959685.814725726260110.1852742737399
9615787.654029862358369.3459701376417
9763100.33698382939-37.3369838293898
9811595.251906050313419.7480939496866
997099.6696450708296-29.6696450708296
1006695.604894279878-29.6048942798781
1016790.9476401227802-23.9476401227802
1028386.7046538049625-3.70465380496248
1037985.6134381074776-6.61343810747763
1047783.9238287047327-6.92382870473267
10510282.043750126876219.9562498731238
10611684.855342497571231.1446575024288
10710090.08480852967369.9151914703264
10813592.131697306269642.8683026937304
10971100.304984657393-29.3049846573926
1106096.3754401165778-36.3754401165778
1118990.5780087576825-1.57800875768251
1127490.2959710435823-16.2959710435823
1137387.3357206008697-14.3357206008697
1149184.39607058055616.6039294194439
1158684.92916300046681.07083699953323
1167484.6019556720088-10.6019556720088
1178782.19795069688974.80204930311027
1188782.3474861027934.65251389720696
11910982.567918326310926.4320816736891
12013786.798743960385350.2012560396147
1214395.8411499026628-52.8411499026628
1226987.3802109827183-18.3802109827183
1237384.0388880747974-11.0388880747974
1247781.643165950148-4.64316595014799
1256980.1725258294112-11.1725258294112
1267677.4334535626778-1.43345356267781
1277876.2178290168341.78217098316604
1287075.5511395930163-5.5511395930163
1298373.6023142626939.39768573730697
1306574.2280411192326-9.22804111923263
13111071.696485925531138.3035140744689
13213277.522524795527654.4774752044724
1335487.0363630790026-33.0363630790026
1345581.9257465595128-26.9257465595128
1356677.2410331193776-11.2410331193776
1366574.827936196252-9.82793619625205
1376072.4399998347437-12.4399998347437
1386569.3823313180988-4.38233131809885
1399667.520009204410628.4799907955894
1405571.4766314549045-16.4766314549045
1417167.93061158494723.06938841505283
1426367.5631851913006-4.56318519130062
1437465.88603045881248.11396954118763
14410666.395130888522939.6048691114771
1453472.7310678236632-38.7310678236632
1464765.7897646640455-18.7897646640455
1475661.6449679766126-5.64496797661265
1485359.4808147949518-6.48081479495183
1495357.0514432264841-4.05144322648414
1505554.92687335856860.073126641431358
1516753.461345575046613.5386544249534
1525254.4182175895574-2.4182175895574
1534652.7819497578604-6.78194975786042
1545150.31190415151410.688095848485872
1555849.04677006520648.95322993479357
1569149.281601042446641.7183989575534
1573355.58945342618-22.58945342618
1584051.185152704084-11.185152704084
1594648.3712083047337-2.3712083047337
1604546.9141296537628-1.91412965376283
1614145.4909438077439-4.49094380774388
1625543.56550711347611.434492886524
1635744.411791578570712.5882084214293
1645445.69833123023468.30166876976542
1654646.4705378011899-0.470537801189934
1665245.83466789224626.1653321077538
1674846.38225193289441.61774806710556
1687746.237785757540630.7622142424594
1697751.366022126960225.6339778730398
1703556.1986663373163-21.1986663373163
1714253.1334347055488-11.1334347055488
1724851.4461335185003-3.44613351850032
1734450.9141967234904-6.91419672349043
1744549.6885799037367-4.68857990373672
175048.7223078845444-48.7223078845444
176039.743925936363-39.743925936363
1774631.3876273902614.61237260974
1785131.994538795991119.0054612040089
1796333.688807884699929.3111921153001
1808437.622897567809446.3771024321906
1813045.2220413753098-15.2220413753098
1823942.6908817301164-3.6908817301164
1834541.92290389808383.07709610191616
1845242.29655727262819.70344272737187
1852843.9241907214072-15.9241907214072
1864041.1419246404493-1.14192464044927
1876240.693045730487821.3069542695122







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
18844.2569043031398-14.5330715665409103.04688017282
18944.4239352663084-15.3086167841225104.156487316739
19044.5909662294771-16.2895164481609105.471448907115
19144.7579971926457-17.4874329064248107.003427291716
19244.9250281558144-18.9108949719365108.760951283565
19345.0920591189831-20.565338230974110.74945646894
19445.2590900821517-22.4532863305747112.971466494878
19545.4261210453204-24.5746466310726115.426888721713
19645.593152008489-26.92708385636118.113387873338
19745.7601829716577-29.5064327283468121.026798671662
19845.9272139348264-32.3071140679577124.16154193761
19946.094244897995-35.3225263649633127.511016160953

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
188 & 44.2569043031398 & -14.5330715665409 & 103.04688017282 \tabularnewline
189 & 44.4239352663084 & -15.3086167841225 & 104.156487316739 \tabularnewline
190 & 44.5909662294771 & -16.2895164481609 & 105.471448907115 \tabularnewline
191 & 44.7579971926457 & -17.4874329064248 & 107.003427291716 \tabularnewline
192 & 44.9250281558144 & -18.9108949719365 & 108.760951283565 \tabularnewline
193 & 45.0920591189831 & -20.565338230974 & 110.74945646894 \tabularnewline
194 & 45.2590900821517 & -22.4532863305747 & 112.971466494878 \tabularnewline
195 & 45.4261210453204 & -24.5746466310726 & 115.426888721713 \tabularnewline
196 & 45.593152008489 & -26.92708385636 & 118.113387873338 \tabularnewline
197 & 45.7601829716577 & -29.5064327283468 & 121.026798671662 \tabularnewline
198 & 45.9272139348264 & -32.3071140679577 & 124.16154193761 \tabularnewline
199 & 46.094244897995 & -35.3225263649633 & 127.511016160953 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=122203&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]188[/C][C]44.2569043031398[/C][C]-14.5330715665409[/C][C]103.04688017282[/C][/ROW]
[ROW][C]189[/C][C]44.4239352663084[/C][C]-15.3086167841225[/C][C]104.156487316739[/C][/ROW]
[ROW][C]190[/C][C]44.5909662294771[/C][C]-16.2895164481609[/C][C]105.471448907115[/C][/ROW]
[ROW][C]191[/C][C]44.7579971926457[/C][C]-17.4874329064248[/C][C]107.003427291716[/C][/ROW]
[ROW][C]192[/C][C]44.9250281558144[/C][C]-18.9108949719365[/C][C]108.760951283565[/C][/ROW]
[ROW][C]193[/C][C]45.0920591189831[/C][C]-20.565338230974[/C][C]110.74945646894[/C][/ROW]
[ROW][C]194[/C][C]45.2590900821517[/C][C]-22.4532863305747[/C][C]112.971466494878[/C][/ROW]
[ROW][C]195[/C][C]45.4261210453204[/C][C]-24.5746466310726[/C][C]115.426888721713[/C][/ROW]
[ROW][C]196[/C][C]45.593152008489[/C][C]-26.92708385636[/C][C]118.113387873338[/C][/ROW]
[ROW][C]197[/C][C]45.7601829716577[/C][C]-29.5064327283468[/C][C]121.026798671662[/C][/ROW]
[ROW][C]198[/C][C]45.9272139348264[/C][C]-32.3071140679577[/C][C]124.16154193761[/C][/ROW]
[ROW][C]199[/C][C]46.094244897995[/C][C]-35.3225263649633[/C][C]127.511016160953[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=122203&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=122203&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
18844.2569043031398-14.5330715665409103.04688017282
18944.4239352663084-15.3086167841225104.156487316739
19044.5909662294771-16.2895164481609105.471448907115
19144.7579971926457-17.4874329064248107.003427291716
19244.9250281558144-18.9108949719365108.760951283565
19345.0920591189831-20.565338230974110.74945646894
19445.2590900821517-22.4532863305747112.971466494878
19545.4261210453204-24.5746466310726115.426888721713
19645.593152008489-26.92708385636118.113387873338
19745.7601829716577-29.5064327283468121.026798671662
19845.9272139348264-32.3071140679577124.16154193761
19946.094244897995-35.3225263649633127.511016160953



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