Free Statistics

of Irreproducible Research!

Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationFri, 20 May 2011 05:27:09 +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/20/t13058690932ond23u942xt926.htm/, Retrieved Sun, 12 May 2024 23:44:57 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=122410, Retrieved Sun, 12 May 2024 23:44:57 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywordsKDGP2W102
Estimated Impact94
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [Exonential Smooth...] [2011-05-20 05:27:09] [d41d8cd98f00b204e9800998ecf8427e] [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
30
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 time3 seconds
R Server'Gwilym Jenkins' @ www.wessa.org

\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 & 3 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ www.wessa.org \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=122410&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]3 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Gwilym Jenkins' @ www.wessa.org[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=122410&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=122410&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 time3 seconds
R Server'Gwilym Jenkins' @ www.wessa.org







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.155095379150641
beta0.13725398518357
gammaFALSE

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.155095379150641 \tabularnewline
beta & 0.13725398518357 \tabularnewline
gamma & FALSE \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=122410&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]0.155095379150641[/C][/ROW]
[ROW][C]beta[/C][C]0.13725398518357[/C][/ROW]
[ROW][C]gamma[/C][C]FALSE[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=122410&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=122410&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
alpha0.155095379150641
beta0.13725398518357
gammaFALSE







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
31291245
499130.881914190113-31.8819141901131
5116131.364928978027-15.3649289780271
6168134.08257155614433.9174284438556
7118145.165695907088-27.1656959070881
8129146.196821292765-17.1968212927654
9205148.40799644045856.5920035595423
10147163.268177303956-16.2681773039558
11150166.481772636165-16.4817726361653
12267169.31138526221197.6886147377888
13126191.927839774288-65.9278397742877
14129187.764702060816-58.7647020608163
15124183.46158272868-59.46158272868
1697177.784594428339-80.784594428339
17102167.080806812423-65.0808068124227
18127157.427199092523-30.4271990925232
19222152.50048805160769.4995119483926
20214164.55141614908349.4485838509167
21118174.545172645963-56.545172645963
22141166.896084254248-25.8960842542484
23154163.449266018761-9.44926601876057
24226162.35212243158363.6478775684174
2589173.946909619913-84.9469096199135
2677160.687028104626-83.6870281046255
2782145.84106422174-63.8410642217403
2897132.714103602917-35.7141036029173
29127123.1892420940293.81075790597107
30121119.8756253189331.12437468106735
31117116.1692979988060.83070200119407
32117112.4351069377334.56489306226665
33106109.377246628417-3.37724662841678
34112105.0157041538036.98429584619664
35134102.40986694845131.5901330515488
36169104.29275505187764.7072449481226
3775112.689406996829-37.6894069968294
38108104.4024996832683.59750031673163
39115102.59558255349612.4044174465042
4085102.418636101337-17.418636101337
4110197.24547335213273.75452664786731
4210895.436094638934612.5639053610654
4310995.260463475986813.7395365240132
4412495.559647092672728.4403529073273
4510598.7442822429726.25571775702798
469598.6213513277845-3.6213513277845
4713596.889443270539738.1105567294603
48164102.4412382250861.5587617749203
4988112.940171041041-24.9401710410411
5085109.492606210489-24.4926062104887
51112105.5930712696526.40692873034806
5287106.622298647886-19.6222986478857
5391103.196804261453-12.1968042614535
5487100.663330773181-13.6633307731806
558797.6115482076485-10.6115482076485
5614294.807190120164647.1928098798354
5795101.972635866189-6.97263586618871
58108100.5888415681397.41115843186108
59139101.59367203068237.406327969318
60159108.04690035352350.9530996464766
6161117.685832379025-56.6858323790253
6282109.423766105269-27.4237661052693
63124105.11632880189218.8836711981081
6493108.392946418558-15.3929464185582
65108106.0257423161621.97425768383771
6675106.394138248061-31.3941382480615
6787100.918948734477-13.9189487344771
6810397.8577813155055.14221868449495
699097.8623776531892-7.86237765318921
7010895.68265115025112.3173488497491
7112396.89491203749326.105087962507
72129100.8012985364128.1987014635903
7357105.632673512721-48.6326735127214
746597.5125912191803-32.5125912191803
756791.2005487524956-24.2005487524956
767185.6624974774495-14.6624974774495
777681.2916265692531-5.29162656925311
786778.2614891545763-11.2614891545763
7911074.065725151536335.9342748484637
8011877.954755458783140.0452445412169
819983.333839665393915.6661603346061
828585.2653333074398-0.265333307439761
8310784.72027763076722.279722369233
8414188.146134585854452.8538654141456
855897.4390243349273-39.4390243349273
866591.5781567469786-26.5781567469786
877087.1461688751446-17.1461688751446
888683.81204037369522.18795962630483
899383.52312196328389.47687803671619
907484.5664197687747-10.5664197687747
918782.27616247544184.72383752455816
927382.4579119313513-9.45791193135126
9310180.238802667123520.7611973328765
9410083.148490746182616.8515092538174
959685.810530080430710.1894699195693
9615787.656225820057369.3437741799427
9763100.152633548222-37.1526335482224
9811595.341055382962919.6589446170371
997099.7591794483923-29.7591794483923
1006695.879283516409-29.8792835164089
1016791.3447059794791-24.3447059794791
1028387.1502789167894-4.15027891678942
1037985.9995652843691-6.99956528436913
1047784.2579375443475-7.25793754434754
10510282.321734413731919.6782655862681
10611684.982112189877431.0178878101226
10710090.06150498531039.93849501468965
10813592.08314666674542.916853333255
10971100.13317008561-29.1331700856098
1106096.3883966445052-36.3883966445052
1118990.7437545924378-1.74375459243777
1127490.4352163308046-16.4352163308046
1137387.4982362488881-14.4982362488881
1149184.55304221931926.44695778068076
1158684.99359034775571.00640965224426
1167484.6117585055056-10.6117585055056
1178782.2021050950484.79789490495205
1188782.28455271332654.71544728667352
11910982.45459297716626.5454070228339
12013786.575443383367350.4245566166327
1214395.4732502247282-52.4732502247282
1226987.2950605442206-18.2950605442206
1237384.0282948019983-11.0282948019983
1247781.6538064757393-4.65380647573929
1256980.1689041193823-11.1689041193823
1267677.4357826366945-1.43578263669451
1277876.18165915685571.81834084314427
1287075.4709430478392-5.47094304783924
1298373.51323021489229.48676978510784
1306574.0773387466259-9.07733874662586
13111071.569006351800838.4309936481992
13213277.247094979261354.7529050207387
1335486.6221868532595-32.6221868532595
1345581.751362263785-26.751362263785
1356677.221606915982-11.2216069159821
1366574.8615653662618-9.8615653662618
1376072.5025323092084-12.5025323092084
1386569.4677503404864-4.46775034048645
1399667.584018875972828.4159811240272
1405571.4053062403205-16.4053062403205
1417167.92579176500183.07420823499822
1426367.5329020542694-4.53290205426944
1437465.86369072293148.1363092770686
14410666.332616875672239.6673831243278
1453472.5362846685988-38.5362846685988
1464765.7905853792488-18.7905853792488
1475661.7073489943339-5.70734899433391
1485359.5317671600699-6.53176716006992
1495357.0892771530311-4.08927715303106
1505554.93855574049430.0614442595057341
1516753.432900031330713.5670999686693
1525254.310718197653-2.310718197653
1534652.6767708167873-6.67677081678733
1545150.22353736540540.776462634594637
1555848.94279489846339.05720510153672
1569149.139162205174541.8608377948255
1573355.3143322248737-22.3143322248737
1584051.0612144888181-11.0612144888181
1594648.317938166158-2.31793816615794
1604546.8813605863997-1.88136058639971
1614145.4724447857964-4.4724447857964
1625543.566456814441611.4335431855584
1635744.370805158593212.6291948414068
1645445.62943701541348.37056298458665
1654646.4057627650067-0.405762765006742
1665245.81228328674566.18771671325445
1674846.37314277313211.62685722686787
1687746.261265684532330.7387343154677
1693051.3188557532931-21.3188557532931
1703547.8487298876248-12.8487298876248
1714245.4187645955059-3.41876459550591
1724844.37856653502583.6214334649742
1734444.5073617779747-0.507361777974722
1744543.98499951430131.01500048569874
175043.7203553842112-43.7203553842112
176035.5867690069288-35.5867690069288
1774627.957112411063718.0428875889363
1785129.029254966134321.9707450338657
1796331.178291392171131.8217086078289
1808435.532570061936348.4674299380637
1813043.5002716140874-13.5002716140874
1823941.5696825221683-2.56968252216831
1834541.27967527879563.72032472120442
1845242.04441535318719.95558464681292
1852843.9881445285592-15.9881445285592
1864041.5677742218044-1.56777422180443
1876241.350562786001220.6494372139988

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
3 & 129 & 124 & 5 \tabularnewline
4 & 99 & 130.881914190113 & -31.8819141901131 \tabularnewline
5 & 116 & 131.364928978027 & -15.3649289780271 \tabularnewline
6 & 168 & 134.082571556144 & 33.9174284438556 \tabularnewline
7 & 118 & 145.165695907088 & -27.1656959070881 \tabularnewline
8 & 129 & 146.196821292765 & -17.1968212927654 \tabularnewline
9 & 205 & 148.407996440458 & 56.5920035595423 \tabularnewline
10 & 147 & 163.268177303956 & -16.2681773039558 \tabularnewline
11 & 150 & 166.481772636165 & -16.4817726361653 \tabularnewline
12 & 267 & 169.311385262211 & 97.6886147377888 \tabularnewline
13 & 126 & 191.927839774288 & -65.9278397742877 \tabularnewline
14 & 129 & 187.764702060816 & -58.7647020608163 \tabularnewline
15 & 124 & 183.46158272868 & -59.46158272868 \tabularnewline
16 & 97 & 177.784594428339 & -80.784594428339 \tabularnewline
17 & 102 & 167.080806812423 & -65.0808068124227 \tabularnewline
18 & 127 & 157.427199092523 & -30.4271990925232 \tabularnewline
19 & 222 & 152.500488051607 & 69.4995119483926 \tabularnewline
20 & 214 & 164.551416149083 & 49.4485838509167 \tabularnewline
21 & 118 & 174.545172645963 & -56.545172645963 \tabularnewline
22 & 141 & 166.896084254248 & -25.8960842542484 \tabularnewline
23 & 154 & 163.449266018761 & -9.44926601876057 \tabularnewline
24 & 226 & 162.352122431583 & 63.6478775684174 \tabularnewline
25 & 89 & 173.946909619913 & -84.9469096199135 \tabularnewline
26 & 77 & 160.687028104626 & -83.6870281046255 \tabularnewline
27 & 82 & 145.84106422174 & -63.8410642217403 \tabularnewline
28 & 97 & 132.714103602917 & -35.7141036029173 \tabularnewline
29 & 127 & 123.189242094029 & 3.81075790597107 \tabularnewline
30 & 121 & 119.875625318933 & 1.12437468106735 \tabularnewline
31 & 117 & 116.169297998806 & 0.83070200119407 \tabularnewline
32 & 117 & 112.435106937733 & 4.56489306226665 \tabularnewline
33 & 106 & 109.377246628417 & -3.37724662841678 \tabularnewline
34 & 112 & 105.015704153803 & 6.98429584619664 \tabularnewline
35 & 134 & 102.409866948451 & 31.5901330515488 \tabularnewline
36 & 169 & 104.292755051877 & 64.7072449481226 \tabularnewline
37 & 75 & 112.689406996829 & -37.6894069968294 \tabularnewline
38 & 108 & 104.402499683268 & 3.59750031673163 \tabularnewline
39 & 115 & 102.595582553496 & 12.4044174465042 \tabularnewline
40 & 85 & 102.418636101337 & -17.418636101337 \tabularnewline
41 & 101 & 97.2454733521327 & 3.75452664786731 \tabularnewline
42 & 108 & 95.4360946389346 & 12.5639053610654 \tabularnewline
43 & 109 & 95.2604634759868 & 13.7395365240132 \tabularnewline
44 & 124 & 95.5596470926727 & 28.4403529073273 \tabularnewline
45 & 105 & 98.744282242972 & 6.25571775702798 \tabularnewline
46 & 95 & 98.6213513277845 & -3.6213513277845 \tabularnewline
47 & 135 & 96.8894432705397 & 38.1105567294603 \tabularnewline
48 & 164 & 102.44123822508 & 61.5587617749203 \tabularnewline
49 & 88 & 112.940171041041 & -24.9401710410411 \tabularnewline
50 & 85 & 109.492606210489 & -24.4926062104887 \tabularnewline
51 & 112 & 105.593071269652 & 6.40692873034806 \tabularnewline
52 & 87 & 106.622298647886 & -19.6222986478857 \tabularnewline
53 & 91 & 103.196804261453 & -12.1968042614535 \tabularnewline
54 & 87 & 100.663330773181 & -13.6633307731806 \tabularnewline
55 & 87 & 97.6115482076485 & -10.6115482076485 \tabularnewline
56 & 142 & 94.8071901201646 & 47.1928098798354 \tabularnewline
57 & 95 & 101.972635866189 & -6.97263586618871 \tabularnewline
58 & 108 & 100.588841568139 & 7.41115843186108 \tabularnewline
59 & 139 & 101.593672030682 & 37.406327969318 \tabularnewline
60 & 159 & 108.046900353523 & 50.9530996464766 \tabularnewline
61 & 61 & 117.685832379025 & -56.6858323790253 \tabularnewline
62 & 82 & 109.423766105269 & -27.4237661052693 \tabularnewline
63 & 124 & 105.116328801892 & 18.8836711981081 \tabularnewline
64 & 93 & 108.392946418558 & -15.3929464185582 \tabularnewline
65 & 108 & 106.025742316162 & 1.97425768383771 \tabularnewline
66 & 75 & 106.394138248061 & -31.3941382480615 \tabularnewline
67 & 87 & 100.918948734477 & -13.9189487344771 \tabularnewline
68 & 103 & 97.857781315505 & 5.14221868449495 \tabularnewline
69 & 90 & 97.8623776531892 & -7.86237765318921 \tabularnewline
70 & 108 & 95.682651150251 & 12.3173488497491 \tabularnewline
71 & 123 & 96.894912037493 & 26.105087962507 \tabularnewline
72 & 129 & 100.80129853641 & 28.1987014635903 \tabularnewline
73 & 57 & 105.632673512721 & -48.6326735127214 \tabularnewline
74 & 65 & 97.5125912191803 & -32.5125912191803 \tabularnewline
75 & 67 & 91.2005487524956 & -24.2005487524956 \tabularnewline
76 & 71 & 85.6624974774495 & -14.6624974774495 \tabularnewline
77 & 76 & 81.2916265692531 & -5.29162656925311 \tabularnewline
78 & 67 & 78.2614891545763 & -11.2614891545763 \tabularnewline
79 & 110 & 74.0657251515363 & 35.9342748484637 \tabularnewline
80 & 118 & 77.9547554587831 & 40.0452445412169 \tabularnewline
81 & 99 & 83.3338396653939 & 15.6661603346061 \tabularnewline
82 & 85 & 85.2653333074398 & -0.265333307439761 \tabularnewline
83 & 107 & 84.720277630767 & 22.279722369233 \tabularnewline
84 & 141 & 88.1461345858544 & 52.8538654141456 \tabularnewline
85 & 58 & 97.4390243349273 & -39.4390243349273 \tabularnewline
86 & 65 & 91.5781567469786 & -26.5781567469786 \tabularnewline
87 & 70 & 87.1461688751446 & -17.1461688751446 \tabularnewline
88 & 86 & 83.8120403736952 & 2.18795962630483 \tabularnewline
89 & 93 & 83.5231219632838 & 9.47687803671619 \tabularnewline
90 & 74 & 84.5664197687747 & -10.5664197687747 \tabularnewline
91 & 87 & 82.2761624754418 & 4.72383752455816 \tabularnewline
92 & 73 & 82.4579119313513 & -9.45791193135126 \tabularnewline
93 & 101 & 80.2388026671235 & 20.7611973328765 \tabularnewline
94 & 100 & 83.1484907461826 & 16.8515092538174 \tabularnewline
95 & 96 & 85.8105300804307 & 10.1894699195693 \tabularnewline
96 & 157 & 87.6562258200573 & 69.3437741799427 \tabularnewline
97 & 63 & 100.152633548222 & -37.1526335482224 \tabularnewline
98 & 115 & 95.3410553829629 & 19.6589446170371 \tabularnewline
99 & 70 & 99.7591794483923 & -29.7591794483923 \tabularnewline
100 & 66 & 95.879283516409 & -29.8792835164089 \tabularnewline
101 & 67 & 91.3447059794791 & -24.3447059794791 \tabularnewline
102 & 83 & 87.1502789167894 & -4.15027891678942 \tabularnewline
103 & 79 & 85.9995652843691 & -6.99956528436913 \tabularnewline
104 & 77 & 84.2579375443475 & -7.25793754434754 \tabularnewline
105 & 102 & 82.3217344137319 & 19.6782655862681 \tabularnewline
106 & 116 & 84.9821121898774 & 31.0178878101226 \tabularnewline
107 & 100 & 90.0615049853103 & 9.93849501468965 \tabularnewline
108 & 135 & 92.083146666745 & 42.916853333255 \tabularnewline
109 & 71 & 100.13317008561 & -29.1331700856098 \tabularnewline
110 & 60 & 96.3883966445052 & -36.3883966445052 \tabularnewline
111 & 89 & 90.7437545924378 & -1.74375459243777 \tabularnewline
112 & 74 & 90.4352163308046 & -16.4352163308046 \tabularnewline
113 & 73 & 87.4982362488881 & -14.4982362488881 \tabularnewline
114 & 91 & 84.5530422193192 & 6.44695778068076 \tabularnewline
115 & 86 & 84.9935903477557 & 1.00640965224426 \tabularnewline
116 & 74 & 84.6117585055056 & -10.6117585055056 \tabularnewline
117 & 87 & 82.202105095048 & 4.79789490495205 \tabularnewline
118 & 87 & 82.2845527133265 & 4.71544728667352 \tabularnewline
119 & 109 & 82.454592977166 & 26.5454070228339 \tabularnewline
120 & 137 & 86.5754433833673 & 50.4245566166327 \tabularnewline
121 & 43 & 95.4732502247282 & -52.4732502247282 \tabularnewline
122 & 69 & 87.2950605442206 & -18.2950605442206 \tabularnewline
123 & 73 & 84.0282948019983 & -11.0282948019983 \tabularnewline
124 & 77 & 81.6538064757393 & -4.65380647573929 \tabularnewline
125 & 69 & 80.1689041193823 & -11.1689041193823 \tabularnewline
126 & 76 & 77.4357826366945 & -1.43578263669451 \tabularnewline
127 & 78 & 76.1816591568557 & 1.81834084314427 \tabularnewline
128 & 70 & 75.4709430478392 & -5.47094304783924 \tabularnewline
129 & 83 & 73.5132302148922 & 9.48676978510784 \tabularnewline
130 & 65 & 74.0773387466259 & -9.07733874662586 \tabularnewline
131 & 110 & 71.5690063518008 & 38.4309936481992 \tabularnewline
132 & 132 & 77.2470949792613 & 54.7529050207387 \tabularnewline
133 & 54 & 86.6221868532595 & -32.6221868532595 \tabularnewline
134 & 55 & 81.751362263785 & -26.751362263785 \tabularnewline
135 & 66 & 77.221606915982 & -11.2216069159821 \tabularnewline
136 & 65 & 74.8615653662618 & -9.8615653662618 \tabularnewline
137 & 60 & 72.5025323092084 & -12.5025323092084 \tabularnewline
138 & 65 & 69.4677503404864 & -4.46775034048645 \tabularnewline
139 & 96 & 67.5840188759728 & 28.4159811240272 \tabularnewline
140 & 55 & 71.4053062403205 & -16.4053062403205 \tabularnewline
141 & 71 & 67.9257917650018 & 3.07420823499822 \tabularnewline
142 & 63 & 67.5329020542694 & -4.53290205426944 \tabularnewline
143 & 74 & 65.8636907229314 & 8.1363092770686 \tabularnewline
144 & 106 & 66.3326168756722 & 39.6673831243278 \tabularnewline
145 & 34 & 72.5362846685988 & -38.5362846685988 \tabularnewline
146 & 47 & 65.7905853792488 & -18.7905853792488 \tabularnewline
147 & 56 & 61.7073489943339 & -5.70734899433391 \tabularnewline
148 & 53 & 59.5317671600699 & -6.53176716006992 \tabularnewline
149 & 53 & 57.0892771530311 & -4.08927715303106 \tabularnewline
150 & 55 & 54.9385557404943 & 0.0614442595057341 \tabularnewline
151 & 67 & 53.4329000313307 & 13.5670999686693 \tabularnewline
152 & 52 & 54.310718197653 & -2.310718197653 \tabularnewline
153 & 46 & 52.6767708167873 & -6.67677081678733 \tabularnewline
154 & 51 & 50.2235373654054 & 0.776462634594637 \tabularnewline
155 & 58 & 48.9427948984633 & 9.05720510153672 \tabularnewline
156 & 91 & 49.1391622051745 & 41.8608377948255 \tabularnewline
157 & 33 & 55.3143322248737 & -22.3143322248737 \tabularnewline
158 & 40 & 51.0612144888181 & -11.0612144888181 \tabularnewline
159 & 46 & 48.317938166158 & -2.31793816615794 \tabularnewline
160 & 45 & 46.8813605863997 & -1.88136058639971 \tabularnewline
161 & 41 & 45.4724447857964 & -4.4724447857964 \tabularnewline
162 & 55 & 43.5664568144416 & 11.4335431855584 \tabularnewline
163 & 57 & 44.3708051585932 & 12.6291948414068 \tabularnewline
164 & 54 & 45.6294370154134 & 8.37056298458665 \tabularnewline
165 & 46 & 46.4057627650067 & -0.405762765006742 \tabularnewline
166 & 52 & 45.8122832867456 & 6.18771671325445 \tabularnewline
167 & 48 & 46.3731427731321 & 1.62685722686787 \tabularnewline
168 & 77 & 46.2612656845323 & 30.7387343154677 \tabularnewline
169 & 30 & 51.3188557532931 & -21.3188557532931 \tabularnewline
170 & 35 & 47.8487298876248 & -12.8487298876248 \tabularnewline
171 & 42 & 45.4187645955059 & -3.41876459550591 \tabularnewline
172 & 48 & 44.3785665350258 & 3.6214334649742 \tabularnewline
173 & 44 & 44.5073617779747 & -0.507361777974722 \tabularnewline
174 & 45 & 43.9849995143013 & 1.01500048569874 \tabularnewline
175 & 0 & 43.7203553842112 & -43.7203553842112 \tabularnewline
176 & 0 & 35.5867690069288 & -35.5867690069288 \tabularnewline
177 & 46 & 27.9571124110637 & 18.0428875889363 \tabularnewline
178 & 51 & 29.0292549661343 & 21.9707450338657 \tabularnewline
179 & 63 & 31.1782913921711 & 31.8217086078289 \tabularnewline
180 & 84 & 35.5325700619363 & 48.4674299380637 \tabularnewline
181 & 30 & 43.5002716140874 & -13.5002716140874 \tabularnewline
182 & 39 & 41.5696825221683 & -2.56968252216831 \tabularnewline
183 & 45 & 41.2796752787956 & 3.72032472120442 \tabularnewline
184 & 52 & 42.0444153531871 & 9.95558464681292 \tabularnewline
185 & 28 & 43.9881445285592 & -15.9881445285592 \tabularnewline
186 & 40 & 41.5677742218044 & -1.56777422180443 \tabularnewline
187 & 62 & 41.3505627860012 & 20.6494372139988 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=122410&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]130.881914190113[/C][C]-31.8819141901131[/C][/ROW]
[ROW][C]5[/C][C]116[/C][C]131.364928978027[/C][C]-15.3649289780271[/C][/ROW]
[ROW][C]6[/C][C]168[/C][C]134.082571556144[/C][C]33.9174284438556[/C][/ROW]
[ROW][C]7[/C][C]118[/C][C]145.165695907088[/C][C]-27.1656959070881[/C][/ROW]
[ROW][C]8[/C][C]129[/C][C]146.196821292765[/C][C]-17.1968212927654[/C][/ROW]
[ROW][C]9[/C][C]205[/C][C]148.407996440458[/C][C]56.5920035595423[/C][/ROW]
[ROW][C]10[/C][C]147[/C][C]163.268177303956[/C][C]-16.2681773039558[/C][/ROW]
[ROW][C]11[/C][C]150[/C][C]166.481772636165[/C][C]-16.4817726361653[/C][/ROW]
[ROW][C]12[/C][C]267[/C][C]169.311385262211[/C][C]97.6886147377888[/C][/ROW]
[ROW][C]13[/C][C]126[/C][C]191.927839774288[/C][C]-65.9278397742877[/C][/ROW]
[ROW][C]14[/C][C]129[/C][C]187.764702060816[/C][C]-58.7647020608163[/C][/ROW]
[ROW][C]15[/C][C]124[/C][C]183.46158272868[/C][C]-59.46158272868[/C][/ROW]
[ROW][C]16[/C][C]97[/C][C]177.784594428339[/C][C]-80.784594428339[/C][/ROW]
[ROW][C]17[/C][C]102[/C][C]167.080806812423[/C][C]-65.0808068124227[/C][/ROW]
[ROW][C]18[/C][C]127[/C][C]157.427199092523[/C][C]-30.4271990925232[/C][/ROW]
[ROW][C]19[/C][C]222[/C][C]152.500488051607[/C][C]69.4995119483926[/C][/ROW]
[ROW][C]20[/C][C]214[/C][C]164.551416149083[/C][C]49.4485838509167[/C][/ROW]
[ROW][C]21[/C][C]118[/C][C]174.545172645963[/C][C]-56.545172645963[/C][/ROW]
[ROW][C]22[/C][C]141[/C][C]166.896084254248[/C][C]-25.8960842542484[/C][/ROW]
[ROW][C]23[/C][C]154[/C][C]163.449266018761[/C][C]-9.44926601876057[/C][/ROW]
[ROW][C]24[/C][C]226[/C][C]162.352122431583[/C][C]63.6478775684174[/C][/ROW]
[ROW][C]25[/C][C]89[/C][C]173.946909619913[/C][C]-84.9469096199135[/C][/ROW]
[ROW][C]26[/C][C]77[/C][C]160.687028104626[/C][C]-83.6870281046255[/C][/ROW]
[ROW][C]27[/C][C]82[/C][C]145.84106422174[/C][C]-63.8410642217403[/C][/ROW]
[ROW][C]28[/C][C]97[/C][C]132.714103602917[/C][C]-35.7141036029173[/C][/ROW]
[ROW][C]29[/C][C]127[/C][C]123.189242094029[/C][C]3.81075790597107[/C][/ROW]
[ROW][C]30[/C][C]121[/C][C]119.875625318933[/C][C]1.12437468106735[/C][/ROW]
[ROW][C]31[/C][C]117[/C][C]116.169297998806[/C][C]0.83070200119407[/C][/ROW]
[ROW][C]32[/C][C]117[/C][C]112.435106937733[/C][C]4.56489306226665[/C][/ROW]
[ROW][C]33[/C][C]106[/C][C]109.377246628417[/C][C]-3.37724662841678[/C][/ROW]
[ROW][C]34[/C][C]112[/C][C]105.015704153803[/C][C]6.98429584619664[/C][/ROW]
[ROW][C]35[/C][C]134[/C][C]102.409866948451[/C][C]31.5901330515488[/C][/ROW]
[ROW][C]36[/C][C]169[/C][C]104.292755051877[/C][C]64.7072449481226[/C][/ROW]
[ROW][C]37[/C][C]75[/C][C]112.689406996829[/C][C]-37.6894069968294[/C][/ROW]
[ROW][C]38[/C][C]108[/C][C]104.402499683268[/C][C]3.59750031673163[/C][/ROW]
[ROW][C]39[/C][C]115[/C][C]102.595582553496[/C][C]12.4044174465042[/C][/ROW]
[ROW][C]40[/C][C]85[/C][C]102.418636101337[/C][C]-17.418636101337[/C][/ROW]
[ROW][C]41[/C][C]101[/C][C]97.2454733521327[/C][C]3.75452664786731[/C][/ROW]
[ROW][C]42[/C][C]108[/C][C]95.4360946389346[/C][C]12.5639053610654[/C][/ROW]
[ROW][C]43[/C][C]109[/C][C]95.2604634759868[/C][C]13.7395365240132[/C][/ROW]
[ROW][C]44[/C][C]124[/C][C]95.5596470926727[/C][C]28.4403529073273[/C][/ROW]
[ROW][C]45[/C][C]105[/C][C]98.744282242972[/C][C]6.25571775702798[/C][/ROW]
[ROW][C]46[/C][C]95[/C][C]98.6213513277845[/C][C]-3.6213513277845[/C][/ROW]
[ROW][C]47[/C][C]135[/C][C]96.8894432705397[/C][C]38.1105567294603[/C][/ROW]
[ROW][C]48[/C][C]164[/C][C]102.44123822508[/C][C]61.5587617749203[/C][/ROW]
[ROW][C]49[/C][C]88[/C][C]112.940171041041[/C][C]-24.9401710410411[/C][/ROW]
[ROW][C]50[/C][C]85[/C][C]109.492606210489[/C][C]-24.4926062104887[/C][/ROW]
[ROW][C]51[/C][C]112[/C][C]105.593071269652[/C][C]6.40692873034806[/C][/ROW]
[ROW][C]52[/C][C]87[/C][C]106.622298647886[/C][C]-19.6222986478857[/C][/ROW]
[ROW][C]53[/C][C]91[/C][C]103.196804261453[/C][C]-12.1968042614535[/C][/ROW]
[ROW][C]54[/C][C]87[/C][C]100.663330773181[/C][C]-13.6633307731806[/C][/ROW]
[ROW][C]55[/C][C]87[/C][C]97.6115482076485[/C][C]-10.6115482076485[/C][/ROW]
[ROW][C]56[/C][C]142[/C][C]94.8071901201646[/C][C]47.1928098798354[/C][/ROW]
[ROW][C]57[/C][C]95[/C][C]101.972635866189[/C][C]-6.97263586618871[/C][/ROW]
[ROW][C]58[/C][C]108[/C][C]100.588841568139[/C][C]7.41115843186108[/C][/ROW]
[ROW][C]59[/C][C]139[/C][C]101.593672030682[/C][C]37.406327969318[/C][/ROW]
[ROW][C]60[/C][C]159[/C][C]108.046900353523[/C][C]50.9530996464766[/C][/ROW]
[ROW][C]61[/C][C]61[/C][C]117.685832379025[/C][C]-56.6858323790253[/C][/ROW]
[ROW][C]62[/C][C]82[/C][C]109.423766105269[/C][C]-27.4237661052693[/C][/ROW]
[ROW][C]63[/C][C]124[/C][C]105.116328801892[/C][C]18.8836711981081[/C][/ROW]
[ROW][C]64[/C][C]93[/C][C]108.392946418558[/C][C]-15.3929464185582[/C][/ROW]
[ROW][C]65[/C][C]108[/C][C]106.025742316162[/C][C]1.97425768383771[/C][/ROW]
[ROW][C]66[/C][C]75[/C][C]106.394138248061[/C][C]-31.3941382480615[/C][/ROW]
[ROW][C]67[/C][C]87[/C][C]100.918948734477[/C][C]-13.9189487344771[/C][/ROW]
[ROW][C]68[/C][C]103[/C][C]97.857781315505[/C][C]5.14221868449495[/C][/ROW]
[ROW][C]69[/C][C]90[/C][C]97.8623776531892[/C][C]-7.86237765318921[/C][/ROW]
[ROW][C]70[/C][C]108[/C][C]95.682651150251[/C][C]12.3173488497491[/C][/ROW]
[ROW][C]71[/C][C]123[/C][C]96.894912037493[/C][C]26.105087962507[/C][/ROW]
[ROW][C]72[/C][C]129[/C][C]100.80129853641[/C][C]28.1987014635903[/C][/ROW]
[ROW][C]73[/C][C]57[/C][C]105.632673512721[/C][C]-48.6326735127214[/C][/ROW]
[ROW][C]74[/C][C]65[/C][C]97.5125912191803[/C][C]-32.5125912191803[/C][/ROW]
[ROW][C]75[/C][C]67[/C][C]91.2005487524956[/C][C]-24.2005487524956[/C][/ROW]
[ROW][C]76[/C][C]71[/C][C]85.6624974774495[/C][C]-14.6624974774495[/C][/ROW]
[ROW][C]77[/C][C]76[/C][C]81.2916265692531[/C][C]-5.29162656925311[/C][/ROW]
[ROW][C]78[/C][C]67[/C][C]78.2614891545763[/C][C]-11.2614891545763[/C][/ROW]
[ROW][C]79[/C][C]110[/C][C]74.0657251515363[/C][C]35.9342748484637[/C][/ROW]
[ROW][C]80[/C][C]118[/C][C]77.9547554587831[/C][C]40.0452445412169[/C][/ROW]
[ROW][C]81[/C][C]99[/C][C]83.3338396653939[/C][C]15.6661603346061[/C][/ROW]
[ROW][C]82[/C][C]85[/C][C]85.2653333074398[/C][C]-0.265333307439761[/C][/ROW]
[ROW][C]83[/C][C]107[/C][C]84.720277630767[/C][C]22.279722369233[/C][/ROW]
[ROW][C]84[/C][C]141[/C][C]88.1461345858544[/C][C]52.8538654141456[/C][/ROW]
[ROW][C]85[/C][C]58[/C][C]97.4390243349273[/C][C]-39.4390243349273[/C][/ROW]
[ROW][C]86[/C][C]65[/C][C]91.5781567469786[/C][C]-26.5781567469786[/C][/ROW]
[ROW][C]87[/C][C]70[/C][C]87.1461688751446[/C][C]-17.1461688751446[/C][/ROW]
[ROW][C]88[/C][C]86[/C][C]83.8120403736952[/C][C]2.18795962630483[/C][/ROW]
[ROW][C]89[/C][C]93[/C][C]83.5231219632838[/C][C]9.47687803671619[/C][/ROW]
[ROW][C]90[/C][C]74[/C][C]84.5664197687747[/C][C]-10.5664197687747[/C][/ROW]
[ROW][C]91[/C][C]87[/C][C]82.2761624754418[/C][C]4.72383752455816[/C][/ROW]
[ROW][C]92[/C][C]73[/C][C]82.4579119313513[/C][C]-9.45791193135126[/C][/ROW]
[ROW][C]93[/C][C]101[/C][C]80.2388026671235[/C][C]20.7611973328765[/C][/ROW]
[ROW][C]94[/C][C]100[/C][C]83.1484907461826[/C][C]16.8515092538174[/C][/ROW]
[ROW][C]95[/C][C]96[/C][C]85.8105300804307[/C][C]10.1894699195693[/C][/ROW]
[ROW][C]96[/C][C]157[/C][C]87.6562258200573[/C][C]69.3437741799427[/C][/ROW]
[ROW][C]97[/C][C]63[/C][C]100.152633548222[/C][C]-37.1526335482224[/C][/ROW]
[ROW][C]98[/C][C]115[/C][C]95.3410553829629[/C][C]19.6589446170371[/C][/ROW]
[ROW][C]99[/C][C]70[/C][C]99.7591794483923[/C][C]-29.7591794483923[/C][/ROW]
[ROW][C]100[/C][C]66[/C][C]95.879283516409[/C][C]-29.8792835164089[/C][/ROW]
[ROW][C]101[/C][C]67[/C][C]91.3447059794791[/C][C]-24.3447059794791[/C][/ROW]
[ROW][C]102[/C][C]83[/C][C]87.1502789167894[/C][C]-4.15027891678942[/C][/ROW]
[ROW][C]103[/C][C]79[/C][C]85.9995652843691[/C][C]-6.99956528436913[/C][/ROW]
[ROW][C]104[/C][C]77[/C][C]84.2579375443475[/C][C]-7.25793754434754[/C][/ROW]
[ROW][C]105[/C][C]102[/C][C]82.3217344137319[/C][C]19.6782655862681[/C][/ROW]
[ROW][C]106[/C][C]116[/C][C]84.9821121898774[/C][C]31.0178878101226[/C][/ROW]
[ROW][C]107[/C][C]100[/C][C]90.0615049853103[/C][C]9.93849501468965[/C][/ROW]
[ROW][C]108[/C][C]135[/C][C]92.083146666745[/C][C]42.916853333255[/C][/ROW]
[ROW][C]109[/C][C]71[/C][C]100.13317008561[/C][C]-29.1331700856098[/C][/ROW]
[ROW][C]110[/C][C]60[/C][C]96.3883966445052[/C][C]-36.3883966445052[/C][/ROW]
[ROW][C]111[/C][C]89[/C][C]90.7437545924378[/C][C]-1.74375459243777[/C][/ROW]
[ROW][C]112[/C][C]74[/C][C]90.4352163308046[/C][C]-16.4352163308046[/C][/ROW]
[ROW][C]113[/C][C]73[/C][C]87.4982362488881[/C][C]-14.4982362488881[/C][/ROW]
[ROW][C]114[/C][C]91[/C][C]84.5530422193192[/C][C]6.44695778068076[/C][/ROW]
[ROW][C]115[/C][C]86[/C][C]84.9935903477557[/C][C]1.00640965224426[/C][/ROW]
[ROW][C]116[/C][C]74[/C][C]84.6117585055056[/C][C]-10.6117585055056[/C][/ROW]
[ROW][C]117[/C][C]87[/C][C]82.202105095048[/C][C]4.79789490495205[/C][/ROW]
[ROW][C]118[/C][C]87[/C][C]82.2845527133265[/C][C]4.71544728667352[/C][/ROW]
[ROW][C]119[/C][C]109[/C][C]82.454592977166[/C][C]26.5454070228339[/C][/ROW]
[ROW][C]120[/C][C]137[/C][C]86.5754433833673[/C][C]50.4245566166327[/C][/ROW]
[ROW][C]121[/C][C]43[/C][C]95.4732502247282[/C][C]-52.4732502247282[/C][/ROW]
[ROW][C]122[/C][C]69[/C][C]87.2950605442206[/C][C]-18.2950605442206[/C][/ROW]
[ROW][C]123[/C][C]73[/C][C]84.0282948019983[/C][C]-11.0282948019983[/C][/ROW]
[ROW][C]124[/C][C]77[/C][C]81.6538064757393[/C][C]-4.65380647573929[/C][/ROW]
[ROW][C]125[/C][C]69[/C][C]80.1689041193823[/C][C]-11.1689041193823[/C][/ROW]
[ROW][C]126[/C][C]76[/C][C]77.4357826366945[/C][C]-1.43578263669451[/C][/ROW]
[ROW][C]127[/C][C]78[/C][C]76.1816591568557[/C][C]1.81834084314427[/C][/ROW]
[ROW][C]128[/C][C]70[/C][C]75.4709430478392[/C][C]-5.47094304783924[/C][/ROW]
[ROW][C]129[/C][C]83[/C][C]73.5132302148922[/C][C]9.48676978510784[/C][/ROW]
[ROW][C]130[/C][C]65[/C][C]74.0773387466259[/C][C]-9.07733874662586[/C][/ROW]
[ROW][C]131[/C][C]110[/C][C]71.5690063518008[/C][C]38.4309936481992[/C][/ROW]
[ROW][C]132[/C][C]132[/C][C]77.2470949792613[/C][C]54.7529050207387[/C][/ROW]
[ROW][C]133[/C][C]54[/C][C]86.6221868532595[/C][C]-32.6221868532595[/C][/ROW]
[ROW][C]134[/C][C]55[/C][C]81.751362263785[/C][C]-26.751362263785[/C][/ROW]
[ROW][C]135[/C][C]66[/C][C]77.221606915982[/C][C]-11.2216069159821[/C][/ROW]
[ROW][C]136[/C][C]65[/C][C]74.8615653662618[/C][C]-9.8615653662618[/C][/ROW]
[ROW][C]137[/C][C]60[/C][C]72.5025323092084[/C][C]-12.5025323092084[/C][/ROW]
[ROW][C]138[/C][C]65[/C][C]69.4677503404864[/C][C]-4.46775034048645[/C][/ROW]
[ROW][C]139[/C][C]96[/C][C]67.5840188759728[/C][C]28.4159811240272[/C][/ROW]
[ROW][C]140[/C][C]55[/C][C]71.4053062403205[/C][C]-16.4053062403205[/C][/ROW]
[ROW][C]141[/C][C]71[/C][C]67.9257917650018[/C][C]3.07420823499822[/C][/ROW]
[ROW][C]142[/C][C]63[/C][C]67.5329020542694[/C][C]-4.53290205426944[/C][/ROW]
[ROW][C]143[/C][C]74[/C][C]65.8636907229314[/C][C]8.1363092770686[/C][/ROW]
[ROW][C]144[/C][C]106[/C][C]66.3326168756722[/C][C]39.6673831243278[/C][/ROW]
[ROW][C]145[/C][C]34[/C][C]72.5362846685988[/C][C]-38.5362846685988[/C][/ROW]
[ROW][C]146[/C][C]47[/C][C]65.7905853792488[/C][C]-18.7905853792488[/C][/ROW]
[ROW][C]147[/C][C]56[/C][C]61.7073489943339[/C][C]-5.70734899433391[/C][/ROW]
[ROW][C]148[/C][C]53[/C][C]59.5317671600699[/C][C]-6.53176716006992[/C][/ROW]
[ROW][C]149[/C][C]53[/C][C]57.0892771530311[/C][C]-4.08927715303106[/C][/ROW]
[ROW][C]150[/C][C]55[/C][C]54.9385557404943[/C][C]0.0614442595057341[/C][/ROW]
[ROW][C]151[/C][C]67[/C][C]53.4329000313307[/C][C]13.5670999686693[/C][/ROW]
[ROW][C]152[/C][C]52[/C][C]54.310718197653[/C][C]-2.310718197653[/C][/ROW]
[ROW][C]153[/C][C]46[/C][C]52.6767708167873[/C][C]-6.67677081678733[/C][/ROW]
[ROW][C]154[/C][C]51[/C][C]50.2235373654054[/C][C]0.776462634594637[/C][/ROW]
[ROW][C]155[/C][C]58[/C][C]48.9427948984633[/C][C]9.05720510153672[/C][/ROW]
[ROW][C]156[/C][C]91[/C][C]49.1391622051745[/C][C]41.8608377948255[/C][/ROW]
[ROW][C]157[/C][C]33[/C][C]55.3143322248737[/C][C]-22.3143322248737[/C][/ROW]
[ROW][C]158[/C][C]40[/C][C]51.0612144888181[/C][C]-11.0612144888181[/C][/ROW]
[ROW][C]159[/C][C]46[/C][C]48.317938166158[/C][C]-2.31793816615794[/C][/ROW]
[ROW][C]160[/C][C]45[/C][C]46.8813605863997[/C][C]-1.88136058639971[/C][/ROW]
[ROW][C]161[/C][C]41[/C][C]45.4724447857964[/C][C]-4.4724447857964[/C][/ROW]
[ROW][C]162[/C][C]55[/C][C]43.5664568144416[/C][C]11.4335431855584[/C][/ROW]
[ROW][C]163[/C][C]57[/C][C]44.3708051585932[/C][C]12.6291948414068[/C][/ROW]
[ROW][C]164[/C][C]54[/C][C]45.6294370154134[/C][C]8.37056298458665[/C][/ROW]
[ROW][C]165[/C][C]46[/C][C]46.4057627650067[/C][C]-0.405762765006742[/C][/ROW]
[ROW][C]166[/C][C]52[/C][C]45.8122832867456[/C][C]6.18771671325445[/C][/ROW]
[ROW][C]167[/C][C]48[/C][C]46.3731427731321[/C][C]1.62685722686787[/C][/ROW]
[ROW][C]168[/C][C]77[/C][C]46.2612656845323[/C][C]30.7387343154677[/C][/ROW]
[ROW][C]169[/C][C]30[/C][C]51.3188557532931[/C][C]-21.3188557532931[/C][/ROW]
[ROW][C]170[/C][C]35[/C][C]47.8487298876248[/C][C]-12.8487298876248[/C][/ROW]
[ROW][C]171[/C][C]42[/C][C]45.4187645955059[/C][C]-3.41876459550591[/C][/ROW]
[ROW][C]172[/C][C]48[/C][C]44.3785665350258[/C][C]3.6214334649742[/C][/ROW]
[ROW][C]173[/C][C]44[/C][C]44.5073617779747[/C][C]-0.507361777974722[/C][/ROW]
[ROW][C]174[/C][C]45[/C][C]43.9849995143013[/C][C]1.01500048569874[/C][/ROW]
[ROW][C]175[/C][C]0[/C][C]43.7203553842112[/C][C]-43.7203553842112[/C][/ROW]
[ROW][C]176[/C][C]0[/C][C]35.5867690069288[/C][C]-35.5867690069288[/C][/ROW]
[ROW][C]177[/C][C]46[/C][C]27.9571124110637[/C][C]18.0428875889363[/C][/ROW]
[ROW][C]178[/C][C]51[/C][C]29.0292549661343[/C][C]21.9707450338657[/C][/ROW]
[ROW][C]179[/C][C]63[/C][C]31.1782913921711[/C][C]31.8217086078289[/C][/ROW]
[ROW][C]180[/C][C]84[/C][C]35.5325700619363[/C][C]48.4674299380637[/C][/ROW]
[ROW][C]181[/C][C]30[/C][C]43.5002716140874[/C][C]-13.5002716140874[/C][/ROW]
[ROW][C]182[/C][C]39[/C][C]41.5696825221683[/C][C]-2.56968252216831[/C][/ROW]
[ROW][C]183[/C][C]45[/C][C]41.2796752787956[/C][C]3.72032472120442[/C][/ROW]
[ROW][C]184[/C][C]52[/C][C]42.0444153531871[/C][C]9.95558464681292[/C][/ROW]
[ROW][C]185[/C][C]28[/C][C]43.9881445285592[/C][C]-15.9881445285592[/C][/ROW]
[ROW][C]186[/C][C]40[/C][C]41.5677742218044[/C][C]-1.56777422180443[/C][/ROW]
[ROW][C]187[/C][C]62[/C][C]41.3505627860012[/C][C]20.6494372139988[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=122410&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=122410&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
499130.881914190113-31.8819141901131
5116131.364928978027-15.3649289780271
6168134.08257155614433.9174284438556
7118145.165695907088-27.1656959070881
8129146.196821292765-17.1968212927654
9205148.40799644045856.5920035595423
10147163.268177303956-16.2681773039558
11150166.481772636165-16.4817726361653
12267169.31138526221197.6886147377888
13126191.927839774288-65.9278397742877
14129187.764702060816-58.7647020608163
15124183.46158272868-59.46158272868
1697177.784594428339-80.784594428339
17102167.080806812423-65.0808068124227
18127157.427199092523-30.4271990925232
19222152.50048805160769.4995119483926
20214164.55141614908349.4485838509167
21118174.545172645963-56.545172645963
22141166.896084254248-25.8960842542484
23154163.449266018761-9.44926601876057
24226162.35212243158363.6478775684174
2589173.946909619913-84.9469096199135
2677160.687028104626-83.6870281046255
2782145.84106422174-63.8410642217403
2897132.714103602917-35.7141036029173
29127123.1892420940293.81075790597107
30121119.8756253189331.12437468106735
31117116.1692979988060.83070200119407
32117112.4351069377334.56489306226665
33106109.377246628417-3.37724662841678
34112105.0157041538036.98429584619664
35134102.40986694845131.5901330515488
36169104.29275505187764.7072449481226
3775112.689406996829-37.6894069968294
38108104.4024996832683.59750031673163
39115102.59558255349612.4044174465042
4085102.418636101337-17.418636101337
4110197.24547335213273.75452664786731
4210895.436094638934612.5639053610654
4310995.260463475986813.7395365240132
4412495.559647092672728.4403529073273
4510598.7442822429726.25571775702798
469598.6213513277845-3.6213513277845
4713596.889443270539738.1105567294603
48164102.4412382250861.5587617749203
4988112.940171041041-24.9401710410411
5085109.492606210489-24.4926062104887
51112105.5930712696526.40692873034806
5287106.622298647886-19.6222986478857
5391103.196804261453-12.1968042614535
5487100.663330773181-13.6633307731806
558797.6115482076485-10.6115482076485
5614294.807190120164647.1928098798354
5795101.972635866189-6.97263586618871
58108100.5888415681397.41115843186108
59139101.59367203068237.406327969318
60159108.04690035352350.9530996464766
6161117.685832379025-56.6858323790253
6282109.423766105269-27.4237661052693
63124105.11632880189218.8836711981081
6493108.392946418558-15.3929464185582
65108106.0257423161621.97425768383771
6675106.394138248061-31.3941382480615
6787100.918948734477-13.9189487344771
6810397.8577813155055.14221868449495
699097.8623776531892-7.86237765318921
7010895.68265115025112.3173488497491
7112396.89491203749326.105087962507
72129100.8012985364128.1987014635903
7357105.632673512721-48.6326735127214
746597.5125912191803-32.5125912191803
756791.2005487524956-24.2005487524956
767185.6624974774495-14.6624974774495
777681.2916265692531-5.29162656925311
786778.2614891545763-11.2614891545763
7911074.065725151536335.9342748484637
8011877.954755458783140.0452445412169
819983.333839665393915.6661603346061
828585.2653333074398-0.265333307439761
8310784.72027763076722.279722369233
8414188.146134585854452.8538654141456
855897.4390243349273-39.4390243349273
866591.5781567469786-26.5781567469786
877087.1461688751446-17.1461688751446
888683.81204037369522.18795962630483
899383.52312196328389.47687803671619
907484.5664197687747-10.5664197687747
918782.27616247544184.72383752455816
927382.4579119313513-9.45791193135126
9310180.238802667123520.7611973328765
9410083.148490746182616.8515092538174
959685.810530080430710.1894699195693
9615787.656225820057369.3437741799427
9763100.152633548222-37.1526335482224
9811595.341055382962919.6589446170371
997099.7591794483923-29.7591794483923
1006695.879283516409-29.8792835164089
1016791.3447059794791-24.3447059794791
1028387.1502789167894-4.15027891678942
1037985.9995652843691-6.99956528436913
1047784.2579375443475-7.25793754434754
10510282.321734413731919.6782655862681
10611684.982112189877431.0178878101226
10710090.06150498531039.93849501468965
10813592.08314666674542.916853333255
10971100.13317008561-29.1331700856098
1106096.3883966445052-36.3883966445052
1118990.7437545924378-1.74375459243777
1127490.4352163308046-16.4352163308046
1137387.4982362488881-14.4982362488881
1149184.55304221931926.44695778068076
1158684.99359034775571.00640965224426
1167484.6117585055056-10.6117585055056
1178782.2021050950484.79789490495205
1188782.28455271332654.71544728667352
11910982.45459297716626.5454070228339
12013786.575443383367350.4245566166327
1214395.4732502247282-52.4732502247282
1226987.2950605442206-18.2950605442206
1237384.0282948019983-11.0282948019983
1247781.6538064757393-4.65380647573929
1256980.1689041193823-11.1689041193823
1267677.4357826366945-1.43578263669451
1277876.18165915685571.81834084314427
1287075.4709430478392-5.47094304783924
1298373.51323021489229.48676978510784
1306574.0773387466259-9.07733874662586
13111071.569006351800838.4309936481992
13213277.247094979261354.7529050207387
1335486.6221868532595-32.6221868532595
1345581.751362263785-26.751362263785
1356677.221606915982-11.2216069159821
1366574.8615653662618-9.8615653662618
1376072.5025323092084-12.5025323092084
1386569.4677503404864-4.46775034048645
1399667.584018875972828.4159811240272
1405571.4053062403205-16.4053062403205
1417167.92579176500183.07420823499822
1426367.5329020542694-4.53290205426944
1437465.86369072293148.1363092770686
14410666.332616875672239.6673831243278
1453472.5362846685988-38.5362846685988
1464765.7905853792488-18.7905853792488
1475661.7073489943339-5.70734899433391
1485359.5317671600699-6.53176716006992
1495357.0892771530311-4.08927715303106
1505554.93855574049430.0614442595057341
1516753.432900031330713.5670999686693
1525254.310718197653-2.310718197653
1534652.6767708167873-6.67677081678733
1545150.22353736540540.776462634594637
1555848.94279489846339.05720510153672
1569149.139162205174541.8608377948255
1573355.3143322248737-22.3143322248737
1584051.0612144888181-11.0612144888181
1594648.317938166158-2.31793816615794
1604546.8813605863997-1.88136058639971
1614145.4724447857964-4.4724447857964
1625543.566456814441611.4335431855584
1635744.370805158593212.6291948414068
1645445.62943701541348.37056298458665
1654646.4057627650067-0.405762765006742
1665245.81228328674566.18771671325445
1674846.37314277313211.62685722686787
1687746.261265684532330.7387343154677
1693051.3188557532931-21.3188557532931
1703547.8487298876248-12.8487298876248
1714245.4187645955059-3.41876459550591
1724844.37856653502583.6214334649742
1734444.5073617779747-0.507361777974722
1744543.98499951430131.01500048569874
175043.7203553842112-43.7203553842112
176035.5867690069288-35.5867690069288
1774627.957112411063718.0428875889363
1785129.029254966134321.9707450338657
1796331.178291392171131.8217086078289
1808435.532570061936348.4674299380637
1813043.5002716140874-13.5002716140874
1823941.5696825221683-2.56968252216831
1834541.27967527879563.72032472120442
1845242.04441535318719.95558464681292
1852843.9881445285592-15.9881445285592
1864041.5677742218044-1.56777422180443
1876241.350562786001220.6494372139988







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
18845.0187122269264-13.6151969793061103.652621433159
18945.4842293738992-14.054771201188105.023229948986
19045.9497465208719-14.7068682367719106.606361278516
19146.4152636678446-15.5851244221473108.415651757837
19246.8807808148173-16.699704078044110.461265707679
19347.3462979617901-18.0572995152328112.749895438813
19447.8118151087628-19.6613015812104115.284931798736
19548.2773322557355-21.5121127868512118.066777298322
19648.7428494027083-23.6075610646198121.093259870036
19749.208366549681-25.9433671864647124.360100285827
19849.6738836966537-28.5136219995843127.861389392892
19950.1394008436264-31.311238359003131.590040046256

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
188 & 45.0187122269264 & -13.6151969793061 & 103.652621433159 \tabularnewline
189 & 45.4842293738992 & -14.054771201188 & 105.023229948986 \tabularnewline
190 & 45.9497465208719 & -14.7068682367719 & 106.606361278516 \tabularnewline
191 & 46.4152636678446 & -15.5851244221473 & 108.415651757837 \tabularnewline
192 & 46.8807808148173 & -16.699704078044 & 110.461265707679 \tabularnewline
193 & 47.3462979617901 & -18.0572995152328 & 112.749895438813 \tabularnewline
194 & 47.8118151087628 & -19.6613015812104 & 115.284931798736 \tabularnewline
195 & 48.2773322557355 & -21.5121127868512 & 118.066777298322 \tabularnewline
196 & 48.7428494027083 & -23.6075610646198 & 121.093259870036 \tabularnewline
197 & 49.208366549681 & -25.9433671864647 & 124.360100285827 \tabularnewline
198 & 49.6738836966537 & -28.5136219995843 & 127.861389392892 \tabularnewline
199 & 50.1394008436264 & -31.311238359003 & 131.590040046256 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=122410&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]45.0187122269264[/C][C]-13.6151969793061[/C][C]103.652621433159[/C][/ROW]
[ROW][C]189[/C][C]45.4842293738992[/C][C]-14.054771201188[/C][C]105.023229948986[/C][/ROW]
[ROW][C]190[/C][C]45.9497465208719[/C][C]-14.7068682367719[/C][C]106.606361278516[/C][/ROW]
[ROW][C]191[/C][C]46.4152636678446[/C][C]-15.5851244221473[/C][C]108.415651757837[/C][/ROW]
[ROW][C]192[/C][C]46.8807808148173[/C][C]-16.699704078044[/C][C]110.461265707679[/C][/ROW]
[ROW][C]193[/C][C]47.3462979617901[/C][C]-18.0572995152328[/C][C]112.749895438813[/C][/ROW]
[ROW][C]194[/C][C]47.8118151087628[/C][C]-19.6613015812104[/C][C]115.284931798736[/C][/ROW]
[ROW][C]195[/C][C]48.2773322557355[/C][C]-21.5121127868512[/C][C]118.066777298322[/C][/ROW]
[ROW][C]196[/C][C]48.7428494027083[/C][C]-23.6075610646198[/C][C]121.093259870036[/C][/ROW]
[ROW][C]197[/C][C]49.208366549681[/C][C]-25.9433671864647[/C][C]124.360100285827[/C][/ROW]
[ROW][C]198[/C][C]49.6738836966537[/C][C]-28.5136219995843[/C][C]127.861389392892[/C][/ROW]
[ROW][C]199[/C][C]50.1394008436264[/C][C]-31.311238359003[/C][C]131.590040046256[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=122410&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=122410&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
18845.0187122269264-13.6151969793061103.652621433159
18945.4842293738992-14.054771201188105.023229948986
19045.9497465208719-14.7068682367719106.606361278516
19146.4152636678446-15.5851244221473108.415651757837
19246.8807808148173-16.699704078044110.461265707679
19347.3462979617901-18.0572995152328112.749895438813
19447.8118151087628-19.6613015812104115.284931798736
19548.2773322557355-21.5121127868512118.066777298322
19648.7428494027083-23.6075610646198121.093259870036
19749.208366549681-25.9433671864647124.360100285827
19849.6738836966537-28.5136219995843127.861389392892
19950.1394008436264-31.311238359003131.590040046256



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')