Free Statistics

of Irreproducible Research!

Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationThu, 18 Aug 2011 06:15:26 -0400
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2011/Aug/18/t1313662641pqbt024sdykr95x.htm/, Retrieved Wed, 15 May 2024 12:52:51 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=124019, Retrieved Wed, 15 May 2024 12:52:51 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywordsLynn Pelgrims
Estimated Impact136
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [Exponential Smoothing] [Tijdreeks B - Sta...] [2011-07-20 13:42:35] [9287d6673621c679f6316b90c6bec81c]
- R P     [Exponential Smoothing] [Tijdreeks B - Sta...] [2011-08-18 10:15:26] [d41d8cd98f00b204e9800998ecf8427e] [Current]
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Dataseries X:
1070
1240
1200
1280
1180
1190
1190
1230
1170
1190
1190
1400
1130
1260
1260
1260
1130
1220
1180
1280
1140
1160
1170
1410
1100
1280
1330
1260
1070
1260
1270
1410
1160
1130
1160
1300
1080
1380
1260
1250
990
1180
1240
1500
1150
1110
1080
1270
1050
1490
1280
1230
960
1100
1270
1530
1290
1120
1100
1310
1020
1510
1260
1160
970
1020
1210
1530
1350
1070
1140
1250
930
1510
1230
1180
960
960
1240
1640
1350
1100
1120
1290
890
1560
1250
1170
900
860
1310
1610
1440
1130
1220
1400
930
1490
1250
1160
910
880
1300
1550
1460
1120
1270
1410




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time1 seconds
R Server'Gertrude Mary Cox' @ cox.wessa.net

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input & view raw input (R code)  \tabularnewline
Raw Output & view raw output of R engine  \tabularnewline
Computing time & 1 seconds \tabularnewline
R Server & 'Gertrude Mary Cox' @ cox.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=124019&T=0

[TABLE]
[ROW][C]Summary of computational transaction[/C][/ROW]
[ROW][C]Raw Input[/C][C]view raw input (R code) [/C][/ROW]
[ROW][C]Raw Output[/C][C]view raw output of R engine [/C][/ROW]
[ROW][C]Computing time[/C][C]1 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Gertrude Mary Cox' @ cox.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=124019&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=124019&T=0

As an alternative you can also use a QR Code:  

The GUIDs for individual cells are displayed in the table below:

Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time1 seconds
R Server'Gertrude Mary Cox' @ cox.wessa.net







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.0632012955179426
betaFALSE
gammaFALSE

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.0632012955179426 \tabularnewline
beta & FALSE \tabularnewline
gamma & FALSE \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=124019&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]0.0632012955179426[/C][/ROW]
[ROW][C]beta[/C][C]FALSE[/C][/ROW]
[ROW][C]gamma[/C][C]FALSE[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=124019&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=124019&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
alpha0.0632012955179426
betaFALSE
gammaFALSE







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
212401070170
312001080.74422023805119.25577976195
412801088.28134001701191.718659982992
511801100.398207702979.601792297103
611901105.4291441016284.5708558983758
711901110.7741317574679.2258682425372
812301115.78130926893114.218690731075
911701123.0000784954946.9999215045077
1011901125.9705344238264.0294655761811
1111901130.0172795995559.982720400445
1214001133.80826523755266.191734762446
1311301150.63192773071-20.6319277307086
1412601149.3279631691110.672036830905
1512601156.32257927442103.677420725582
1612601162.8751265802397.1248734197666
1711301169.01354440738-39.013544407379
1812201166.5478378580953.4521621419142
1911801169.9260837536910.0739162463101
2012801170.5627683114109.437231688604
2111401177.47934313201-37.4793431320129
2211601175.11060009091-15.1106000909083
2311701174.15559058911-4.15559058910935
2414101173.89295188024236.107048119765
2511001188.81522320232-88.8152232023217
2612801183.2019860342296.7980139657802
2713301189.31974592042140.680254079579
2812601198.2109202320461.7890797679563
2910701202.11607012224-132.11607012224
3012601193.7661633317866.233836668225
3112701197.9522276163372.0477723836693
3214101202.50574017016207.49425982984
3311601215.61964620394-55.6196462039429
3411301212.1044125076-82.1044125076041
3511601206.91530726938-46.9153072693839
3613001203.9501990703496.0498009296634
3710801210.02067092333-130.020670923332
3813801201.80319607687178.196803923135
3912601213.0654649419646.9345350580361
4012501216.0317883621633.968211637836
419901218.1786233441-228.178623344103
4211801203.75743873925-23.7574387392549
4312401202.2559378327537.7440621672542
4415001204.64141145983295.358588540174
4511501223.30845689792-73.3084568979159
4611101218.67526744955-108.675267449546
4710801211.80684975598-131.806849755976
4812701203.4764860932666.5235139067404
4910501207.68085835457-157.680858354571
5014901197.71522382818292.284776171819
5112801216.1880003424163.8119996575879
5212301220.221001390369.77899860963771
539601220.83904677136-260.83904677136
5411001204.35368109374-104.353681093744
5512701197.7583932565572.2416067434465
5615301202.32415639304327.675843606963
5712901223.0336942189366.9663057810681
5811201227.26605150035-107.266051500346
5911001220.48669808043-120.48669808043
6013101212.8717826690797.1282173309323
6110201219.01041183573-199.010411835731
6215101206.43269598615303.567304013847
6312601225.6185428767234.3814571232824
6411601227.7914955087-67.7914955087035
659701223.50698516745-253.506985167455
6610201207.48501528202-187.485015282024
6712101195.63571942614.3642805740017
6815301196.54356056746333.456439432542
6913501217.6184395384132.381560461605
7010701225.98512566226-155.985125662256
7111401216.12666363887-76.1266636388718
7212501211.3153598734438.6846401265634
739301213.76027924608-283.760279246081
7415101195.8262619812314.173738018805
7512301215.682449241714.3175507583014
7611801216.58733699827-36.5873369982671
779601214.27496990043-254.274969900425
789601198.20446238493-238.204462384932
7912401183.1496317640556.8503682359503
8016401186.74264868723453.257351312766
8113501215.38910049323134.610899506768
8211001223.8966837329-123.896683732895
8311201216.0662528106-96.0662528105995
8412901209.9947411774280.0052588225847
858901215.05117718325-325.051177183251
8615601194.50752167564365.492478324363
8712501217.607119807832.3928801921995
8811701219.6543918015-49.654391801505
899001216.51616991149-316.516169911494
908601196.51193792071-336.511937920711
9113101175.24394748687134.756052513132
9216101183.76070458458426.239295415418
9314401210.69958025549229.300419744508
9411301225.19166384615-95.1916638461526
9512201219.175427368570.824572631432829
9614001219.22754142712180.772458572878
979301230.65259500289-300.652595002892
9814901211.65096149788278.349038502122
9912501229.2429813373920.7570186626144
10011601230.55485180795-70.5548518079529
1019101226.09569376861-316.095693768614
1028801206.11803641479-326.118036414794
10313001185.50695402161114.493045978388
10415501192.74306285524357.256937144759
10514601215.32216411556244.677835884438
10611201230.78612032799-110.786120327985
10712701223.7842939978546.2157060021502
10814101226.70518649046183.294813509538

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
2 & 1240 & 1070 & 170 \tabularnewline
3 & 1200 & 1080.74422023805 & 119.25577976195 \tabularnewline
4 & 1280 & 1088.28134001701 & 191.718659982992 \tabularnewline
5 & 1180 & 1100.3982077029 & 79.601792297103 \tabularnewline
6 & 1190 & 1105.42914410162 & 84.5708558983758 \tabularnewline
7 & 1190 & 1110.77413175746 & 79.2258682425372 \tabularnewline
8 & 1230 & 1115.78130926893 & 114.218690731075 \tabularnewline
9 & 1170 & 1123.00007849549 & 46.9999215045077 \tabularnewline
10 & 1190 & 1125.97053442382 & 64.0294655761811 \tabularnewline
11 & 1190 & 1130.01727959955 & 59.982720400445 \tabularnewline
12 & 1400 & 1133.80826523755 & 266.191734762446 \tabularnewline
13 & 1130 & 1150.63192773071 & -20.6319277307086 \tabularnewline
14 & 1260 & 1149.3279631691 & 110.672036830905 \tabularnewline
15 & 1260 & 1156.32257927442 & 103.677420725582 \tabularnewline
16 & 1260 & 1162.87512658023 & 97.1248734197666 \tabularnewline
17 & 1130 & 1169.01354440738 & -39.013544407379 \tabularnewline
18 & 1220 & 1166.54783785809 & 53.4521621419142 \tabularnewline
19 & 1180 & 1169.92608375369 & 10.0739162463101 \tabularnewline
20 & 1280 & 1170.5627683114 & 109.437231688604 \tabularnewline
21 & 1140 & 1177.47934313201 & -37.4793431320129 \tabularnewline
22 & 1160 & 1175.11060009091 & -15.1106000909083 \tabularnewline
23 & 1170 & 1174.15559058911 & -4.15559058910935 \tabularnewline
24 & 1410 & 1173.89295188024 & 236.107048119765 \tabularnewline
25 & 1100 & 1188.81522320232 & -88.8152232023217 \tabularnewline
26 & 1280 & 1183.20198603422 & 96.7980139657802 \tabularnewline
27 & 1330 & 1189.31974592042 & 140.680254079579 \tabularnewline
28 & 1260 & 1198.21092023204 & 61.7890797679563 \tabularnewline
29 & 1070 & 1202.11607012224 & -132.11607012224 \tabularnewline
30 & 1260 & 1193.76616333178 & 66.233836668225 \tabularnewline
31 & 1270 & 1197.95222761633 & 72.0477723836693 \tabularnewline
32 & 1410 & 1202.50574017016 & 207.49425982984 \tabularnewline
33 & 1160 & 1215.61964620394 & -55.6196462039429 \tabularnewline
34 & 1130 & 1212.1044125076 & -82.1044125076041 \tabularnewline
35 & 1160 & 1206.91530726938 & -46.9153072693839 \tabularnewline
36 & 1300 & 1203.95019907034 & 96.0498009296634 \tabularnewline
37 & 1080 & 1210.02067092333 & -130.020670923332 \tabularnewline
38 & 1380 & 1201.80319607687 & 178.196803923135 \tabularnewline
39 & 1260 & 1213.06546494196 & 46.9345350580361 \tabularnewline
40 & 1250 & 1216.03178836216 & 33.968211637836 \tabularnewline
41 & 990 & 1218.1786233441 & -228.178623344103 \tabularnewline
42 & 1180 & 1203.75743873925 & -23.7574387392549 \tabularnewline
43 & 1240 & 1202.25593783275 & 37.7440621672542 \tabularnewline
44 & 1500 & 1204.64141145983 & 295.358588540174 \tabularnewline
45 & 1150 & 1223.30845689792 & -73.3084568979159 \tabularnewline
46 & 1110 & 1218.67526744955 & -108.675267449546 \tabularnewline
47 & 1080 & 1211.80684975598 & -131.806849755976 \tabularnewline
48 & 1270 & 1203.47648609326 & 66.5235139067404 \tabularnewline
49 & 1050 & 1207.68085835457 & -157.680858354571 \tabularnewline
50 & 1490 & 1197.71522382818 & 292.284776171819 \tabularnewline
51 & 1280 & 1216.18800034241 & 63.8119996575879 \tabularnewline
52 & 1230 & 1220.22100139036 & 9.77899860963771 \tabularnewline
53 & 960 & 1220.83904677136 & -260.83904677136 \tabularnewline
54 & 1100 & 1204.35368109374 & -104.353681093744 \tabularnewline
55 & 1270 & 1197.75839325655 & 72.2416067434465 \tabularnewline
56 & 1530 & 1202.32415639304 & 327.675843606963 \tabularnewline
57 & 1290 & 1223.03369421893 & 66.9663057810681 \tabularnewline
58 & 1120 & 1227.26605150035 & -107.266051500346 \tabularnewline
59 & 1100 & 1220.48669808043 & -120.48669808043 \tabularnewline
60 & 1310 & 1212.87178266907 & 97.1282173309323 \tabularnewline
61 & 1020 & 1219.01041183573 & -199.010411835731 \tabularnewline
62 & 1510 & 1206.43269598615 & 303.567304013847 \tabularnewline
63 & 1260 & 1225.61854287672 & 34.3814571232824 \tabularnewline
64 & 1160 & 1227.7914955087 & -67.7914955087035 \tabularnewline
65 & 970 & 1223.50698516745 & -253.506985167455 \tabularnewline
66 & 1020 & 1207.48501528202 & -187.485015282024 \tabularnewline
67 & 1210 & 1195.635719426 & 14.3642805740017 \tabularnewline
68 & 1530 & 1196.54356056746 & 333.456439432542 \tabularnewline
69 & 1350 & 1217.6184395384 & 132.381560461605 \tabularnewline
70 & 1070 & 1225.98512566226 & -155.985125662256 \tabularnewline
71 & 1140 & 1216.12666363887 & -76.1266636388718 \tabularnewline
72 & 1250 & 1211.31535987344 & 38.6846401265634 \tabularnewline
73 & 930 & 1213.76027924608 & -283.760279246081 \tabularnewline
74 & 1510 & 1195.8262619812 & 314.173738018805 \tabularnewline
75 & 1230 & 1215.6824492417 & 14.3175507583014 \tabularnewline
76 & 1180 & 1216.58733699827 & -36.5873369982671 \tabularnewline
77 & 960 & 1214.27496990043 & -254.274969900425 \tabularnewline
78 & 960 & 1198.20446238493 & -238.204462384932 \tabularnewline
79 & 1240 & 1183.14963176405 & 56.8503682359503 \tabularnewline
80 & 1640 & 1186.74264868723 & 453.257351312766 \tabularnewline
81 & 1350 & 1215.38910049323 & 134.610899506768 \tabularnewline
82 & 1100 & 1223.8966837329 & -123.896683732895 \tabularnewline
83 & 1120 & 1216.0662528106 & -96.0662528105995 \tabularnewline
84 & 1290 & 1209.99474117742 & 80.0052588225847 \tabularnewline
85 & 890 & 1215.05117718325 & -325.051177183251 \tabularnewline
86 & 1560 & 1194.50752167564 & 365.492478324363 \tabularnewline
87 & 1250 & 1217.6071198078 & 32.3928801921995 \tabularnewline
88 & 1170 & 1219.6543918015 & -49.654391801505 \tabularnewline
89 & 900 & 1216.51616991149 & -316.516169911494 \tabularnewline
90 & 860 & 1196.51193792071 & -336.511937920711 \tabularnewline
91 & 1310 & 1175.24394748687 & 134.756052513132 \tabularnewline
92 & 1610 & 1183.76070458458 & 426.239295415418 \tabularnewline
93 & 1440 & 1210.69958025549 & 229.300419744508 \tabularnewline
94 & 1130 & 1225.19166384615 & -95.1916638461526 \tabularnewline
95 & 1220 & 1219.17542736857 & 0.824572631432829 \tabularnewline
96 & 1400 & 1219.22754142712 & 180.772458572878 \tabularnewline
97 & 930 & 1230.65259500289 & -300.652595002892 \tabularnewline
98 & 1490 & 1211.65096149788 & 278.349038502122 \tabularnewline
99 & 1250 & 1229.24298133739 & 20.7570186626144 \tabularnewline
100 & 1160 & 1230.55485180795 & -70.5548518079529 \tabularnewline
101 & 910 & 1226.09569376861 & -316.095693768614 \tabularnewline
102 & 880 & 1206.11803641479 & -326.118036414794 \tabularnewline
103 & 1300 & 1185.50695402161 & 114.493045978388 \tabularnewline
104 & 1550 & 1192.74306285524 & 357.256937144759 \tabularnewline
105 & 1460 & 1215.32216411556 & 244.677835884438 \tabularnewline
106 & 1120 & 1230.78612032799 & -110.786120327985 \tabularnewline
107 & 1270 & 1223.78429399785 & 46.2157060021502 \tabularnewline
108 & 1410 & 1226.70518649046 & 183.294813509538 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=124019&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]2[/C][C]1240[/C][C]1070[/C][C]170[/C][/ROW]
[ROW][C]3[/C][C]1200[/C][C]1080.74422023805[/C][C]119.25577976195[/C][/ROW]
[ROW][C]4[/C][C]1280[/C][C]1088.28134001701[/C][C]191.718659982992[/C][/ROW]
[ROW][C]5[/C][C]1180[/C][C]1100.3982077029[/C][C]79.601792297103[/C][/ROW]
[ROW][C]6[/C][C]1190[/C][C]1105.42914410162[/C][C]84.5708558983758[/C][/ROW]
[ROW][C]7[/C][C]1190[/C][C]1110.77413175746[/C][C]79.2258682425372[/C][/ROW]
[ROW][C]8[/C][C]1230[/C][C]1115.78130926893[/C][C]114.218690731075[/C][/ROW]
[ROW][C]9[/C][C]1170[/C][C]1123.00007849549[/C][C]46.9999215045077[/C][/ROW]
[ROW][C]10[/C][C]1190[/C][C]1125.97053442382[/C][C]64.0294655761811[/C][/ROW]
[ROW][C]11[/C][C]1190[/C][C]1130.01727959955[/C][C]59.982720400445[/C][/ROW]
[ROW][C]12[/C][C]1400[/C][C]1133.80826523755[/C][C]266.191734762446[/C][/ROW]
[ROW][C]13[/C][C]1130[/C][C]1150.63192773071[/C][C]-20.6319277307086[/C][/ROW]
[ROW][C]14[/C][C]1260[/C][C]1149.3279631691[/C][C]110.672036830905[/C][/ROW]
[ROW][C]15[/C][C]1260[/C][C]1156.32257927442[/C][C]103.677420725582[/C][/ROW]
[ROW][C]16[/C][C]1260[/C][C]1162.87512658023[/C][C]97.1248734197666[/C][/ROW]
[ROW][C]17[/C][C]1130[/C][C]1169.01354440738[/C][C]-39.013544407379[/C][/ROW]
[ROW][C]18[/C][C]1220[/C][C]1166.54783785809[/C][C]53.4521621419142[/C][/ROW]
[ROW][C]19[/C][C]1180[/C][C]1169.92608375369[/C][C]10.0739162463101[/C][/ROW]
[ROW][C]20[/C][C]1280[/C][C]1170.5627683114[/C][C]109.437231688604[/C][/ROW]
[ROW][C]21[/C][C]1140[/C][C]1177.47934313201[/C][C]-37.4793431320129[/C][/ROW]
[ROW][C]22[/C][C]1160[/C][C]1175.11060009091[/C][C]-15.1106000909083[/C][/ROW]
[ROW][C]23[/C][C]1170[/C][C]1174.15559058911[/C][C]-4.15559058910935[/C][/ROW]
[ROW][C]24[/C][C]1410[/C][C]1173.89295188024[/C][C]236.107048119765[/C][/ROW]
[ROW][C]25[/C][C]1100[/C][C]1188.81522320232[/C][C]-88.8152232023217[/C][/ROW]
[ROW][C]26[/C][C]1280[/C][C]1183.20198603422[/C][C]96.7980139657802[/C][/ROW]
[ROW][C]27[/C][C]1330[/C][C]1189.31974592042[/C][C]140.680254079579[/C][/ROW]
[ROW][C]28[/C][C]1260[/C][C]1198.21092023204[/C][C]61.7890797679563[/C][/ROW]
[ROW][C]29[/C][C]1070[/C][C]1202.11607012224[/C][C]-132.11607012224[/C][/ROW]
[ROW][C]30[/C][C]1260[/C][C]1193.76616333178[/C][C]66.233836668225[/C][/ROW]
[ROW][C]31[/C][C]1270[/C][C]1197.95222761633[/C][C]72.0477723836693[/C][/ROW]
[ROW][C]32[/C][C]1410[/C][C]1202.50574017016[/C][C]207.49425982984[/C][/ROW]
[ROW][C]33[/C][C]1160[/C][C]1215.61964620394[/C][C]-55.6196462039429[/C][/ROW]
[ROW][C]34[/C][C]1130[/C][C]1212.1044125076[/C][C]-82.1044125076041[/C][/ROW]
[ROW][C]35[/C][C]1160[/C][C]1206.91530726938[/C][C]-46.9153072693839[/C][/ROW]
[ROW][C]36[/C][C]1300[/C][C]1203.95019907034[/C][C]96.0498009296634[/C][/ROW]
[ROW][C]37[/C][C]1080[/C][C]1210.02067092333[/C][C]-130.020670923332[/C][/ROW]
[ROW][C]38[/C][C]1380[/C][C]1201.80319607687[/C][C]178.196803923135[/C][/ROW]
[ROW][C]39[/C][C]1260[/C][C]1213.06546494196[/C][C]46.9345350580361[/C][/ROW]
[ROW][C]40[/C][C]1250[/C][C]1216.03178836216[/C][C]33.968211637836[/C][/ROW]
[ROW][C]41[/C][C]990[/C][C]1218.1786233441[/C][C]-228.178623344103[/C][/ROW]
[ROW][C]42[/C][C]1180[/C][C]1203.75743873925[/C][C]-23.7574387392549[/C][/ROW]
[ROW][C]43[/C][C]1240[/C][C]1202.25593783275[/C][C]37.7440621672542[/C][/ROW]
[ROW][C]44[/C][C]1500[/C][C]1204.64141145983[/C][C]295.358588540174[/C][/ROW]
[ROW][C]45[/C][C]1150[/C][C]1223.30845689792[/C][C]-73.3084568979159[/C][/ROW]
[ROW][C]46[/C][C]1110[/C][C]1218.67526744955[/C][C]-108.675267449546[/C][/ROW]
[ROW][C]47[/C][C]1080[/C][C]1211.80684975598[/C][C]-131.806849755976[/C][/ROW]
[ROW][C]48[/C][C]1270[/C][C]1203.47648609326[/C][C]66.5235139067404[/C][/ROW]
[ROW][C]49[/C][C]1050[/C][C]1207.68085835457[/C][C]-157.680858354571[/C][/ROW]
[ROW][C]50[/C][C]1490[/C][C]1197.71522382818[/C][C]292.284776171819[/C][/ROW]
[ROW][C]51[/C][C]1280[/C][C]1216.18800034241[/C][C]63.8119996575879[/C][/ROW]
[ROW][C]52[/C][C]1230[/C][C]1220.22100139036[/C][C]9.77899860963771[/C][/ROW]
[ROW][C]53[/C][C]960[/C][C]1220.83904677136[/C][C]-260.83904677136[/C][/ROW]
[ROW][C]54[/C][C]1100[/C][C]1204.35368109374[/C][C]-104.353681093744[/C][/ROW]
[ROW][C]55[/C][C]1270[/C][C]1197.75839325655[/C][C]72.2416067434465[/C][/ROW]
[ROW][C]56[/C][C]1530[/C][C]1202.32415639304[/C][C]327.675843606963[/C][/ROW]
[ROW][C]57[/C][C]1290[/C][C]1223.03369421893[/C][C]66.9663057810681[/C][/ROW]
[ROW][C]58[/C][C]1120[/C][C]1227.26605150035[/C][C]-107.266051500346[/C][/ROW]
[ROW][C]59[/C][C]1100[/C][C]1220.48669808043[/C][C]-120.48669808043[/C][/ROW]
[ROW][C]60[/C][C]1310[/C][C]1212.87178266907[/C][C]97.1282173309323[/C][/ROW]
[ROW][C]61[/C][C]1020[/C][C]1219.01041183573[/C][C]-199.010411835731[/C][/ROW]
[ROW][C]62[/C][C]1510[/C][C]1206.43269598615[/C][C]303.567304013847[/C][/ROW]
[ROW][C]63[/C][C]1260[/C][C]1225.61854287672[/C][C]34.3814571232824[/C][/ROW]
[ROW][C]64[/C][C]1160[/C][C]1227.7914955087[/C][C]-67.7914955087035[/C][/ROW]
[ROW][C]65[/C][C]970[/C][C]1223.50698516745[/C][C]-253.506985167455[/C][/ROW]
[ROW][C]66[/C][C]1020[/C][C]1207.48501528202[/C][C]-187.485015282024[/C][/ROW]
[ROW][C]67[/C][C]1210[/C][C]1195.635719426[/C][C]14.3642805740017[/C][/ROW]
[ROW][C]68[/C][C]1530[/C][C]1196.54356056746[/C][C]333.456439432542[/C][/ROW]
[ROW][C]69[/C][C]1350[/C][C]1217.6184395384[/C][C]132.381560461605[/C][/ROW]
[ROW][C]70[/C][C]1070[/C][C]1225.98512566226[/C][C]-155.985125662256[/C][/ROW]
[ROW][C]71[/C][C]1140[/C][C]1216.12666363887[/C][C]-76.1266636388718[/C][/ROW]
[ROW][C]72[/C][C]1250[/C][C]1211.31535987344[/C][C]38.6846401265634[/C][/ROW]
[ROW][C]73[/C][C]930[/C][C]1213.76027924608[/C][C]-283.760279246081[/C][/ROW]
[ROW][C]74[/C][C]1510[/C][C]1195.8262619812[/C][C]314.173738018805[/C][/ROW]
[ROW][C]75[/C][C]1230[/C][C]1215.6824492417[/C][C]14.3175507583014[/C][/ROW]
[ROW][C]76[/C][C]1180[/C][C]1216.58733699827[/C][C]-36.5873369982671[/C][/ROW]
[ROW][C]77[/C][C]960[/C][C]1214.27496990043[/C][C]-254.274969900425[/C][/ROW]
[ROW][C]78[/C][C]960[/C][C]1198.20446238493[/C][C]-238.204462384932[/C][/ROW]
[ROW][C]79[/C][C]1240[/C][C]1183.14963176405[/C][C]56.8503682359503[/C][/ROW]
[ROW][C]80[/C][C]1640[/C][C]1186.74264868723[/C][C]453.257351312766[/C][/ROW]
[ROW][C]81[/C][C]1350[/C][C]1215.38910049323[/C][C]134.610899506768[/C][/ROW]
[ROW][C]82[/C][C]1100[/C][C]1223.8966837329[/C][C]-123.896683732895[/C][/ROW]
[ROW][C]83[/C][C]1120[/C][C]1216.0662528106[/C][C]-96.0662528105995[/C][/ROW]
[ROW][C]84[/C][C]1290[/C][C]1209.99474117742[/C][C]80.0052588225847[/C][/ROW]
[ROW][C]85[/C][C]890[/C][C]1215.05117718325[/C][C]-325.051177183251[/C][/ROW]
[ROW][C]86[/C][C]1560[/C][C]1194.50752167564[/C][C]365.492478324363[/C][/ROW]
[ROW][C]87[/C][C]1250[/C][C]1217.6071198078[/C][C]32.3928801921995[/C][/ROW]
[ROW][C]88[/C][C]1170[/C][C]1219.6543918015[/C][C]-49.654391801505[/C][/ROW]
[ROW][C]89[/C][C]900[/C][C]1216.51616991149[/C][C]-316.516169911494[/C][/ROW]
[ROW][C]90[/C][C]860[/C][C]1196.51193792071[/C][C]-336.511937920711[/C][/ROW]
[ROW][C]91[/C][C]1310[/C][C]1175.24394748687[/C][C]134.756052513132[/C][/ROW]
[ROW][C]92[/C][C]1610[/C][C]1183.76070458458[/C][C]426.239295415418[/C][/ROW]
[ROW][C]93[/C][C]1440[/C][C]1210.69958025549[/C][C]229.300419744508[/C][/ROW]
[ROW][C]94[/C][C]1130[/C][C]1225.19166384615[/C][C]-95.1916638461526[/C][/ROW]
[ROW][C]95[/C][C]1220[/C][C]1219.17542736857[/C][C]0.824572631432829[/C][/ROW]
[ROW][C]96[/C][C]1400[/C][C]1219.22754142712[/C][C]180.772458572878[/C][/ROW]
[ROW][C]97[/C][C]930[/C][C]1230.65259500289[/C][C]-300.652595002892[/C][/ROW]
[ROW][C]98[/C][C]1490[/C][C]1211.65096149788[/C][C]278.349038502122[/C][/ROW]
[ROW][C]99[/C][C]1250[/C][C]1229.24298133739[/C][C]20.7570186626144[/C][/ROW]
[ROW][C]100[/C][C]1160[/C][C]1230.55485180795[/C][C]-70.5548518079529[/C][/ROW]
[ROW][C]101[/C][C]910[/C][C]1226.09569376861[/C][C]-316.095693768614[/C][/ROW]
[ROW][C]102[/C][C]880[/C][C]1206.11803641479[/C][C]-326.118036414794[/C][/ROW]
[ROW][C]103[/C][C]1300[/C][C]1185.50695402161[/C][C]114.493045978388[/C][/ROW]
[ROW][C]104[/C][C]1550[/C][C]1192.74306285524[/C][C]357.256937144759[/C][/ROW]
[ROW][C]105[/C][C]1460[/C][C]1215.32216411556[/C][C]244.677835884438[/C][/ROW]
[ROW][C]106[/C][C]1120[/C][C]1230.78612032799[/C][C]-110.786120327985[/C][/ROW]
[ROW][C]107[/C][C]1270[/C][C]1223.78429399785[/C][C]46.2157060021502[/C][/ROW]
[ROW][C]108[/C][C]1410[/C][C]1226.70518649046[/C][C]183.294813509538[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=124019&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=124019&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
212401070170
312001080.74422023805119.25577976195
412801088.28134001701191.718659982992
511801100.398207702979.601792297103
611901105.4291441016284.5708558983758
711901110.7741317574679.2258682425372
812301115.78130926893114.218690731075
911701123.0000784954946.9999215045077
1011901125.9705344238264.0294655761811
1111901130.0172795995559.982720400445
1214001133.80826523755266.191734762446
1311301150.63192773071-20.6319277307086
1412601149.3279631691110.672036830905
1512601156.32257927442103.677420725582
1612601162.8751265802397.1248734197666
1711301169.01354440738-39.013544407379
1812201166.5478378580953.4521621419142
1911801169.9260837536910.0739162463101
2012801170.5627683114109.437231688604
2111401177.47934313201-37.4793431320129
2211601175.11060009091-15.1106000909083
2311701174.15559058911-4.15559058910935
2414101173.89295188024236.107048119765
2511001188.81522320232-88.8152232023217
2612801183.2019860342296.7980139657802
2713301189.31974592042140.680254079579
2812601198.2109202320461.7890797679563
2910701202.11607012224-132.11607012224
3012601193.7661633317866.233836668225
3112701197.9522276163372.0477723836693
3214101202.50574017016207.49425982984
3311601215.61964620394-55.6196462039429
3411301212.1044125076-82.1044125076041
3511601206.91530726938-46.9153072693839
3613001203.9501990703496.0498009296634
3710801210.02067092333-130.020670923332
3813801201.80319607687178.196803923135
3912601213.0654649419646.9345350580361
4012501216.0317883621633.968211637836
419901218.1786233441-228.178623344103
4211801203.75743873925-23.7574387392549
4312401202.2559378327537.7440621672542
4415001204.64141145983295.358588540174
4511501223.30845689792-73.3084568979159
4611101218.67526744955-108.675267449546
4710801211.80684975598-131.806849755976
4812701203.4764860932666.5235139067404
4910501207.68085835457-157.680858354571
5014901197.71522382818292.284776171819
5112801216.1880003424163.8119996575879
5212301220.221001390369.77899860963771
539601220.83904677136-260.83904677136
5411001204.35368109374-104.353681093744
5512701197.7583932565572.2416067434465
5615301202.32415639304327.675843606963
5712901223.0336942189366.9663057810681
5811201227.26605150035-107.266051500346
5911001220.48669808043-120.48669808043
6013101212.8717826690797.1282173309323
6110201219.01041183573-199.010411835731
6215101206.43269598615303.567304013847
6312601225.6185428767234.3814571232824
6411601227.7914955087-67.7914955087035
659701223.50698516745-253.506985167455
6610201207.48501528202-187.485015282024
6712101195.63571942614.3642805740017
6815301196.54356056746333.456439432542
6913501217.6184395384132.381560461605
7010701225.98512566226-155.985125662256
7111401216.12666363887-76.1266636388718
7212501211.3153598734438.6846401265634
739301213.76027924608-283.760279246081
7415101195.8262619812314.173738018805
7512301215.682449241714.3175507583014
7611801216.58733699827-36.5873369982671
779601214.27496990043-254.274969900425
789601198.20446238493-238.204462384932
7912401183.1496317640556.8503682359503
8016401186.74264868723453.257351312766
8113501215.38910049323134.610899506768
8211001223.8966837329-123.896683732895
8311201216.0662528106-96.0662528105995
8412901209.9947411774280.0052588225847
858901215.05117718325-325.051177183251
8615601194.50752167564365.492478324363
8712501217.607119807832.3928801921995
8811701219.6543918015-49.654391801505
899001216.51616991149-316.516169911494
908601196.51193792071-336.511937920711
9113101175.24394748687134.756052513132
9216101183.76070458458426.239295415418
9314401210.69958025549229.300419744508
9411301225.19166384615-95.1916638461526
9512201219.175427368570.824572631432829
9614001219.22754142712180.772458572878
979301230.65259500289-300.652595002892
9814901211.65096149788278.349038502122
9912501229.2429813373920.7570186626144
10011601230.55485180795-70.5548518079529
1019101226.09569376861-316.095693768614
1028801206.11803641479-326.118036414794
10313001185.50695402161114.493045978388
10415501192.74306285524357.256937144759
10514601215.32216411556244.677835884438
10611201230.78612032799-110.786120327985
10712701223.7842939978546.2157060021502
10814101226.70518649046183.294813509538







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
1091238.28965616598893.5035484820151583.07576384995
1101238.28965616598892.81562729451583.76368503747
1111238.28965616598892.1290732026311584.45023912934
1121238.28965616598891.4438780882311585.13543424374
1131238.28965616598890.7600339131531585.81927841882
1141238.28965616598890.077532718181586.50177961379
1151238.28965616598889.3963666219431587.18294571003
1161238.28965616598888.716527819861587.86278451211
1171238.28965616598888.0380085830941588.54130374888
1181238.28965616598887.3608012575251589.21851107444
1191238.28965616598886.6848982627441589.89441406922
1201238.28965616598886.0102920910651590.5690202409

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
109 & 1238.28965616598 & 893.503548482015 & 1583.07576384995 \tabularnewline
110 & 1238.28965616598 & 892.8156272945 & 1583.76368503747 \tabularnewline
111 & 1238.28965616598 & 892.129073202631 & 1584.45023912934 \tabularnewline
112 & 1238.28965616598 & 891.443878088231 & 1585.13543424374 \tabularnewline
113 & 1238.28965616598 & 890.760033913153 & 1585.81927841882 \tabularnewline
114 & 1238.28965616598 & 890.07753271818 & 1586.50177961379 \tabularnewline
115 & 1238.28965616598 & 889.396366621943 & 1587.18294571003 \tabularnewline
116 & 1238.28965616598 & 888.71652781986 & 1587.86278451211 \tabularnewline
117 & 1238.28965616598 & 888.038008583094 & 1588.54130374888 \tabularnewline
118 & 1238.28965616598 & 887.360801257525 & 1589.21851107444 \tabularnewline
119 & 1238.28965616598 & 886.684898262744 & 1589.89441406922 \tabularnewline
120 & 1238.28965616598 & 886.010292091065 & 1590.5690202409 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=124019&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]109[/C][C]1238.28965616598[/C][C]893.503548482015[/C][C]1583.07576384995[/C][/ROW]
[ROW][C]110[/C][C]1238.28965616598[/C][C]892.8156272945[/C][C]1583.76368503747[/C][/ROW]
[ROW][C]111[/C][C]1238.28965616598[/C][C]892.129073202631[/C][C]1584.45023912934[/C][/ROW]
[ROW][C]112[/C][C]1238.28965616598[/C][C]891.443878088231[/C][C]1585.13543424374[/C][/ROW]
[ROW][C]113[/C][C]1238.28965616598[/C][C]890.760033913153[/C][C]1585.81927841882[/C][/ROW]
[ROW][C]114[/C][C]1238.28965616598[/C][C]890.07753271818[/C][C]1586.50177961379[/C][/ROW]
[ROW][C]115[/C][C]1238.28965616598[/C][C]889.396366621943[/C][C]1587.18294571003[/C][/ROW]
[ROW][C]116[/C][C]1238.28965616598[/C][C]888.71652781986[/C][C]1587.86278451211[/C][/ROW]
[ROW][C]117[/C][C]1238.28965616598[/C][C]888.038008583094[/C][C]1588.54130374888[/C][/ROW]
[ROW][C]118[/C][C]1238.28965616598[/C][C]887.360801257525[/C][C]1589.21851107444[/C][/ROW]
[ROW][C]119[/C][C]1238.28965616598[/C][C]886.684898262744[/C][C]1589.89441406922[/C][/ROW]
[ROW][C]120[/C][C]1238.28965616598[/C][C]886.010292091065[/C][C]1590.5690202409[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=124019&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=124019&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
1091238.28965616598893.5035484820151583.07576384995
1101238.28965616598892.81562729451583.76368503747
1111238.28965616598892.1290732026311584.45023912934
1121238.28965616598891.4438780882311585.13543424374
1131238.28965616598890.7600339131531585.81927841882
1141238.28965616598890.077532718181586.50177961379
1151238.28965616598889.3963666219431587.18294571003
1161238.28965616598888.716527819861587.86278451211
1171238.28965616598888.0380085830941588.54130374888
1181238.28965616598887.3608012575251589.21851107444
1191238.28965616598886.6848982627441589.89441406922
1201238.28965616598886.0102920910651590.5690202409



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