Free Statistics

of Irreproducible Research!

Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationSun, 10 Jan 2016 13:10:49 +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/2016/Jan/10/t14524314772i4ztdoyclv8u50.htm/, Retrieved Sun, 05 May 2024 06:57:20 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=287793, Retrieved Sun, 05 May 2024 06:57:20 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact84
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [] [2016-01-10 13:10:49] [6520bd704600aa2d143562671c58b650] [Current]
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Dataseries X:
13408
7820
9079
8307
7865
10028
9054
7143
8006
7638
7600
2904
13224
8079
9678
7746
9007
8362
7458
7753
7352
7117
6971
3304
11812
6867
8296
6489
7784
7506
6514
6323
6201
7169
6744
2087
10668
6406
7730
7105
7694
7160
6820
6025
5877
7191
5778
2273
11321
6759
7150
6363
6442
6453
6228
5325
6504
6817
5789
1894
11068
7174
8269
7060
6681
8953
7815
5925
6805
7044
7169
2824
10717
5245
6237
5871
5508
15801
1236
2656
3425
3533
4287
1380
8584
5522
6423
5173
5583
5716
4752
4977
4999
5285
5747
1713
9923
6737
7433
6388
6855
7658
6585
6847
6353
7361
6929
1714
11798
8378
8131
7676
7505
8168
6455
6141
6554
6888
5339
1624
9187
5047
5289
4169
3862
4253
3768
3066
4108
3890
3420
1221
5984
4064
5151
4027
3530
4819
3855
3584
4322
4154
4656
1464
7780
5060
6084
4778
4989
4903
4142
4101
4595
5034
5407
1782
8395
5291
6116
4210
4621
5299
4293
4542
3831
4360
4088
1508
6743
4159
5105
4283
4019
4206
3948
3407
3701
4159
4208
2622
6229
4432
4986
4226
4349
4688
4002
3381
4250
4154
4350
2713




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' @ fisher.wessa.net

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input & view raw input (R code)  \tabularnewline
Raw Output & view raw output of R engine  \tabularnewline
Computing time & 2 seconds \tabularnewline
R Server & 'Sir Ronald Aylmer Fisher' @ fisher.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=287793&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' @ fisher.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=287793&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=287793&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' @ fisher.wessa.net







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.212945813391554
beta0
gamma0.236336633395025

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.212945813391554 \tabularnewline
beta & 0 \tabularnewline
gamma & 0.236336633395025 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=287793&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]0.212945813391554[/C][/ROW]
[ROW][C]beta[/C][C]0[/C][/ROW]
[ROW][C]gamma[/C][C]0.236336633395025[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=287793&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=287793&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
alpha0.212945813391554
beta0
gamma0.236336633395025







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
131322413420.3755777516-196.375577751553
1480798187.27314871636-108.273148716361
1596789749.19350371554-71.1935037155381
1677467811.60144251367-65.6014425136718
1790079090.18181880171-83.1818188017132
1883628403.8575913329-41.8575913329023
1974588791.47354103298-1333.47354103298
2077536685.292479357281067.70752064272
2173527687.52318425832-335.523184258322
2271177239.03776731515-122.03776731515
2369717130.84988494446-159.84988494446
2433042709.16659744606594.833402553945
251181213048.575459756-1236.57545975596
2668677825.10460511335-958.104605113347
2782969108.58472226889-812.584722268894
2864897167.19596092476-678.19596092476
2977848182.68362815922-398.683628159222
3075067503.784420917842.215579082158
3165147633.56129562069-1119.56129562069
3263236155.08946041957167.910539580433
3362016634.23852494711-433.23852494711
3471696246.34985798921922.65014201079
3567446360.11340165248383.886598347523
3620872564.94755642917-477.947556429166
371066810704.7559527112-36.7559527112317
3864066507.01873860166-101.018738601659
3977307798.53332172598-68.5333217259758
4071056233.86085006303871.139149936967
4176947544.54108258573149.458917414267
4271607084.2778628161975.7221371838104
4368207017.42106622574-197.421066225737
4460256003.3405732338221.659426766184
4558776326.1147676685-449.1147676685
4671916182.623930725241008.37606927476
4757786218.71630506723-440.716305067225
4822732324.35824032477-51.3582403247688
491132110422.6270616133898.372938386683
5067596441.75066005765317.249339942351
5171507837.25352456817-687.253524568167
5263636324.9127397414738.0872602585287
5364427285.27972422976-843.279724229765
5464536631.12538069915-178.12538069915
5562286466.90881227331-238.908812273307
5653255553.01542129309-228.015421293086
5765045712.22642211872791.77357788128
5868176087.23091924116729.769080758844
5957895815.24594654156-26.2459465415604
6018942225.04468723847-331.04468723847
61110689897.674922470561170.32507752944
6271746116.213978114141057.78602188586
6382697439.70235390054829.297646099464
6470606376.7407819632683.259218036805
6566817329.98894665416-648.988946654159
6689536829.478872998522123.52112700148
6778157131.67838145877683.321618541232
6859256296.90131189095-371.901311890946
6968056669.01738988087135.982610119133
7070446913.79828395289130.20171604711
7171696325.57979100884843.420208991158
7228242423.39070654736400.609293452641
731071712127.2443172014-1410.24431720143
7452457199.64472264295-1954.64472264295
7562377876.24831125339-1639.24831125339
7658716296.52706162172-425.52706162172
7755086724.36244691746-1216.36244691746
78158016580.570043864529220.42995613548
7912368079.35515479728-6843.35515479728
8026565566.4525737409-2910.4525737409
8134255380.48434767729-1955.48434767729
8235335115.33258078274-1582.33258078274
8342874435.79196527868-148.791965278684
8413801646.3361752085-266.336175208504
8585847279.977880865831304.02211913417
8655224443.740140783681078.25985921632
8764235492.80387568449930.196124315508
8851734892.43471484972280.565285150285
8955835239.50092255356343.499077446445
9057166722.80316298578-1006.80316298578
9147524131.77384090693620.226159093067
9249773947.049056391751029.95094360825
9349994714.44600890012284.553991099879
9452854983.53246580788301.467534192119
9557474965.24282682646781.757173173542
9617131871.91844095071-158.918440950715
9799238976.39676907984946.603230920156
9867375457.900056412561279.09994358744
9974336659.90603279115773.09396720885
10063885758.3848954519629.615104548102
10168556248.6754267658606.324573234196
10276587751.9005397382-93.9005397381989
10365855196.01012932421388.9898706758
10468475183.204191128691663.79580887131
10563536063.64809054946289.351909450542
10673616399.90643273945961.093567260553
10769296615.0787310983313.921268901702
10817142334.57417766809-620.574177668088
1091179811151.4775876228646.522412377182
11083786866.427912633951511.57208736605
11181318197.16214204626-66.1621420462616
11276766901.45231723318774.547682766822
11375057482.6718934987122.328106501287
11481688927.71435174978-759.714351749775
11564556185.429397486269.570602514
11661415943.86158892613197.138411073868
11765546262.79468670919291.205313290809
11868886728.7858890733159.2141109267
11953396652.49211893906-1313.49211893906
12016242091.11201881862-467.112018818618
121918710753.1861040025-1566.18610400247
12250476513.47352768652-1466.47352768652
12352896789.5143744538-1500.5143744538
12441695570.39568917042-1401.39568917042
12538625466.07886894733-1604.07886894733
12642535997.40498076048-1744.40498076048
12737684058.44162402294-290.441624022943
12830663789.19380825669-723.193808256693
12941083802.52952584534305.470474154656
13038904086.89421886532-196.89421886532
13134203799.48051696199-379.48051696199
13212211210.2098986205610.7901013794419
13359846636.97873631144-652.978736311443
13440643984.7388795451279.2611204548762
13551514374.94410536376776.055894636242
13640273875.97264521481151.027354785189
13735304008.45959960498-478.459599604983
13848194568.4345772398250.565422760199
13938553487.10341457464367.896585425356
14035843297.71157329365286.288426706349
14143223700.8421565565621.157843443498
14241543955.0647478866198.935252113404
14346563717.14140195791938.858598042094
14414641302.21140125086161.788598749142
14577807172.50788564536607.492114354642
14650604583.99964817611476.000351823887
14760845271.34003251327812.65996748673
14847784541.44680211894236.553197881065
14949894574.09275193636414.907248063642
15049035643.08273867973-740.082738679734
15141424180.52706344152-38.5270634415174
15241013849.87696087091251.123039129092
15345954365.32697093715229.673029062847
15450344465.51475812421568.485241875794
15554074417.8469598699989.153040130095
15617821507.33495113395274.66504886605
15783958351.03578480843.9642151920034
15852915269.9308840838221.0691159161834
15961165989.20169815849126.798301841514
16042104931.70476970152-721.704769701519
16146214793.28525553991-172.285255539906
16252995521.28507541199-222.285075411985
16342934272.3731726334920.626827366511
16445424000.98393313364541.016066866363
16538314594.07162031075-763.071620310748
16643604542.29757737997-182.297577379974
16740884407.51083324533-319.510833245327
16815081402.66116989086105.33883010914
16967437362.05281983528-619.052819835277
17041594552.49458267975-393.494582679752
17151055085.2794182629419.7205817370641
17242834034.78511601216248.214883987835
17340194187.52447718582-168.524477185823
17442064811.21886812758-605.218868127577
17539483682.13672320121265.863276798792
17634073576.86522373897-169.865223738965
17737013729.73858350079-28.7385835007872
17841593909.62766760195249.37233239805
17942083851.1446722933356.855327706703
18026221303.961690900961318.03830909904
18162297950.99226645717-1721.99226645717
18244324775.13027180728-343.130271807276
18349865446.19406603574-460.194066035742
18442264286.04235498535-60.0423549853476
18543494297.0172439472451.9827560527574
18646884910.98617637265-222.986176372655
18740023972.3097116445329.6902883554708
18833813724.36467560706-343.364675607058
18942503876.30541693769373.694583062309
19041544209.92789893522-55.9278989352224
19143504102.0518150617247.948184938298
19227131566.954581609021146.04541839098

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 13224 & 13420.3755777516 & -196.375577751553 \tabularnewline
14 & 8079 & 8187.27314871636 & -108.273148716361 \tabularnewline
15 & 9678 & 9749.19350371554 & -71.1935037155381 \tabularnewline
16 & 7746 & 7811.60144251367 & -65.6014425136718 \tabularnewline
17 & 9007 & 9090.18181880171 & -83.1818188017132 \tabularnewline
18 & 8362 & 8403.8575913329 & -41.8575913329023 \tabularnewline
19 & 7458 & 8791.47354103298 & -1333.47354103298 \tabularnewline
20 & 7753 & 6685.29247935728 & 1067.70752064272 \tabularnewline
21 & 7352 & 7687.52318425832 & -335.523184258322 \tabularnewline
22 & 7117 & 7239.03776731515 & -122.03776731515 \tabularnewline
23 & 6971 & 7130.84988494446 & -159.84988494446 \tabularnewline
24 & 3304 & 2709.16659744606 & 594.833402553945 \tabularnewline
25 & 11812 & 13048.575459756 & -1236.57545975596 \tabularnewline
26 & 6867 & 7825.10460511335 & -958.104605113347 \tabularnewline
27 & 8296 & 9108.58472226889 & -812.584722268894 \tabularnewline
28 & 6489 & 7167.19596092476 & -678.19596092476 \tabularnewline
29 & 7784 & 8182.68362815922 & -398.683628159222 \tabularnewline
30 & 7506 & 7503.78442091784 & 2.215579082158 \tabularnewline
31 & 6514 & 7633.56129562069 & -1119.56129562069 \tabularnewline
32 & 6323 & 6155.08946041957 & 167.910539580433 \tabularnewline
33 & 6201 & 6634.23852494711 & -433.23852494711 \tabularnewline
34 & 7169 & 6246.34985798921 & 922.65014201079 \tabularnewline
35 & 6744 & 6360.11340165248 & 383.886598347523 \tabularnewline
36 & 2087 & 2564.94755642917 & -477.947556429166 \tabularnewline
37 & 10668 & 10704.7559527112 & -36.7559527112317 \tabularnewline
38 & 6406 & 6507.01873860166 & -101.018738601659 \tabularnewline
39 & 7730 & 7798.53332172598 & -68.5333217259758 \tabularnewline
40 & 7105 & 6233.86085006303 & 871.139149936967 \tabularnewline
41 & 7694 & 7544.54108258573 & 149.458917414267 \tabularnewline
42 & 7160 & 7084.27786281619 & 75.7221371838104 \tabularnewline
43 & 6820 & 7017.42106622574 & -197.421066225737 \tabularnewline
44 & 6025 & 6003.34057323382 & 21.659426766184 \tabularnewline
45 & 5877 & 6326.1147676685 & -449.1147676685 \tabularnewline
46 & 7191 & 6182.62393072524 & 1008.37606927476 \tabularnewline
47 & 5778 & 6218.71630506723 & -440.716305067225 \tabularnewline
48 & 2273 & 2324.35824032477 & -51.3582403247688 \tabularnewline
49 & 11321 & 10422.6270616133 & 898.372938386683 \tabularnewline
50 & 6759 & 6441.75066005765 & 317.249339942351 \tabularnewline
51 & 7150 & 7837.25352456817 & -687.253524568167 \tabularnewline
52 & 6363 & 6324.91273974147 & 38.0872602585287 \tabularnewline
53 & 6442 & 7285.27972422976 & -843.279724229765 \tabularnewline
54 & 6453 & 6631.12538069915 & -178.12538069915 \tabularnewline
55 & 6228 & 6466.90881227331 & -238.908812273307 \tabularnewline
56 & 5325 & 5553.01542129309 & -228.015421293086 \tabularnewline
57 & 6504 & 5712.22642211872 & 791.77357788128 \tabularnewline
58 & 6817 & 6087.23091924116 & 729.769080758844 \tabularnewline
59 & 5789 & 5815.24594654156 & -26.2459465415604 \tabularnewline
60 & 1894 & 2225.04468723847 & -331.04468723847 \tabularnewline
61 & 11068 & 9897.67492247056 & 1170.32507752944 \tabularnewline
62 & 7174 & 6116.21397811414 & 1057.78602188586 \tabularnewline
63 & 8269 & 7439.70235390054 & 829.297646099464 \tabularnewline
64 & 7060 & 6376.7407819632 & 683.259218036805 \tabularnewline
65 & 6681 & 7329.98894665416 & -648.988946654159 \tabularnewline
66 & 8953 & 6829.47887299852 & 2123.52112700148 \tabularnewline
67 & 7815 & 7131.67838145877 & 683.321618541232 \tabularnewline
68 & 5925 & 6296.90131189095 & -371.901311890946 \tabularnewline
69 & 6805 & 6669.01738988087 & 135.982610119133 \tabularnewline
70 & 7044 & 6913.79828395289 & 130.20171604711 \tabularnewline
71 & 7169 & 6325.57979100884 & 843.420208991158 \tabularnewline
72 & 2824 & 2423.39070654736 & 400.609293452641 \tabularnewline
73 & 10717 & 12127.2443172014 & -1410.24431720143 \tabularnewline
74 & 5245 & 7199.64472264295 & -1954.64472264295 \tabularnewline
75 & 6237 & 7876.24831125339 & -1639.24831125339 \tabularnewline
76 & 5871 & 6296.52706162172 & -425.52706162172 \tabularnewline
77 & 5508 & 6724.36244691746 & -1216.36244691746 \tabularnewline
78 & 15801 & 6580.57004386452 & 9220.42995613548 \tabularnewline
79 & 1236 & 8079.35515479728 & -6843.35515479728 \tabularnewline
80 & 2656 & 5566.4525737409 & -2910.4525737409 \tabularnewline
81 & 3425 & 5380.48434767729 & -1955.48434767729 \tabularnewline
82 & 3533 & 5115.33258078274 & -1582.33258078274 \tabularnewline
83 & 4287 & 4435.79196527868 & -148.791965278684 \tabularnewline
84 & 1380 & 1646.3361752085 & -266.336175208504 \tabularnewline
85 & 8584 & 7279.97788086583 & 1304.02211913417 \tabularnewline
86 & 5522 & 4443.74014078368 & 1078.25985921632 \tabularnewline
87 & 6423 & 5492.80387568449 & 930.196124315508 \tabularnewline
88 & 5173 & 4892.43471484972 & 280.565285150285 \tabularnewline
89 & 5583 & 5239.50092255356 & 343.499077446445 \tabularnewline
90 & 5716 & 6722.80316298578 & -1006.80316298578 \tabularnewline
91 & 4752 & 4131.77384090693 & 620.226159093067 \tabularnewline
92 & 4977 & 3947.04905639175 & 1029.95094360825 \tabularnewline
93 & 4999 & 4714.44600890012 & 284.553991099879 \tabularnewline
94 & 5285 & 4983.53246580788 & 301.467534192119 \tabularnewline
95 & 5747 & 4965.24282682646 & 781.757173173542 \tabularnewline
96 & 1713 & 1871.91844095071 & -158.918440950715 \tabularnewline
97 & 9923 & 8976.39676907984 & 946.603230920156 \tabularnewline
98 & 6737 & 5457.90005641256 & 1279.09994358744 \tabularnewline
99 & 7433 & 6659.90603279115 & 773.09396720885 \tabularnewline
100 & 6388 & 5758.3848954519 & 629.615104548102 \tabularnewline
101 & 6855 & 6248.6754267658 & 606.324573234196 \tabularnewline
102 & 7658 & 7751.9005397382 & -93.9005397381989 \tabularnewline
103 & 6585 & 5196.0101293242 & 1388.9898706758 \tabularnewline
104 & 6847 & 5183.20419112869 & 1663.79580887131 \tabularnewline
105 & 6353 & 6063.64809054946 & 289.351909450542 \tabularnewline
106 & 7361 & 6399.90643273945 & 961.093567260553 \tabularnewline
107 & 6929 & 6615.0787310983 & 313.921268901702 \tabularnewline
108 & 1714 & 2334.57417766809 & -620.574177668088 \tabularnewline
109 & 11798 & 11151.4775876228 & 646.522412377182 \tabularnewline
110 & 8378 & 6866.42791263395 & 1511.57208736605 \tabularnewline
111 & 8131 & 8197.16214204626 & -66.1621420462616 \tabularnewline
112 & 7676 & 6901.45231723318 & 774.547682766822 \tabularnewline
113 & 7505 & 7482.67189349871 & 22.328106501287 \tabularnewline
114 & 8168 & 8927.71435174978 & -759.714351749775 \tabularnewline
115 & 6455 & 6185.429397486 & 269.570602514 \tabularnewline
116 & 6141 & 5943.86158892613 & 197.138411073868 \tabularnewline
117 & 6554 & 6262.79468670919 & 291.205313290809 \tabularnewline
118 & 6888 & 6728.7858890733 & 159.2141109267 \tabularnewline
119 & 5339 & 6652.49211893906 & -1313.49211893906 \tabularnewline
120 & 1624 & 2091.11201881862 & -467.112018818618 \tabularnewline
121 & 9187 & 10753.1861040025 & -1566.18610400247 \tabularnewline
122 & 5047 & 6513.47352768652 & -1466.47352768652 \tabularnewline
123 & 5289 & 6789.5143744538 & -1500.5143744538 \tabularnewline
124 & 4169 & 5570.39568917042 & -1401.39568917042 \tabularnewline
125 & 3862 & 5466.07886894733 & -1604.07886894733 \tabularnewline
126 & 4253 & 5997.40498076048 & -1744.40498076048 \tabularnewline
127 & 3768 & 4058.44162402294 & -290.441624022943 \tabularnewline
128 & 3066 & 3789.19380825669 & -723.193808256693 \tabularnewline
129 & 4108 & 3802.52952584534 & 305.470474154656 \tabularnewline
130 & 3890 & 4086.89421886532 & -196.89421886532 \tabularnewline
131 & 3420 & 3799.48051696199 & -379.48051696199 \tabularnewline
132 & 1221 & 1210.20989862056 & 10.7901013794419 \tabularnewline
133 & 5984 & 6636.97873631144 & -652.978736311443 \tabularnewline
134 & 4064 & 3984.73887954512 & 79.2611204548762 \tabularnewline
135 & 5151 & 4374.94410536376 & 776.055894636242 \tabularnewline
136 & 4027 & 3875.97264521481 & 151.027354785189 \tabularnewline
137 & 3530 & 4008.45959960498 & -478.459599604983 \tabularnewline
138 & 4819 & 4568.4345772398 & 250.565422760199 \tabularnewline
139 & 3855 & 3487.10341457464 & 367.896585425356 \tabularnewline
140 & 3584 & 3297.71157329365 & 286.288426706349 \tabularnewline
141 & 4322 & 3700.8421565565 & 621.157843443498 \tabularnewline
142 & 4154 & 3955.0647478866 & 198.935252113404 \tabularnewline
143 & 4656 & 3717.14140195791 & 938.858598042094 \tabularnewline
144 & 1464 & 1302.21140125086 & 161.788598749142 \tabularnewline
145 & 7780 & 7172.50788564536 & 607.492114354642 \tabularnewline
146 & 5060 & 4583.99964817611 & 476.000351823887 \tabularnewline
147 & 6084 & 5271.34003251327 & 812.65996748673 \tabularnewline
148 & 4778 & 4541.44680211894 & 236.553197881065 \tabularnewline
149 & 4989 & 4574.09275193636 & 414.907248063642 \tabularnewline
150 & 4903 & 5643.08273867973 & -740.082738679734 \tabularnewline
151 & 4142 & 4180.52706344152 & -38.5270634415174 \tabularnewline
152 & 4101 & 3849.87696087091 & 251.123039129092 \tabularnewline
153 & 4595 & 4365.32697093715 & 229.673029062847 \tabularnewline
154 & 5034 & 4465.51475812421 & 568.485241875794 \tabularnewline
155 & 5407 & 4417.8469598699 & 989.153040130095 \tabularnewline
156 & 1782 & 1507.33495113395 & 274.66504886605 \tabularnewline
157 & 8395 & 8351.035784808 & 43.9642151920034 \tabularnewline
158 & 5291 & 5269.93088408382 & 21.0691159161834 \tabularnewline
159 & 6116 & 5989.20169815849 & 126.798301841514 \tabularnewline
160 & 4210 & 4931.70476970152 & -721.704769701519 \tabularnewline
161 & 4621 & 4793.28525553991 & -172.285255539906 \tabularnewline
162 & 5299 & 5521.28507541199 & -222.285075411985 \tabularnewline
163 & 4293 & 4272.37317263349 & 20.626827366511 \tabularnewline
164 & 4542 & 4000.98393313364 & 541.016066866363 \tabularnewline
165 & 3831 & 4594.07162031075 & -763.071620310748 \tabularnewline
166 & 4360 & 4542.29757737997 & -182.297577379974 \tabularnewline
167 & 4088 & 4407.51083324533 & -319.510833245327 \tabularnewline
168 & 1508 & 1402.66116989086 & 105.33883010914 \tabularnewline
169 & 6743 & 7362.05281983528 & -619.052819835277 \tabularnewline
170 & 4159 & 4552.49458267975 & -393.494582679752 \tabularnewline
171 & 5105 & 5085.27941826294 & 19.7205817370641 \tabularnewline
172 & 4283 & 4034.78511601216 & 248.214883987835 \tabularnewline
173 & 4019 & 4187.52447718582 & -168.524477185823 \tabularnewline
174 & 4206 & 4811.21886812758 & -605.218868127577 \tabularnewline
175 & 3948 & 3682.13672320121 & 265.863276798792 \tabularnewline
176 & 3407 & 3576.86522373897 & -169.865223738965 \tabularnewline
177 & 3701 & 3729.73858350079 & -28.7385835007872 \tabularnewline
178 & 4159 & 3909.62766760195 & 249.37233239805 \tabularnewline
179 & 4208 & 3851.1446722933 & 356.855327706703 \tabularnewline
180 & 2622 & 1303.96169090096 & 1318.03830909904 \tabularnewline
181 & 6229 & 7950.99226645717 & -1721.99226645717 \tabularnewline
182 & 4432 & 4775.13027180728 & -343.130271807276 \tabularnewline
183 & 4986 & 5446.19406603574 & -460.194066035742 \tabularnewline
184 & 4226 & 4286.04235498535 & -60.0423549853476 \tabularnewline
185 & 4349 & 4297.01724394724 & 51.9827560527574 \tabularnewline
186 & 4688 & 4910.98617637265 & -222.986176372655 \tabularnewline
187 & 4002 & 3972.30971164453 & 29.6902883554708 \tabularnewline
188 & 3381 & 3724.36467560706 & -343.364675607058 \tabularnewline
189 & 4250 & 3876.30541693769 & 373.694583062309 \tabularnewline
190 & 4154 & 4209.92789893522 & -55.9278989352224 \tabularnewline
191 & 4350 & 4102.0518150617 & 247.948184938298 \tabularnewline
192 & 2713 & 1566.95458160902 & 1146.04541839098 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=287793&T=2

[TABLE]
[ROW][C]Interpolation Forecasts of Exponential Smoothing[/C][/ROW]
[ROW][C]t[/C][C]Observed[/C][C]Fitted[/C][C]Residuals[/C][/ROW]
[ROW][C]13[/C][C]13224[/C][C]13420.3755777516[/C][C]-196.375577751553[/C][/ROW]
[ROW][C]14[/C][C]8079[/C][C]8187.27314871636[/C][C]-108.273148716361[/C][/ROW]
[ROW][C]15[/C][C]9678[/C][C]9749.19350371554[/C][C]-71.1935037155381[/C][/ROW]
[ROW][C]16[/C][C]7746[/C][C]7811.60144251367[/C][C]-65.6014425136718[/C][/ROW]
[ROW][C]17[/C][C]9007[/C][C]9090.18181880171[/C][C]-83.1818188017132[/C][/ROW]
[ROW][C]18[/C][C]8362[/C][C]8403.8575913329[/C][C]-41.8575913329023[/C][/ROW]
[ROW][C]19[/C][C]7458[/C][C]8791.47354103298[/C][C]-1333.47354103298[/C][/ROW]
[ROW][C]20[/C][C]7753[/C][C]6685.29247935728[/C][C]1067.70752064272[/C][/ROW]
[ROW][C]21[/C][C]7352[/C][C]7687.52318425832[/C][C]-335.523184258322[/C][/ROW]
[ROW][C]22[/C][C]7117[/C][C]7239.03776731515[/C][C]-122.03776731515[/C][/ROW]
[ROW][C]23[/C][C]6971[/C][C]7130.84988494446[/C][C]-159.84988494446[/C][/ROW]
[ROW][C]24[/C][C]3304[/C][C]2709.16659744606[/C][C]594.833402553945[/C][/ROW]
[ROW][C]25[/C][C]11812[/C][C]13048.575459756[/C][C]-1236.57545975596[/C][/ROW]
[ROW][C]26[/C][C]6867[/C][C]7825.10460511335[/C][C]-958.104605113347[/C][/ROW]
[ROW][C]27[/C][C]8296[/C][C]9108.58472226889[/C][C]-812.584722268894[/C][/ROW]
[ROW][C]28[/C][C]6489[/C][C]7167.19596092476[/C][C]-678.19596092476[/C][/ROW]
[ROW][C]29[/C][C]7784[/C][C]8182.68362815922[/C][C]-398.683628159222[/C][/ROW]
[ROW][C]30[/C][C]7506[/C][C]7503.78442091784[/C][C]2.215579082158[/C][/ROW]
[ROW][C]31[/C][C]6514[/C][C]7633.56129562069[/C][C]-1119.56129562069[/C][/ROW]
[ROW][C]32[/C][C]6323[/C][C]6155.08946041957[/C][C]167.910539580433[/C][/ROW]
[ROW][C]33[/C][C]6201[/C][C]6634.23852494711[/C][C]-433.23852494711[/C][/ROW]
[ROW][C]34[/C][C]7169[/C][C]6246.34985798921[/C][C]922.65014201079[/C][/ROW]
[ROW][C]35[/C][C]6744[/C][C]6360.11340165248[/C][C]383.886598347523[/C][/ROW]
[ROW][C]36[/C][C]2087[/C][C]2564.94755642917[/C][C]-477.947556429166[/C][/ROW]
[ROW][C]37[/C][C]10668[/C][C]10704.7559527112[/C][C]-36.7559527112317[/C][/ROW]
[ROW][C]38[/C][C]6406[/C][C]6507.01873860166[/C][C]-101.018738601659[/C][/ROW]
[ROW][C]39[/C][C]7730[/C][C]7798.53332172598[/C][C]-68.5333217259758[/C][/ROW]
[ROW][C]40[/C][C]7105[/C][C]6233.86085006303[/C][C]871.139149936967[/C][/ROW]
[ROW][C]41[/C][C]7694[/C][C]7544.54108258573[/C][C]149.458917414267[/C][/ROW]
[ROW][C]42[/C][C]7160[/C][C]7084.27786281619[/C][C]75.7221371838104[/C][/ROW]
[ROW][C]43[/C][C]6820[/C][C]7017.42106622574[/C][C]-197.421066225737[/C][/ROW]
[ROW][C]44[/C][C]6025[/C][C]6003.34057323382[/C][C]21.659426766184[/C][/ROW]
[ROW][C]45[/C][C]5877[/C][C]6326.1147676685[/C][C]-449.1147676685[/C][/ROW]
[ROW][C]46[/C][C]7191[/C][C]6182.62393072524[/C][C]1008.37606927476[/C][/ROW]
[ROW][C]47[/C][C]5778[/C][C]6218.71630506723[/C][C]-440.716305067225[/C][/ROW]
[ROW][C]48[/C][C]2273[/C][C]2324.35824032477[/C][C]-51.3582403247688[/C][/ROW]
[ROW][C]49[/C][C]11321[/C][C]10422.6270616133[/C][C]898.372938386683[/C][/ROW]
[ROW][C]50[/C][C]6759[/C][C]6441.75066005765[/C][C]317.249339942351[/C][/ROW]
[ROW][C]51[/C][C]7150[/C][C]7837.25352456817[/C][C]-687.253524568167[/C][/ROW]
[ROW][C]52[/C][C]6363[/C][C]6324.91273974147[/C][C]38.0872602585287[/C][/ROW]
[ROW][C]53[/C][C]6442[/C][C]7285.27972422976[/C][C]-843.279724229765[/C][/ROW]
[ROW][C]54[/C][C]6453[/C][C]6631.12538069915[/C][C]-178.12538069915[/C][/ROW]
[ROW][C]55[/C][C]6228[/C][C]6466.90881227331[/C][C]-238.908812273307[/C][/ROW]
[ROW][C]56[/C][C]5325[/C][C]5553.01542129309[/C][C]-228.015421293086[/C][/ROW]
[ROW][C]57[/C][C]6504[/C][C]5712.22642211872[/C][C]791.77357788128[/C][/ROW]
[ROW][C]58[/C][C]6817[/C][C]6087.23091924116[/C][C]729.769080758844[/C][/ROW]
[ROW][C]59[/C][C]5789[/C][C]5815.24594654156[/C][C]-26.2459465415604[/C][/ROW]
[ROW][C]60[/C][C]1894[/C][C]2225.04468723847[/C][C]-331.04468723847[/C][/ROW]
[ROW][C]61[/C][C]11068[/C][C]9897.67492247056[/C][C]1170.32507752944[/C][/ROW]
[ROW][C]62[/C][C]7174[/C][C]6116.21397811414[/C][C]1057.78602188586[/C][/ROW]
[ROW][C]63[/C][C]8269[/C][C]7439.70235390054[/C][C]829.297646099464[/C][/ROW]
[ROW][C]64[/C][C]7060[/C][C]6376.7407819632[/C][C]683.259218036805[/C][/ROW]
[ROW][C]65[/C][C]6681[/C][C]7329.98894665416[/C][C]-648.988946654159[/C][/ROW]
[ROW][C]66[/C][C]8953[/C][C]6829.47887299852[/C][C]2123.52112700148[/C][/ROW]
[ROW][C]67[/C][C]7815[/C][C]7131.67838145877[/C][C]683.321618541232[/C][/ROW]
[ROW][C]68[/C][C]5925[/C][C]6296.90131189095[/C][C]-371.901311890946[/C][/ROW]
[ROW][C]69[/C][C]6805[/C][C]6669.01738988087[/C][C]135.982610119133[/C][/ROW]
[ROW][C]70[/C][C]7044[/C][C]6913.79828395289[/C][C]130.20171604711[/C][/ROW]
[ROW][C]71[/C][C]7169[/C][C]6325.57979100884[/C][C]843.420208991158[/C][/ROW]
[ROW][C]72[/C][C]2824[/C][C]2423.39070654736[/C][C]400.609293452641[/C][/ROW]
[ROW][C]73[/C][C]10717[/C][C]12127.2443172014[/C][C]-1410.24431720143[/C][/ROW]
[ROW][C]74[/C][C]5245[/C][C]7199.64472264295[/C][C]-1954.64472264295[/C][/ROW]
[ROW][C]75[/C][C]6237[/C][C]7876.24831125339[/C][C]-1639.24831125339[/C][/ROW]
[ROW][C]76[/C][C]5871[/C][C]6296.52706162172[/C][C]-425.52706162172[/C][/ROW]
[ROW][C]77[/C][C]5508[/C][C]6724.36244691746[/C][C]-1216.36244691746[/C][/ROW]
[ROW][C]78[/C][C]15801[/C][C]6580.57004386452[/C][C]9220.42995613548[/C][/ROW]
[ROW][C]79[/C][C]1236[/C][C]8079.35515479728[/C][C]-6843.35515479728[/C][/ROW]
[ROW][C]80[/C][C]2656[/C][C]5566.4525737409[/C][C]-2910.4525737409[/C][/ROW]
[ROW][C]81[/C][C]3425[/C][C]5380.48434767729[/C][C]-1955.48434767729[/C][/ROW]
[ROW][C]82[/C][C]3533[/C][C]5115.33258078274[/C][C]-1582.33258078274[/C][/ROW]
[ROW][C]83[/C][C]4287[/C][C]4435.79196527868[/C][C]-148.791965278684[/C][/ROW]
[ROW][C]84[/C][C]1380[/C][C]1646.3361752085[/C][C]-266.336175208504[/C][/ROW]
[ROW][C]85[/C][C]8584[/C][C]7279.97788086583[/C][C]1304.02211913417[/C][/ROW]
[ROW][C]86[/C][C]5522[/C][C]4443.74014078368[/C][C]1078.25985921632[/C][/ROW]
[ROW][C]87[/C][C]6423[/C][C]5492.80387568449[/C][C]930.196124315508[/C][/ROW]
[ROW][C]88[/C][C]5173[/C][C]4892.43471484972[/C][C]280.565285150285[/C][/ROW]
[ROW][C]89[/C][C]5583[/C][C]5239.50092255356[/C][C]343.499077446445[/C][/ROW]
[ROW][C]90[/C][C]5716[/C][C]6722.80316298578[/C][C]-1006.80316298578[/C][/ROW]
[ROW][C]91[/C][C]4752[/C][C]4131.77384090693[/C][C]620.226159093067[/C][/ROW]
[ROW][C]92[/C][C]4977[/C][C]3947.04905639175[/C][C]1029.95094360825[/C][/ROW]
[ROW][C]93[/C][C]4999[/C][C]4714.44600890012[/C][C]284.553991099879[/C][/ROW]
[ROW][C]94[/C][C]5285[/C][C]4983.53246580788[/C][C]301.467534192119[/C][/ROW]
[ROW][C]95[/C][C]5747[/C][C]4965.24282682646[/C][C]781.757173173542[/C][/ROW]
[ROW][C]96[/C][C]1713[/C][C]1871.91844095071[/C][C]-158.918440950715[/C][/ROW]
[ROW][C]97[/C][C]9923[/C][C]8976.39676907984[/C][C]946.603230920156[/C][/ROW]
[ROW][C]98[/C][C]6737[/C][C]5457.90005641256[/C][C]1279.09994358744[/C][/ROW]
[ROW][C]99[/C][C]7433[/C][C]6659.90603279115[/C][C]773.09396720885[/C][/ROW]
[ROW][C]100[/C][C]6388[/C][C]5758.3848954519[/C][C]629.615104548102[/C][/ROW]
[ROW][C]101[/C][C]6855[/C][C]6248.6754267658[/C][C]606.324573234196[/C][/ROW]
[ROW][C]102[/C][C]7658[/C][C]7751.9005397382[/C][C]-93.9005397381989[/C][/ROW]
[ROW][C]103[/C][C]6585[/C][C]5196.0101293242[/C][C]1388.9898706758[/C][/ROW]
[ROW][C]104[/C][C]6847[/C][C]5183.20419112869[/C][C]1663.79580887131[/C][/ROW]
[ROW][C]105[/C][C]6353[/C][C]6063.64809054946[/C][C]289.351909450542[/C][/ROW]
[ROW][C]106[/C][C]7361[/C][C]6399.90643273945[/C][C]961.093567260553[/C][/ROW]
[ROW][C]107[/C][C]6929[/C][C]6615.0787310983[/C][C]313.921268901702[/C][/ROW]
[ROW][C]108[/C][C]1714[/C][C]2334.57417766809[/C][C]-620.574177668088[/C][/ROW]
[ROW][C]109[/C][C]11798[/C][C]11151.4775876228[/C][C]646.522412377182[/C][/ROW]
[ROW][C]110[/C][C]8378[/C][C]6866.42791263395[/C][C]1511.57208736605[/C][/ROW]
[ROW][C]111[/C][C]8131[/C][C]8197.16214204626[/C][C]-66.1621420462616[/C][/ROW]
[ROW][C]112[/C][C]7676[/C][C]6901.45231723318[/C][C]774.547682766822[/C][/ROW]
[ROW][C]113[/C][C]7505[/C][C]7482.67189349871[/C][C]22.328106501287[/C][/ROW]
[ROW][C]114[/C][C]8168[/C][C]8927.71435174978[/C][C]-759.714351749775[/C][/ROW]
[ROW][C]115[/C][C]6455[/C][C]6185.429397486[/C][C]269.570602514[/C][/ROW]
[ROW][C]116[/C][C]6141[/C][C]5943.86158892613[/C][C]197.138411073868[/C][/ROW]
[ROW][C]117[/C][C]6554[/C][C]6262.79468670919[/C][C]291.205313290809[/C][/ROW]
[ROW][C]118[/C][C]6888[/C][C]6728.7858890733[/C][C]159.2141109267[/C][/ROW]
[ROW][C]119[/C][C]5339[/C][C]6652.49211893906[/C][C]-1313.49211893906[/C][/ROW]
[ROW][C]120[/C][C]1624[/C][C]2091.11201881862[/C][C]-467.112018818618[/C][/ROW]
[ROW][C]121[/C][C]9187[/C][C]10753.1861040025[/C][C]-1566.18610400247[/C][/ROW]
[ROW][C]122[/C][C]5047[/C][C]6513.47352768652[/C][C]-1466.47352768652[/C][/ROW]
[ROW][C]123[/C][C]5289[/C][C]6789.5143744538[/C][C]-1500.5143744538[/C][/ROW]
[ROW][C]124[/C][C]4169[/C][C]5570.39568917042[/C][C]-1401.39568917042[/C][/ROW]
[ROW][C]125[/C][C]3862[/C][C]5466.07886894733[/C][C]-1604.07886894733[/C][/ROW]
[ROW][C]126[/C][C]4253[/C][C]5997.40498076048[/C][C]-1744.40498076048[/C][/ROW]
[ROW][C]127[/C][C]3768[/C][C]4058.44162402294[/C][C]-290.441624022943[/C][/ROW]
[ROW][C]128[/C][C]3066[/C][C]3789.19380825669[/C][C]-723.193808256693[/C][/ROW]
[ROW][C]129[/C][C]4108[/C][C]3802.52952584534[/C][C]305.470474154656[/C][/ROW]
[ROW][C]130[/C][C]3890[/C][C]4086.89421886532[/C][C]-196.89421886532[/C][/ROW]
[ROW][C]131[/C][C]3420[/C][C]3799.48051696199[/C][C]-379.48051696199[/C][/ROW]
[ROW][C]132[/C][C]1221[/C][C]1210.20989862056[/C][C]10.7901013794419[/C][/ROW]
[ROW][C]133[/C][C]5984[/C][C]6636.97873631144[/C][C]-652.978736311443[/C][/ROW]
[ROW][C]134[/C][C]4064[/C][C]3984.73887954512[/C][C]79.2611204548762[/C][/ROW]
[ROW][C]135[/C][C]5151[/C][C]4374.94410536376[/C][C]776.055894636242[/C][/ROW]
[ROW][C]136[/C][C]4027[/C][C]3875.97264521481[/C][C]151.027354785189[/C][/ROW]
[ROW][C]137[/C][C]3530[/C][C]4008.45959960498[/C][C]-478.459599604983[/C][/ROW]
[ROW][C]138[/C][C]4819[/C][C]4568.4345772398[/C][C]250.565422760199[/C][/ROW]
[ROW][C]139[/C][C]3855[/C][C]3487.10341457464[/C][C]367.896585425356[/C][/ROW]
[ROW][C]140[/C][C]3584[/C][C]3297.71157329365[/C][C]286.288426706349[/C][/ROW]
[ROW][C]141[/C][C]4322[/C][C]3700.8421565565[/C][C]621.157843443498[/C][/ROW]
[ROW][C]142[/C][C]4154[/C][C]3955.0647478866[/C][C]198.935252113404[/C][/ROW]
[ROW][C]143[/C][C]4656[/C][C]3717.14140195791[/C][C]938.858598042094[/C][/ROW]
[ROW][C]144[/C][C]1464[/C][C]1302.21140125086[/C][C]161.788598749142[/C][/ROW]
[ROW][C]145[/C][C]7780[/C][C]7172.50788564536[/C][C]607.492114354642[/C][/ROW]
[ROW][C]146[/C][C]5060[/C][C]4583.99964817611[/C][C]476.000351823887[/C][/ROW]
[ROW][C]147[/C][C]6084[/C][C]5271.34003251327[/C][C]812.65996748673[/C][/ROW]
[ROW][C]148[/C][C]4778[/C][C]4541.44680211894[/C][C]236.553197881065[/C][/ROW]
[ROW][C]149[/C][C]4989[/C][C]4574.09275193636[/C][C]414.907248063642[/C][/ROW]
[ROW][C]150[/C][C]4903[/C][C]5643.08273867973[/C][C]-740.082738679734[/C][/ROW]
[ROW][C]151[/C][C]4142[/C][C]4180.52706344152[/C][C]-38.5270634415174[/C][/ROW]
[ROW][C]152[/C][C]4101[/C][C]3849.87696087091[/C][C]251.123039129092[/C][/ROW]
[ROW][C]153[/C][C]4595[/C][C]4365.32697093715[/C][C]229.673029062847[/C][/ROW]
[ROW][C]154[/C][C]5034[/C][C]4465.51475812421[/C][C]568.485241875794[/C][/ROW]
[ROW][C]155[/C][C]5407[/C][C]4417.8469598699[/C][C]989.153040130095[/C][/ROW]
[ROW][C]156[/C][C]1782[/C][C]1507.33495113395[/C][C]274.66504886605[/C][/ROW]
[ROW][C]157[/C][C]8395[/C][C]8351.035784808[/C][C]43.9642151920034[/C][/ROW]
[ROW][C]158[/C][C]5291[/C][C]5269.93088408382[/C][C]21.0691159161834[/C][/ROW]
[ROW][C]159[/C][C]6116[/C][C]5989.20169815849[/C][C]126.798301841514[/C][/ROW]
[ROW][C]160[/C][C]4210[/C][C]4931.70476970152[/C][C]-721.704769701519[/C][/ROW]
[ROW][C]161[/C][C]4621[/C][C]4793.28525553991[/C][C]-172.285255539906[/C][/ROW]
[ROW][C]162[/C][C]5299[/C][C]5521.28507541199[/C][C]-222.285075411985[/C][/ROW]
[ROW][C]163[/C][C]4293[/C][C]4272.37317263349[/C][C]20.626827366511[/C][/ROW]
[ROW][C]164[/C][C]4542[/C][C]4000.98393313364[/C][C]541.016066866363[/C][/ROW]
[ROW][C]165[/C][C]3831[/C][C]4594.07162031075[/C][C]-763.071620310748[/C][/ROW]
[ROW][C]166[/C][C]4360[/C][C]4542.29757737997[/C][C]-182.297577379974[/C][/ROW]
[ROW][C]167[/C][C]4088[/C][C]4407.51083324533[/C][C]-319.510833245327[/C][/ROW]
[ROW][C]168[/C][C]1508[/C][C]1402.66116989086[/C][C]105.33883010914[/C][/ROW]
[ROW][C]169[/C][C]6743[/C][C]7362.05281983528[/C][C]-619.052819835277[/C][/ROW]
[ROW][C]170[/C][C]4159[/C][C]4552.49458267975[/C][C]-393.494582679752[/C][/ROW]
[ROW][C]171[/C][C]5105[/C][C]5085.27941826294[/C][C]19.7205817370641[/C][/ROW]
[ROW][C]172[/C][C]4283[/C][C]4034.78511601216[/C][C]248.214883987835[/C][/ROW]
[ROW][C]173[/C][C]4019[/C][C]4187.52447718582[/C][C]-168.524477185823[/C][/ROW]
[ROW][C]174[/C][C]4206[/C][C]4811.21886812758[/C][C]-605.218868127577[/C][/ROW]
[ROW][C]175[/C][C]3948[/C][C]3682.13672320121[/C][C]265.863276798792[/C][/ROW]
[ROW][C]176[/C][C]3407[/C][C]3576.86522373897[/C][C]-169.865223738965[/C][/ROW]
[ROW][C]177[/C][C]3701[/C][C]3729.73858350079[/C][C]-28.7385835007872[/C][/ROW]
[ROW][C]178[/C][C]4159[/C][C]3909.62766760195[/C][C]249.37233239805[/C][/ROW]
[ROW][C]179[/C][C]4208[/C][C]3851.1446722933[/C][C]356.855327706703[/C][/ROW]
[ROW][C]180[/C][C]2622[/C][C]1303.96169090096[/C][C]1318.03830909904[/C][/ROW]
[ROW][C]181[/C][C]6229[/C][C]7950.99226645717[/C][C]-1721.99226645717[/C][/ROW]
[ROW][C]182[/C][C]4432[/C][C]4775.13027180728[/C][C]-343.130271807276[/C][/ROW]
[ROW][C]183[/C][C]4986[/C][C]5446.19406603574[/C][C]-460.194066035742[/C][/ROW]
[ROW][C]184[/C][C]4226[/C][C]4286.04235498535[/C][C]-60.0423549853476[/C][/ROW]
[ROW][C]185[/C][C]4349[/C][C]4297.01724394724[/C][C]51.9827560527574[/C][/ROW]
[ROW][C]186[/C][C]4688[/C][C]4910.98617637265[/C][C]-222.986176372655[/C][/ROW]
[ROW][C]187[/C][C]4002[/C][C]3972.30971164453[/C][C]29.6902883554708[/C][/ROW]
[ROW][C]188[/C][C]3381[/C][C]3724.36467560706[/C][C]-343.364675607058[/C][/ROW]
[ROW][C]189[/C][C]4250[/C][C]3876.30541693769[/C][C]373.694583062309[/C][/ROW]
[ROW][C]190[/C][C]4154[/C][C]4209.92789893522[/C][C]-55.9278989352224[/C][/ROW]
[ROW][C]191[/C][C]4350[/C][C]4102.0518150617[/C][C]247.948184938298[/C][/ROW]
[ROW][C]192[/C][C]2713[/C][C]1566.95458160902[/C][C]1146.04541839098[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=287793&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=287793&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
131322413420.3755777516-196.375577751553
1480798187.27314871636-108.273148716361
1596789749.19350371554-71.1935037155381
1677467811.60144251367-65.6014425136718
1790079090.18181880171-83.1818188017132
1883628403.8575913329-41.8575913329023
1974588791.47354103298-1333.47354103298
2077536685.292479357281067.70752064272
2173527687.52318425832-335.523184258322
2271177239.03776731515-122.03776731515
2369717130.84988494446-159.84988494446
2433042709.16659744606594.833402553945
251181213048.575459756-1236.57545975596
2668677825.10460511335-958.104605113347
2782969108.58472226889-812.584722268894
2864897167.19596092476-678.19596092476
2977848182.68362815922-398.683628159222
3075067503.784420917842.215579082158
3165147633.56129562069-1119.56129562069
3263236155.08946041957167.910539580433
3362016634.23852494711-433.23852494711
3471696246.34985798921922.65014201079
3567446360.11340165248383.886598347523
3620872564.94755642917-477.947556429166
371066810704.7559527112-36.7559527112317
3864066507.01873860166-101.018738601659
3977307798.53332172598-68.5333217259758
4071056233.86085006303871.139149936967
4176947544.54108258573149.458917414267
4271607084.2778628161975.7221371838104
4368207017.42106622574-197.421066225737
4460256003.3405732338221.659426766184
4558776326.1147676685-449.1147676685
4671916182.623930725241008.37606927476
4757786218.71630506723-440.716305067225
4822732324.35824032477-51.3582403247688
491132110422.6270616133898.372938386683
5067596441.75066005765317.249339942351
5171507837.25352456817-687.253524568167
5263636324.9127397414738.0872602585287
5364427285.27972422976-843.279724229765
5464536631.12538069915-178.12538069915
5562286466.90881227331-238.908812273307
5653255553.01542129309-228.015421293086
5765045712.22642211872791.77357788128
5868176087.23091924116729.769080758844
5957895815.24594654156-26.2459465415604
6018942225.04468723847-331.04468723847
61110689897.674922470561170.32507752944
6271746116.213978114141057.78602188586
6382697439.70235390054829.297646099464
6470606376.7407819632683.259218036805
6566817329.98894665416-648.988946654159
6689536829.478872998522123.52112700148
6778157131.67838145877683.321618541232
6859256296.90131189095-371.901311890946
6968056669.01738988087135.982610119133
7070446913.79828395289130.20171604711
7171696325.57979100884843.420208991158
7228242423.39070654736400.609293452641
731071712127.2443172014-1410.24431720143
7452457199.64472264295-1954.64472264295
7562377876.24831125339-1639.24831125339
7658716296.52706162172-425.52706162172
7755086724.36244691746-1216.36244691746
78158016580.570043864529220.42995613548
7912368079.35515479728-6843.35515479728
8026565566.4525737409-2910.4525737409
8134255380.48434767729-1955.48434767729
8235335115.33258078274-1582.33258078274
8342874435.79196527868-148.791965278684
8413801646.3361752085-266.336175208504
8585847279.977880865831304.02211913417
8655224443.740140783681078.25985921632
8764235492.80387568449930.196124315508
8851734892.43471484972280.565285150285
8955835239.50092255356343.499077446445
9057166722.80316298578-1006.80316298578
9147524131.77384090693620.226159093067
9249773947.049056391751029.95094360825
9349994714.44600890012284.553991099879
9452854983.53246580788301.467534192119
9557474965.24282682646781.757173173542
9617131871.91844095071-158.918440950715
9799238976.39676907984946.603230920156
9867375457.900056412561279.09994358744
9974336659.90603279115773.09396720885
10063885758.3848954519629.615104548102
10168556248.6754267658606.324573234196
10276587751.9005397382-93.9005397381989
10365855196.01012932421388.9898706758
10468475183.204191128691663.79580887131
10563536063.64809054946289.351909450542
10673616399.90643273945961.093567260553
10769296615.0787310983313.921268901702
10817142334.57417766809-620.574177668088
1091179811151.4775876228646.522412377182
11083786866.427912633951511.57208736605
11181318197.16214204626-66.1621420462616
11276766901.45231723318774.547682766822
11375057482.6718934987122.328106501287
11481688927.71435174978-759.714351749775
11564556185.429397486269.570602514
11661415943.86158892613197.138411073868
11765546262.79468670919291.205313290809
11868886728.7858890733159.2141109267
11953396652.49211893906-1313.49211893906
12016242091.11201881862-467.112018818618
121918710753.1861040025-1566.18610400247
12250476513.47352768652-1466.47352768652
12352896789.5143744538-1500.5143744538
12441695570.39568917042-1401.39568917042
12538625466.07886894733-1604.07886894733
12642535997.40498076048-1744.40498076048
12737684058.44162402294-290.441624022943
12830663789.19380825669-723.193808256693
12941083802.52952584534305.470474154656
13038904086.89421886532-196.89421886532
13134203799.48051696199-379.48051696199
13212211210.2098986205610.7901013794419
13359846636.97873631144-652.978736311443
13440643984.7388795451279.2611204548762
13551514374.94410536376776.055894636242
13640273875.97264521481151.027354785189
13735304008.45959960498-478.459599604983
13848194568.4345772398250.565422760199
13938553487.10341457464367.896585425356
14035843297.71157329365286.288426706349
14143223700.8421565565621.157843443498
14241543955.0647478866198.935252113404
14346563717.14140195791938.858598042094
14414641302.21140125086161.788598749142
14577807172.50788564536607.492114354642
14650604583.99964817611476.000351823887
14760845271.34003251327812.65996748673
14847784541.44680211894236.553197881065
14949894574.09275193636414.907248063642
15049035643.08273867973-740.082738679734
15141424180.52706344152-38.5270634415174
15241013849.87696087091251.123039129092
15345954365.32697093715229.673029062847
15450344465.51475812421568.485241875794
15554074417.8469598699989.153040130095
15617821507.33495113395274.66504886605
15783958351.03578480843.9642151920034
15852915269.9308840838221.0691159161834
15961165989.20169815849126.798301841514
16042104931.70476970152-721.704769701519
16146214793.28525553991-172.285255539906
16252995521.28507541199-222.285075411985
16342934272.3731726334920.626827366511
16445424000.98393313364541.016066866363
16538314594.07162031075-763.071620310748
16643604542.29757737997-182.297577379974
16740884407.51083324533-319.510833245327
16815081402.66116989086105.33883010914
16967437362.05281983528-619.052819835277
17041594552.49458267975-393.494582679752
17151055085.2794182629419.7205817370641
17242834034.78511601216248.214883987835
17340194187.52447718582-168.524477185823
17442064811.21886812758-605.218868127577
17539483682.13672320121265.863276798792
17634073576.86522373897-169.865223738965
17737013729.73858350079-28.7385835007872
17841593909.62766760195249.37233239805
17942083851.1446722933356.855327706703
18026221303.961690900961318.03830909904
18162297950.99226645717-1721.99226645717
18244324775.13027180728-343.130271807276
18349865446.19406603574-460.194066035742
18442264286.04235498535-60.0423549853476
18543494297.0172439472451.9827560527574
18646884910.98617637265-222.986176372655
18740023972.3097116445329.6902883554708
18833813724.36467560706-343.364675607058
18942503876.30541693769373.694583062309
19041544209.92789893522-55.9278989352224
19143504102.0518150617247.948184938298
19227131566.954581609021146.04541839098







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
1937536.510396045886636.030528399038436.99026369274
1944888.087544974233934.582141048955841.5929488995
1955649.47627533554528.802288857356770.15026181364
1964591.082817627183467.432887267045714.73274798731
1974641.208991189783409.607241644965872.8107407346
1985236.185291433653815.736454148626656.63412871868
1994321.690647654962979.291196517765664.09009879216
2003971.242705539042609.150697708895333.3347133692
2014369.310815303742828.688466826125909.93316378136
2024560.654639479612890.660272384126230.6490065751
2034519.52052879332785.501583881796253.5394737048
2041885.086299194831231.165742060272539.0068563294

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
193 & 7536.51039604588 & 6636.03052839903 & 8436.99026369274 \tabularnewline
194 & 4888.08754497423 & 3934.58214104895 & 5841.5929488995 \tabularnewline
195 & 5649.4762753355 & 4528.80228885735 & 6770.15026181364 \tabularnewline
196 & 4591.08281762718 & 3467.43288726704 & 5714.73274798731 \tabularnewline
197 & 4641.20899118978 & 3409.60724164496 & 5872.8107407346 \tabularnewline
198 & 5236.18529143365 & 3815.73645414862 & 6656.63412871868 \tabularnewline
199 & 4321.69064765496 & 2979.29119651776 & 5664.09009879216 \tabularnewline
200 & 3971.24270553904 & 2609.15069770889 & 5333.3347133692 \tabularnewline
201 & 4369.31081530374 & 2828.68846682612 & 5909.93316378136 \tabularnewline
202 & 4560.65463947961 & 2890.66027238412 & 6230.6490065751 \tabularnewline
203 & 4519.5205287933 & 2785.50158388179 & 6253.5394737048 \tabularnewline
204 & 1885.08629919483 & 1231.16574206027 & 2539.0068563294 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=287793&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]193[/C][C]7536.51039604588[/C][C]6636.03052839903[/C][C]8436.99026369274[/C][/ROW]
[ROW][C]194[/C][C]4888.08754497423[/C][C]3934.58214104895[/C][C]5841.5929488995[/C][/ROW]
[ROW][C]195[/C][C]5649.4762753355[/C][C]4528.80228885735[/C][C]6770.15026181364[/C][/ROW]
[ROW][C]196[/C][C]4591.08281762718[/C][C]3467.43288726704[/C][C]5714.73274798731[/C][/ROW]
[ROW][C]197[/C][C]4641.20899118978[/C][C]3409.60724164496[/C][C]5872.8107407346[/C][/ROW]
[ROW][C]198[/C][C]5236.18529143365[/C][C]3815.73645414862[/C][C]6656.63412871868[/C][/ROW]
[ROW][C]199[/C][C]4321.69064765496[/C][C]2979.29119651776[/C][C]5664.09009879216[/C][/ROW]
[ROW][C]200[/C][C]3971.24270553904[/C][C]2609.15069770889[/C][C]5333.3347133692[/C][/ROW]
[ROW][C]201[/C][C]4369.31081530374[/C][C]2828.68846682612[/C][C]5909.93316378136[/C][/ROW]
[ROW][C]202[/C][C]4560.65463947961[/C][C]2890.66027238412[/C][C]6230.6490065751[/C][/ROW]
[ROW][C]203[/C][C]4519.5205287933[/C][C]2785.50158388179[/C][C]6253.5394737048[/C][/ROW]
[ROW][C]204[/C][C]1885.08629919483[/C][C]1231.16574206027[/C][C]2539.0068563294[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=287793&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=287793&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
1937536.510396045886636.030528399038436.99026369274
1944888.087544974233934.582141048955841.5929488995
1955649.47627533554528.802288857356770.15026181364
1964591.082817627183467.432887267045714.73274798731
1974641.208991189783409.607241644965872.8107407346
1985236.185291433653815.736454148626656.63412871868
1994321.690647654962979.291196517765664.09009879216
2003971.242705539042609.150697708895333.3347133692
2014369.310815303742828.688466826125909.93316378136
2024560.654639479612890.660272384126230.6490065751
2034519.52052879332785.501583881796253.5394737048
2041885.086299194831231.165742060272539.0068563294



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