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Author's title

Author*The author of this computation has been verified*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationFri, 23 Dec 2011 04:43:39 -0500
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/Dec/23/t13246334424h83uw524cloiqt.htm/, Retrieved Mon, 29 Apr 2024 18:17:42 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=160221, Retrieved Mon, 29 Apr 2024 18:17:42 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact78
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [] [2011-12-23 09:43:39] [1118fb1265e4c78f2f623b6bb1012fba] [Current]
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Dataseries X:
1954
2302
3054
2414
2226
2725
2589
3470
2400
3180
4009
3924
2072
2434
2956
2828
2687
2629
3150
4119
3030
3055
3821
4001
2529
2472
3134
2789
2758
2993
3282
3437
2804
3076
3782
3889
2271
2452
3084
2522
2769
3438
2839
3746
2632
2851
3871
3618
2389
2344
2678
2492
2858
2246
2800
3869
3007
3023
3907
4209
2353
2570
2903
2910
3782
2759
2931
3641
2794
3070
3576
4106
2452
2206
2488
2416
2534
2521
3093
3903
2907
3025
3812
4209
2138
2419
2622
2912
2708
2798
3254
2895
3263
3736
4077
4097
2175
3138
2823
2498
2822
2738
4137
3515
3785
3632
4504
4451
2550
2867
3458
2961
3163
2880
3331
3062
3534
3622
4464
5411
2564
2820
3508
3088
3299
2939
3320
3418
3604
3495
4163
4882
2211
3260
2992
2425
2707
3244
3965
3315
3333
3583
4021
4904
2252
2952
3573
3048
3059
2731
3563
3092
3478
3478
4308
5029
2075
3264
3308
3688
3136
2824
3644
4694
2914
3686
4358
5587
2265
3685
3754
3708
3210
3517
3905
3670
4221
4404
5086
5725
2367
3819
4067
4022
3937
4365
4290




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'Gwilym Jenkins' @ jenkins.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 & 'Gwilym Jenkins' @ jenkins.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=160221&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]'Gwilym Jenkins' @ jenkins.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=160221&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=160221&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'Gwilym Jenkins' @ jenkins.wessa.net







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.117131048873749
betaFALSE
gammaFALSE

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.117131048873749 \tabularnewline
beta & FALSE \tabularnewline
gamma & FALSE \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=160221&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]0.117131048873749[/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=160221&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=160221&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
alpha0.117131048873749
betaFALSE
gammaFALSE







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
223021954348
330541994.761605008061059.23839499194
424142118.83130922082295.168690779184
522262153.4047275664772.595272433527
627252161.90788796989563.092112030112
725892227.86345766451361.136542335491
834702270.16375965491199.8362403451
924002410.70183696326-10.7018369632601
1031802409.44831957488770.551680425122
1140092499.70384611451509.2961538855
1239242676.489287680221247.51071231978
1320722822.61152589548-750.611525895477
1424342734.69161057062-300.691610570615
1529562699.47128683694256.528713163058
1628282729.5187640759698.4812359240359
1726872741.05397453413-54.0539745341293
1826292734.72257580115-105.722575801152
1931502722.33917960793427.660820392071
2041192772.431540062661346.56845993734
2130302930.1565161554399.8434838445714
2230552941.85128814135113.148711858647
2338212955.10451544007865.895484559931
2440013056.52776176162944.472238238383
2525293167.15478565862-638.154785658616
2624723092.40704627062-620.40704627062
2731343019.73811821228114.261881787722
2827893033.12173227236-244.121732272362
2927583004.52749771842-246.527497718424
3029932975.6514733344417.3485266655557
3132822977.68352445919304.316475540805
3234373013.32843242885423.671567571148
3328043062.95352751645-258.953527516446
3430763032.6220292288943.3779707711128
3537823037.70293644332744.297063556678
3638893124.88323217137764.116767828633
3722713214.38503064915-943.385030649154
3824523103.88535251742-651.885352517425
3930843027.5293374316356.4706625683748
4025223034.14380536885-512.143805368854
4127692974.15586427181-205.155864271807
4234382950.12574270705487.87425729295
4328393007.27096618227-168.270966182274
4437462987.56121141835758.438788581655
4526323076.39794223145-444.39794223145
4628513024.34514514054-173.345145140545
4738713004.04104647306866.958953526939
4836183105.58885803016512.411141969842
4923893165.60811254368-776.608112543681
5023443074.64318975758-730.643189757578
5126782989.06218658881-311.062186588811
5224922952.6271464087-460.627146408702
5328582898.67340561013-40.6734056101286
5422462893.90928694975-647.909286949747
5528002818.01899259428-18.0189925942805
5638692815.908409092061053.09159090794
5730072939.2581316952467.7418683047649
5830232947.1928077824475.8071922175604
5939072956.07218371906950.927816280944
6042093067.455356243271141.54464375673
6123533201.1656777027-848.165677702702
6225703101.81914225467-531.819142254671
6329033039.52660831124-136.526608311244
6429103023.53510348057-113.535103480573
6537823010.2366177259771.763382274096
6627593100.63407217402-341.63407217402
6729313060.61811496927-129.618114969267
6836413045.43580920988595.564190790121
6927943115.19486754877-321.194867548772
7030703077.57297581992-7.57297581991907
7135763076.68594521904499.314054780963
7241063135.17112417293970.828875827065
7324523248.88532867548-796.885328675481
7422063155.54531429562-949.54531429562
7524883044.32407567902-556.324075679021
7624162979.16125318102-563.161253181019
7725342913.19758491087-379.197584910871
7825212868.78177405987-347.781774059868
7930932828.04573008506264.954269914937
8039032859.080101623781043.91989837622
8129072981.35553426076-74.3555342607619
8230252972.6461925432352.3538074567691
8338122978.77844892318833.221551076823
8442093076.374563145021132.62543685498
8521383209.04016854493-1071.04016854493
8624193083.58811021734-664.588110217344
8726223005.74420779856-383.744207798564
8829122960.79584623989-48.7958462398929
8927082955.08033758913-247.080337589132
9027982926.13955849124-128.139558491237
9132542911.13043760294342.869562397061
9228952951.29110907339-56.2911090733901
9332632944.69767242536318.302327574643
9437362981.98075791313754.019242086869
9540773070.299822609751006.70017739025
9640973188.21567028886908.784329711137
9721753294.66253202795-1119.66253202795
9831383163.51528526688-25.5152852668834
9928233160.52665314126-337.52665314126
10024983120.99180223598-622.991802235978
10128223048.02011900033-226.020119000331
10227383021.54614539525-283.546145395253
10341372988.3340879811148.665912019
10435153122.87853106131392.121468938695
10537853168.80813000401616.191869995991
10636323240.98333004412391.016669955884
10745043286.783522723171217.21647727683
10844513429.357365413011021.64263458699
10925503549.02343877633-999.023438776328
11028673432.006775543-565.006775542997
11134583365.8269393028792.1730606971287
11229613376.62326658023-415.623266580229
11331633327.94087742935-164.940877429353
11428803308.6211794539-428.621179453897
11533313258.4163311349672.5836688650415
11630623266.91813240023-204.918132400226
11735343242.91585661894291.084143381062
11836223277.01084764368344.989152356322
11944643317.419788909241146.58021109076
12054113451.719931652181959.28006834782
12125643681.21246109519-1117.21246109519
12228203550.35219371229-730.352193712292
12335083464.8052752155343.1947247844723
12430883469.86471863535-381.864718635346
12532993425.13650361371-126.136503613709
12629393410.36200264417-471.362002644168
12733203355.15087687523-35.150876875226
12834183351.03361779866.9663822020011
12936043358.8774603846245.1225396154
13034953387.58892055235107.411079447651
13141633400.17009294871762.829907051287
13248823489.521160073891392.47883992611
13322113652.62366712894-1441.62366712894
13432603483.76477491691-223.764774916908
13529923457.55497212989-465.554972129892
13624253403.02402993593-978.024029935929
13727073288.4670494858-581.467049485803
13832443220.3592040940123.6407959059929
13939653223.12827531469741.871724685314
14033153310.024488556854.97551144314639
14133333310.6072754308722.3927245691275
14235833313.2301587468269.769841253205
14340213344.82858320729676.171416792712
14449043424.029250474671479.97074952533
14522523597.37977666904-1345.37977666904
14629523439.79403229426-487.794032294263
14735733382.65820565728190.341794342719
14830483404.95313967315-356.953139673155
14930593363.14284402446-304.142844024461
15027313327.51827369643-596.518273696431
15135633257.64746262601305.35253737399
15230923293.41372560489-201.413725604886
15334783269.82192466722208.178075332783
15434783294.20604098346183.793959016536
15543083315.73402017973992.26597982027
15650293431.959175157821597.04082484218
15720753619.02224206578-1544.02224206578
15832643438.16929736822-174.169297368216
15933083417.76866488587-109.768664885873
16036883404.91134603432283.08865396568
16131363438.06981699758-302.069816997578
16228243402.68806249955-578.68806249955
16336443334.90572276826309.094277231739
16446943371.110259661291322.88974033871
16529143526.06172249148-612.061722491482
16636863454.37029096058231.629709039419
16743583481.50132173069876.49867826931
16855873584.166531252832002.83346874717
16922653818.76051616663-1553.76051616663
17036853636.7669172094248.2330827905816
17137543642.41650878709111.583491212907
17237083655.4864001498652.5135998501441
17332103661.63737318044-451.63737318044
17435173608.73661394923-91.7366139492301
17539053597.99140813723307.008591862769
17636703633.9516465153736.0483534846303
17742213638.1740279692582.825972030804
17844043706.44104538403697.558954615974
17950863788.146857389471297.85314261053
18057253940.165757267531784.83424273247
18123674149.22526418457-1782.22526418457
18238193940.47134966134-121.471349661338
18340673926.2432830674140.756716932605
18440223942.7302649577479.2697350422636
18539373952.01521216718-15.0152121671808
18643653950.25646461698414.743535383023
18742903998.83580993291.164190070003

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
2 & 2302 & 1954 & 348 \tabularnewline
3 & 3054 & 1994.76160500806 & 1059.23839499194 \tabularnewline
4 & 2414 & 2118.83130922082 & 295.168690779184 \tabularnewline
5 & 2226 & 2153.40472756647 & 72.595272433527 \tabularnewline
6 & 2725 & 2161.90788796989 & 563.092112030112 \tabularnewline
7 & 2589 & 2227.86345766451 & 361.136542335491 \tabularnewline
8 & 3470 & 2270.1637596549 & 1199.8362403451 \tabularnewline
9 & 2400 & 2410.70183696326 & -10.7018369632601 \tabularnewline
10 & 3180 & 2409.44831957488 & 770.551680425122 \tabularnewline
11 & 4009 & 2499.7038461145 & 1509.2961538855 \tabularnewline
12 & 3924 & 2676.48928768022 & 1247.51071231978 \tabularnewline
13 & 2072 & 2822.61152589548 & -750.611525895477 \tabularnewline
14 & 2434 & 2734.69161057062 & -300.691610570615 \tabularnewline
15 & 2956 & 2699.47128683694 & 256.528713163058 \tabularnewline
16 & 2828 & 2729.51876407596 & 98.4812359240359 \tabularnewline
17 & 2687 & 2741.05397453413 & -54.0539745341293 \tabularnewline
18 & 2629 & 2734.72257580115 & -105.722575801152 \tabularnewline
19 & 3150 & 2722.33917960793 & 427.660820392071 \tabularnewline
20 & 4119 & 2772.43154006266 & 1346.56845993734 \tabularnewline
21 & 3030 & 2930.15651615543 & 99.8434838445714 \tabularnewline
22 & 3055 & 2941.85128814135 & 113.148711858647 \tabularnewline
23 & 3821 & 2955.10451544007 & 865.895484559931 \tabularnewline
24 & 4001 & 3056.52776176162 & 944.472238238383 \tabularnewline
25 & 2529 & 3167.15478565862 & -638.154785658616 \tabularnewline
26 & 2472 & 3092.40704627062 & -620.40704627062 \tabularnewline
27 & 3134 & 3019.73811821228 & 114.261881787722 \tabularnewline
28 & 2789 & 3033.12173227236 & -244.121732272362 \tabularnewline
29 & 2758 & 3004.52749771842 & -246.527497718424 \tabularnewline
30 & 2993 & 2975.65147333444 & 17.3485266655557 \tabularnewline
31 & 3282 & 2977.68352445919 & 304.316475540805 \tabularnewline
32 & 3437 & 3013.32843242885 & 423.671567571148 \tabularnewline
33 & 2804 & 3062.95352751645 & -258.953527516446 \tabularnewline
34 & 3076 & 3032.62202922889 & 43.3779707711128 \tabularnewline
35 & 3782 & 3037.70293644332 & 744.297063556678 \tabularnewline
36 & 3889 & 3124.88323217137 & 764.116767828633 \tabularnewline
37 & 2271 & 3214.38503064915 & -943.385030649154 \tabularnewline
38 & 2452 & 3103.88535251742 & -651.885352517425 \tabularnewline
39 & 3084 & 3027.52933743163 & 56.4706625683748 \tabularnewline
40 & 2522 & 3034.14380536885 & -512.143805368854 \tabularnewline
41 & 2769 & 2974.15586427181 & -205.155864271807 \tabularnewline
42 & 3438 & 2950.12574270705 & 487.87425729295 \tabularnewline
43 & 2839 & 3007.27096618227 & -168.270966182274 \tabularnewline
44 & 3746 & 2987.56121141835 & 758.438788581655 \tabularnewline
45 & 2632 & 3076.39794223145 & -444.39794223145 \tabularnewline
46 & 2851 & 3024.34514514054 & -173.345145140545 \tabularnewline
47 & 3871 & 3004.04104647306 & 866.958953526939 \tabularnewline
48 & 3618 & 3105.58885803016 & 512.411141969842 \tabularnewline
49 & 2389 & 3165.60811254368 & -776.608112543681 \tabularnewline
50 & 2344 & 3074.64318975758 & -730.643189757578 \tabularnewline
51 & 2678 & 2989.06218658881 & -311.062186588811 \tabularnewline
52 & 2492 & 2952.6271464087 & -460.627146408702 \tabularnewline
53 & 2858 & 2898.67340561013 & -40.6734056101286 \tabularnewline
54 & 2246 & 2893.90928694975 & -647.909286949747 \tabularnewline
55 & 2800 & 2818.01899259428 & -18.0189925942805 \tabularnewline
56 & 3869 & 2815.90840909206 & 1053.09159090794 \tabularnewline
57 & 3007 & 2939.25813169524 & 67.7418683047649 \tabularnewline
58 & 3023 & 2947.19280778244 & 75.8071922175604 \tabularnewline
59 & 3907 & 2956.07218371906 & 950.927816280944 \tabularnewline
60 & 4209 & 3067.45535624327 & 1141.54464375673 \tabularnewline
61 & 2353 & 3201.1656777027 & -848.165677702702 \tabularnewline
62 & 2570 & 3101.81914225467 & -531.819142254671 \tabularnewline
63 & 2903 & 3039.52660831124 & -136.526608311244 \tabularnewline
64 & 2910 & 3023.53510348057 & -113.535103480573 \tabularnewline
65 & 3782 & 3010.2366177259 & 771.763382274096 \tabularnewline
66 & 2759 & 3100.63407217402 & -341.63407217402 \tabularnewline
67 & 2931 & 3060.61811496927 & -129.618114969267 \tabularnewline
68 & 3641 & 3045.43580920988 & 595.564190790121 \tabularnewline
69 & 2794 & 3115.19486754877 & -321.194867548772 \tabularnewline
70 & 3070 & 3077.57297581992 & -7.57297581991907 \tabularnewline
71 & 3576 & 3076.68594521904 & 499.314054780963 \tabularnewline
72 & 4106 & 3135.17112417293 & 970.828875827065 \tabularnewline
73 & 2452 & 3248.88532867548 & -796.885328675481 \tabularnewline
74 & 2206 & 3155.54531429562 & -949.54531429562 \tabularnewline
75 & 2488 & 3044.32407567902 & -556.324075679021 \tabularnewline
76 & 2416 & 2979.16125318102 & -563.161253181019 \tabularnewline
77 & 2534 & 2913.19758491087 & -379.197584910871 \tabularnewline
78 & 2521 & 2868.78177405987 & -347.781774059868 \tabularnewline
79 & 3093 & 2828.04573008506 & 264.954269914937 \tabularnewline
80 & 3903 & 2859.08010162378 & 1043.91989837622 \tabularnewline
81 & 2907 & 2981.35553426076 & -74.3555342607619 \tabularnewline
82 & 3025 & 2972.64619254323 & 52.3538074567691 \tabularnewline
83 & 3812 & 2978.77844892318 & 833.221551076823 \tabularnewline
84 & 4209 & 3076.37456314502 & 1132.62543685498 \tabularnewline
85 & 2138 & 3209.04016854493 & -1071.04016854493 \tabularnewline
86 & 2419 & 3083.58811021734 & -664.588110217344 \tabularnewline
87 & 2622 & 3005.74420779856 & -383.744207798564 \tabularnewline
88 & 2912 & 2960.79584623989 & -48.7958462398929 \tabularnewline
89 & 2708 & 2955.08033758913 & -247.080337589132 \tabularnewline
90 & 2798 & 2926.13955849124 & -128.139558491237 \tabularnewline
91 & 3254 & 2911.13043760294 & 342.869562397061 \tabularnewline
92 & 2895 & 2951.29110907339 & -56.2911090733901 \tabularnewline
93 & 3263 & 2944.69767242536 & 318.302327574643 \tabularnewline
94 & 3736 & 2981.98075791313 & 754.019242086869 \tabularnewline
95 & 4077 & 3070.29982260975 & 1006.70017739025 \tabularnewline
96 & 4097 & 3188.21567028886 & 908.784329711137 \tabularnewline
97 & 2175 & 3294.66253202795 & -1119.66253202795 \tabularnewline
98 & 3138 & 3163.51528526688 & -25.5152852668834 \tabularnewline
99 & 2823 & 3160.52665314126 & -337.52665314126 \tabularnewline
100 & 2498 & 3120.99180223598 & -622.991802235978 \tabularnewline
101 & 2822 & 3048.02011900033 & -226.020119000331 \tabularnewline
102 & 2738 & 3021.54614539525 & -283.546145395253 \tabularnewline
103 & 4137 & 2988.334087981 & 1148.665912019 \tabularnewline
104 & 3515 & 3122.87853106131 & 392.121468938695 \tabularnewline
105 & 3785 & 3168.80813000401 & 616.191869995991 \tabularnewline
106 & 3632 & 3240.98333004412 & 391.016669955884 \tabularnewline
107 & 4504 & 3286.78352272317 & 1217.21647727683 \tabularnewline
108 & 4451 & 3429.35736541301 & 1021.64263458699 \tabularnewline
109 & 2550 & 3549.02343877633 & -999.023438776328 \tabularnewline
110 & 2867 & 3432.006775543 & -565.006775542997 \tabularnewline
111 & 3458 & 3365.82693930287 & 92.1730606971287 \tabularnewline
112 & 2961 & 3376.62326658023 & -415.623266580229 \tabularnewline
113 & 3163 & 3327.94087742935 & -164.940877429353 \tabularnewline
114 & 2880 & 3308.6211794539 & -428.621179453897 \tabularnewline
115 & 3331 & 3258.41633113496 & 72.5836688650415 \tabularnewline
116 & 3062 & 3266.91813240023 & -204.918132400226 \tabularnewline
117 & 3534 & 3242.91585661894 & 291.084143381062 \tabularnewline
118 & 3622 & 3277.01084764368 & 344.989152356322 \tabularnewline
119 & 4464 & 3317.41978890924 & 1146.58021109076 \tabularnewline
120 & 5411 & 3451.71993165218 & 1959.28006834782 \tabularnewline
121 & 2564 & 3681.21246109519 & -1117.21246109519 \tabularnewline
122 & 2820 & 3550.35219371229 & -730.352193712292 \tabularnewline
123 & 3508 & 3464.80527521553 & 43.1947247844723 \tabularnewline
124 & 3088 & 3469.86471863535 & -381.864718635346 \tabularnewline
125 & 3299 & 3425.13650361371 & -126.136503613709 \tabularnewline
126 & 2939 & 3410.36200264417 & -471.362002644168 \tabularnewline
127 & 3320 & 3355.15087687523 & -35.150876875226 \tabularnewline
128 & 3418 & 3351.033617798 & 66.9663822020011 \tabularnewline
129 & 3604 & 3358.8774603846 & 245.1225396154 \tabularnewline
130 & 3495 & 3387.58892055235 & 107.411079447651 \tabularnewline
131 & 4163 & 3400.17009294871 & 762.829907051287 \tabularnewline
132 & 4882 & 3489.52116007389 & 1392.47883992611 \tabularnewline
133 & 2211 & 3652.62366712894 & -1441.62366712894 \tabularnewline
134 & 3260 & 3483.76477491691 & -223.764774916908 \tabularnewline
135 & 2992 & 3457.55497212989 & -465.554972129892 \tabularnewline
136 & 2425 & 3403.02402993593 & -978.024029935929 \tabularnewline
137 & 2707 & 3288.4670494858 & -581.467049485803 \tabularnewline
138 & 3244 & 3220.35920409401 & 23.6407959059929 \tabularnewline
139 & 3965 & 3223.12827531469 & 741.871724685314 \tabularnewline
140 & 3315 & 3310.02448855685 & 4.97551144314639 \tabularnewline
141 & 3333 & 3310.60727543087 & 22.3927245691275 \tabularnewline
142 & 3583 & 3313.2301587468 & 269.769841253205 \tabularnewline
143 & 4021 & 3344.82858320729 & 676.171416792712 \tabularnewline
144 & 4904 & 3424.02925047467 & 1479.97074952533 \tabularnewline
145 & 2252 & 3597.37977666904 & -1345.37977666904 \tabularnewline
146 & 2952 & 3439.79403229426 & -487.794032294263 \tabularnewline
147 & 3573 & 3382.65820565728 & 190.341794342719 \tabularnewline
148 & 3048 & 3404.95313967315 & -356.953139673155 \tabularnewline
149 & 3059 & 3363.14284402446 & -304.142844024461 \tabularnewline
150 & 2731 & 3327.51827369643 & -596.518273696431 \tabularnewline
151 & 3563 & 3257.64746262601 & 305.35253737399 \tabularnewline
152 & 3092 & 3293.41372560489 & -201.413725604886 \tabularnewline
153 & 3478 & 3269.82192466722 & 208.178075332783 \tabularnewline
154 & 3478 & 3294.20604098346 & 183.793959016536 \tabularnewline
155 & 4308 & 3315.73402017973 & 992.26597982027 \tabularnewline
156 & 5029 & 3431.95917515782 & 1597.04082484218 \tabularnewline
157 & 2075 & 3619.02224206578 & -1544.02224206578 \tabularnewline
158 & 3264 & 3438.16929736822 & -174.169297368216 \tabularnewline
159 & 3308 & 3417.76866488587 & -109.768664885873 \tabularnewline
160 & 3688 & 3404.91134603432 & 283.08865396568 \tabularnewline
161 & 3136 & 3438.06981699758 & -302.069816997578 \tabularnewline
162 & 2824 & 3402.68806249955 & -578.68806249955 \tabularnewline
163 & 3644 & 3334.90572276826 & 309.094277231739 \tabularnewline
164 & 4694 & 3371.11025966129 & 1322.88974033871 \tabularnewline
165 & 2914 & 3526.06172249148 & -612.061722491482 \tabularnewline
166 & 3686 & 3454.37029096058 & 231.629709039419 \tabularnewline
167 & 4358 & 3481.50132173069 & 876.49867826931 \tabularnewline
168 & 5587 & 3584.16653125283 & 2002.83346874717 \tabularnewline
169 & 2265 & 3818.76051616663 & -1553.76051616663 \tabularnewline
170 & 3685 & 3636.76691720942 & 48.2330827905816 \tabularnewline
171 & 3754 & 3642.41650878709 & 111.583491212907 \tabularnewline
172 & 3708 & 3655.48640014986 & 52.5135998501441 \tabularnewline
173 & 3210 & 3661.63737318044 & -451.63737318044 \tabularnewline
174 & 3517 & 3608.73661394923 & -91.7366139492301 \tabularnewline
175 & 3905 & 3597.99140813723 & 307.008591862769 \tabularnewline
176 & 3670 & 3633.95164651537 & 36.0483534846303 \tabularnewline
177 & 4221 & 3638.1740279692 & 582.825972030804 \tabularnewline
178 & 4404 & 3706.44104538403 & 697.558954615974 \tabularnewline
179 & 5086 & 3788.14685738947 & 1297.85314261053 \tabularnewline
180 & 5725 & 3940.16575726753 & 1784.83424273247 \tabularnewline
181 & 2367 & 4149.22526418457 & -1782.22526418457 \tabularnewline
182 & 3819 & 3940.47134966134 & -121.471349661338 \tabularnewline
183 & 4067 & 3926.2432830674 & 140.756716932605 \tabularnewline
184 & 4022 & 3942.73026495774 & 79.2697350422636 \tabularnewline
185 & 3937 & 3952.01521216718 & -15.0152121671808 \tabularnewline
186 & 4365 & 3950.25646461698 & 414.743535383023 \tabularnewline
187 & 4290 & 3998.83580993 & 291.164190070003 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=160221&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]2302[/C][C]1954[/C][C]348[/C][/ROW]
[ROW][C]3[/C][C]3054[/C][C]1994.76160500806[/C][C]1059.23839499194[/C][/ROW]
[ROW][C]4[/C][C]2414[/C][C]2118.83130922082[/C][C]295.168690779184[/C][/ROW]
[ROW][C]5[/C][C]2226[/C][C]2153.40472756647[/C][C]72.595272433527[/C][/ROW]
[ROW][C]6[/C][C]2725[/C][C]2161.90788796989[/C][C]563.092112030112[/C][/ROW]
[ROW][C]7[/C][C]2589[/C][C]2227.86345766451[/C][C]361.136542335491[/C][/ROW]
[ROW][C]8[/C][C]3470[/C][C]2270.1637596549[/C][C]1199.8362403451[/C][/ROW]
[ROW][C]9[/C][C]2400[/C][C]2410.70183696326[/C][C]-10.7018369632601[/C][/ROW]
[ROW][C]10[/C][C]3180[/C][C]2409.44831957488[/C][C]770.551680425122[/C][/ROW]
[ROW][C]11[/C][C]4009[/C][C]2499.7038461145[/C][C]1509.2961538855[/C][/ROW]
[ROW][C]12[/C][C]3924[/C][C]2676.48928768022[/C][C]1247.51071231978[/C][/ROW]
[ROW][C]13[/C][C]2072[/C][C]2822.61152589548[/C][C]-750.611525895477[/C][/ROW]
[ROW][C]14[/C][C]2434[/C][C]2734.69161057062[/C][C]-300.691610570615[/C][/ROW]
[ROW][C]15[/C][C]2956[/C][C]2699.47128683694[/C][C]256.528713163058[/C][/ROW]
[ROW][C]16[/C][C]2828[/C][C]2729.51876407596[/C][C]98.4812359240359[/C][/ROW]
[ROW][C]17[/C][C]2687[/C][C]2741.05397453413[/C][C]-54.0539745341293[/C][/ROW]
[ROW][C]18[/C][C]2629[/C][C]2734.72257580115[/C][C]-105.722575801152[/C][/ROW]
[ROW][C]19[/C][C]3150[/C][C]2722.33917960793[/C][C]427.660820392071[/C][/ROW]
[ROW][C]20[/C][C]4119[/C][C]2772.43154006266[/C][C]1346.56845993734[/C][/ROW]
[ROW][C]21[/C][C]3030[/C][C]2930.15651615543[/C][C]99.8434838445714[/C][/ROW]
[ROW][C]22[/C][C]3055[/C][C]2941.85128814135[/C][C]113.148711858647[/C][/ROW]
[ROW][C]23[/C][C]3821[/C][C]2955.10451544007[/C][C]865.895484559931[/C][/ROW]
[ROW][C]24[/C][C]4001[/C][C]3056.52776176162[/C][C]944.472238238383[/C][/ROW]
[ROW][C]25[/C][C]2529[/C][C]3167.15478565862[/C][C]-638.154785658616[/C][/ROW]
[ROW][C]26[/C][C]2472[/C][C]3092.40704627062[/C][C]-620.40704627062[/C][/ROW]
[ROW][C]27[/C][C]3134[/C][C]3019.73811821228[/C][C]114.261881787722[/C][/ROW]
[ROW][C]28[/C][C]2789[/C][C]3033.12173227236[/C][C]-244.121732272362[/C][/ROW]
[ROW][C]29[/C][C]2758[/C][C]3004.52749771842[/C][C]-246.527497718424[/C][/ROW]
[ROW][C]30[/C][C]2993[/C][C]2975.65147333444[/C][C]17.3485266655557[/C][/ROW]
[ROW][C]31[/C][C]3282[/C][C]2977.68352445919[/C][C]304.316475540805[/C][/ROW]
[ROW][C]32[/C][C]3437[/C][C]3013.32843242885[/C][C]423.671567571148[/C][/ROW]
[ROW][C]33[/C][C]2804[/C][C]3062.95352751645[/C][C]-258.953527516446[/C][/ROW]
[ROW][C]34[/C][C]3076[/C][C]3032.62202922889[/C][C]43.3779707711128[/C][/ROW]
[ROW][C]35[/C][C]3782[/C][C]3037.70293644332[/C][C]744.297063556678[/C][/ROW]
[ROW][C]36[/C][C]3889[/C][C]3124.88323217137[/C][C]764.116767828633[/C][/ROW]
[ROW][C]37[/C][C]2271[/C][C]3214.38503064915[/C][C]-943.385030649154[/C][/ROW]
[ROW][C]38[/C][C]2452[/C][C]3103.88535251742[/C][C]-651.885352517425[/C][/ROW]
[ROW][C]39[/C][C]3084[/C][C]3027.52933743163[/C][C]56.4706625683748[/C][/ROW]
[ROW][C]40[/C][C]2522[/C][C]3034.14380536885[/C][C]-512.143805368854[/C][/ROW]
[ROW][C]41[/C][C]2769[/C][C]2974.15586427181[/C][C]-205.155864271807[/C][/ROW]
[ROW][C]42[/C][C]3438[/C][C]2950.12574270705[/C][C]487.87425729295[/C][/ROW]
[ROW][C]43[/C][C]2839[/C][C]3007.27096618227[/C][C]-168.270966182274[/C][/ROW]
[ROW][C]44[/C][C]3746[/C][C]2987.56121141835[/C][C]758.438788581655[/C][/ROW]
[ROW][C]45[/C][C]2632[/C][C]3076.39794223145[/C][C]-444.39794223145[/C][/ROW]
[ROW][C]46[/C][C]2851[/C][C]3024.34514514054[/C][C]-173.345145140545[/C][/ROW]
[ROW][C]47[/C][C]3871[/C][C]3004.04104647306[/C][C]866.958953526939[/C][/ROW]
[ROW][C]48[/C][C]3618[/C][C]3105.58885803016[/C][C]512.411141969842[/C][/ROW]
[ROW][C]49[/C][C]2389[/C][C]3165.60811254368[/C][C]-776.608112543681[/C][/ROW]
[ROW][C]50[/C][C]2344[/C][C]3074.64318975758[/C][C]-730.643189757578[/C][/ROW]
[ROW][C]51[/C][C]2678[/C][C]2989.06218658881[/C][C]-311.062186588811[/C][/ROW]
[ROW][C]52[/C][C]2492[/C][C]2952.6271464087[/C][C]-460.627146408702[/C][/ROW]
[ROW][C]53[/C][C]2858[/C][C]2898.67340561013[/C][C]-40.6734056101286[/C][/ROW]
[ROW][C]54[/C][C]2246[/C][C]2893.90928694975[/C][C]-647.909286949747[/C][/ROW]
[ROW][C]55[/C][C]2800[/C][C]2818.01899259428[/C][C]-18.0189925942805[/C][/ROW]
[ROW][C]56[/C][C]3869[/C][C]2815.90840909206[/C][C]1053.09159090794[/C][/ROW]
[ROW][C]57[/C][C]3007[/C][C]2939.25813169524[/C][C]67.7418683047649[/C][/ROW]
[ROW][C]58[/C][C]3023[/C][C]2947.19280778244[/C][C]75.8071922175604[/C][/ROW]
[ROW][C]59[/C][C]3907[/C][C]2956.07218371906[/C][C]950.927816280944[/C][/ROW]
[ROW][C]60[/C][C]4209[/C][C]3067.45535624327[/C][C]1141.54464375673[/C][/ROW]
[ROW][C]61[/C][C]2353[/C][C]3201.1656777027[/C][C]-848.165677702702[/C][/ROW]
[ROW][C]62[/C][C]2570[/C][C]3101.81914225467[/C][C]-531.819142254671[/C][/ROW]
[ROW][C]63[/C][C]2903[/C][C]3039.52660831124[/C][C]-136.526608311244[/C][/ROW]
[ROW][C]64[/C][C]2910[/C][C]3023.53510348057[/C][C]-113.535103480573[/C][/ROW]
[ROW][C]65[/C][C]3782[/C][C]3010.2366177259[/C][C]771.763382274096[/C][/ROW]
[ROW][C]66[/C][C]2759[/C][C]3100.63407217402[/C][C]-341.63407217402[/C][/ROW]
[ROW][C]67[/C][C]2931[/C][C]3060.61811496927[/C][C]-129.618114969267[/C][/ROW]
[ROW][C]68[/C][C]3641[/C][C]3045.43580920988[/C][C]595.564190790121[/C][/ROW]
[ROW][C]69[/C][C]2794[/C][C]3115.19486754877[/C][C]-321.194867548772[/C][/ROW]
[ROW][C]70[/C][C]3070[/C][C]3077.57297581992[/C][C]-7.57297581991907[/C][/ROW]
[ROW][C]71[/C][C]3576[/C][C]3076.68594521904[/C][C]499.314054780963[/C][/ROW]
[ROW][C]72[/C][C]4106[/C][C]3135.17112417293[/C][C]970.828875827065[/C][/ROW]
[ROW][C]73[/C][C]2452[/C][C]3248.88532867548[/C][C]-796.885328675481[/C][/ROW]
[ROW][C]74[/C][C]2206[/C][C]3155.54531429562[/C][C]-949.54531429562[/C][/ROW]
[ROW][C]75[/C][C]2488[/C][C]3044.32407567902[/C][C]-556.324075679021[/C][/ROW]
[ROW][C]76[/C][C]2416[/C][C]2979.16125318102[/C][C]-563.161253181019[/C][/ROW]
[ROW][C]77[/C][C]2534[/C][C]2913.19758491087[/C][C]-379.197584910871[/C][/ROW]
[ROW][C]78[/C][C]2521[/C][C]2868.78177405987[/C][C]-347.781774059868[/C][/ROW]
[ROW][C]79[/C][C]3093[/C][C]2828.04573008506[/C][C]264.954269914937[/C][/ROW]
[ROW][C]80[/C][C]3903[/C][C]2859.08010162378[/C][C]1043.91989837622[/C][/ROW]
[ROW][C]81[/C][C]2907[/C][C]2981.35553426076[/C][C]-74.3555342607619[/C][/ROW]
[ROW][C]82[/C][C]3025[/C][C]2972.64619254323[/C][C]52.3538074567691[/C][/ROW]
[ROW][C]83[/C][C]3812[/C][C]2978.77844892318[/C][C]833.221551076823[/C][/ROW]
[ROW][C]84[/C][C]4209[/C][C]3076.37456314502[/C][C]1132.62543685498[/C][/ROW]
[ROW][C]85[/C][C]2138[/C][C]3209.04016854493[/C][C]-1071.04016854493[/C][/ROW]
[ROW][C]86[/C][C]2419[/C][C]3083.58811021734[/C][C]-664.588110217344[/C][/ROW]
[ROW][C]87[/C][C]2622[/C][C]3005.74420779856[/C][C]-383.744207798564[/C][/ROW]
[ROW][C]88[/C][C]2912[/C][C]2960.79584623989[/C][C]-48.7958462398929[/C][/ROW]
[ROW][C]89[/C][C]2708[/C][C]2955.08033758913[/C][C]-247.080337589132[/C][/ROW]
[ROW][C]90[/C][C]2798[/C][C]2926.13955849124[/C][C]-128.139558491237[/C][/ROW]
[ROW][C]91[/C][C]3254[/C][C]2911.13043760294[/C][C]342.869562397061[/C][/ROW]
[ROW][C]92[/C][C]2895[/C][C]2951.29110907339[/C][C]-56.2911090733901[/C][/ROW]
[ROW][C]93[/C][C]3263[/C][C]2944.69767242536[/C][C]318.302327574643[/C][/ROW]
[ROW][C]94[/C][C]3736[/C][C]2981.98075791313[/C][C]754.019242086869[/C][/ROW]
[ROW][C]95[/C][C]4077[/C][C]3070.29982260975[/C][C]1006.70017739025[/C][/ROW]
[ROW][C]96[/C][C]4097[/C][C]3188.21567028886[/C][C]908.784329711137[/C][/ROW]
[ROW][C]97[/C][C]2175[/C][C]3294.66253202795[/C][C]-1119.66253202795[/C][/ROW]
[ROW][C]98[/C][C]3138[/C][C]3163.51528526688[/C][C]-25.5152852668834[/C][/ROW]
[ROW][C]99[/C][C]2823[/C][C]3160.52665314126[/C][C]-337.52665314126[/C][/ROW]
[ROW][C]100[/C][C]2498[/C][C]3120.99180223598[/C][C]-622.991802235978[/C][/ROW]
[ROW][C]101[/C][C]2822[/C][C]3048.02011900033[/C][C]-226.020119000331[/C][/ROW]
[ROW][C]102[/C][C]2738[/C][C]3021.54614539525[/C][C]-283.546145395253[/C][/ROW]
[ROW][C]103[/C][C]4137[/C][C]2988.334087981[/C][C]1148.665912019[/C][/ROW]
[ROW][C]104[/C][C]3515[/C][C]3122.87853106131[/C][C]392.121468938695[/C][/ROW]
[ROW][C]105[/C][C]3785[/C][C]3168.80813000401[/C][C]616.191869995991[/C][/ROW]
[ROW][C]106[/C][C]3632[/C][C]3240.98333004412[/C][C]391.016669955884[/C][/ROW]
[ROW][C]107[/C][C]4504[/C][C]3286.78352272317[/C][C]1217.21647727683[/C][/ROW]
[ROW][C]108[/C][C]4451[/C][C]3429.35736541301[/C][C]1021.64263458699[/C][/ROW]
[ROW][C]109[/C][C]2550[/C][C]3549.02343877633[/C][C]-999.023438776328[/C][/ROW]
[ROW][C]110[/C][C]2867[/C][C]3432.006775543[/C][C]-565.006775542997[/C][/ROW]
[ROW][C]111[/C][C]3458[/C][C]3365.82693930287[/C][C]92.1730606971287[/C][/ROW]
[ROW][C]112[/C][C]2961[/C][C]3376.62326658023[/C][C]-415.623266580229[/C][/ROW]
[ROW][C]113[/C][C]3163[/C][C]3327.94087742935[/C][C]-164.940877429353[/C][/ROW]
[ROW][C]114[/C][C]2880[/C][C]3308.6211794539[/C][C]-428.621179453897[/C][/ROW]
[ROW][C]115[/C][C]3331[/C][C]3258.41633113496[/C][C]72.5836688650415[/C][/ROW]
[ROW][C]116[/C][C]3062[/C][C]3266.91813240023[/C][C]-204.918132400226[/C][/ROW]
[ROW][C]117[/C][C]3534[/C][C]3242.91585661894[/C][C]291.084143381062[/C][/ROW]
[ROW][C]118[/C][C]3622[/C][C]3277.01084764368[/C][C]344.989152356322[/C][/ROW]
[ROW][C]119[/C][C]4464[/C][C]3317.41978890924[/C][C]1146.58021109076[/C][/ROW]
[ROW][C]120[/C][C]5411[/C][C]3451.71993165218[/C][C]1959.28006834782[/C][/ROW]
[ROW][C]121[/C][C]2564[/C][C]3681.21246109519[/C][C]-1117.21246109519[/C][/ROW]
[ROW][C]122[/C][C]2820[/C][C]3550.35219371229[/C][C]-730.352193712292[/C][/ROW]
[ROW][C]123[/C][C]3508[/C][C]3464.80527521553[/C][C]43.1947247844723[/C][/ROW]
[ROW][C]124[/C][C]3088[/C][C]3469.86471863535[/C][C]-381.864718635346[/C][/ROW]
[ROW][C]125[/C][C]3299[/C][C]3425.13650361371[/C][C]-126.136503613709[/C][/ROW]
[ROW][C]126[/C][C]2939[/C][C]3410.36200264417[/C][C]-471.362002644168[/C][/ROW]
[ROW][C]127[/C][C]3320[/C][C]3355.15087687523[/C][C]-35.150876875226[/C][/ROW]
[ROW][C]128[/C][C]3418[/C][C]3351.033617798[/C][C]66.9663822020011[/C][/ROW]
[ROW][C]129[/C][C]3604[/C][C]3358.8774603846[/C][C]245.1225396154[/C][/ROW]
[ROW][C]130[/C][C]3495[/C][C]3387.58892055235[/C][C]107.411079447651[/C][/ROW]
[ROW][C]131[/C][C]4163[/C][C]3400.17009294871[/C][C]762.829907051287[/C][/ROW]
[ROW][C]132[/C][C]4882[/C][C]3489.52116007389[/C][C]1392.47883992611[/C][/ROW]
[ROW][C]133[/C][C]2211[/C][C]3652.62366712894[/C][C]-1441.62366712894[/C][/ROW]
[ROW][C]134[/C][C]3260[/C][C]3483.76477491691[/C][C]-223.764774916908[/C][/ROW]
[ROW][C]135[/C][C]2992[/C][C]3457.55497212989[/C][C]-465.554972129892[/C][/ROW]
[ROW][C]136[/C][C]2425[/C][C]3403.02402993593[/C][C]-978.024029935929[/C][/ROW]
[ROW][C]137[/C][C]2707[/C][C]3288.4670494858[/C][C]-581.467049485803[/C][/ROW]
[ROW][C]138[/C][C]3244[/C][C]3220.35920409401[/C][C]23.6407959059929[/C][/ROW]
[ROW][C]139[/C][C]3965[/C][C]3223.12827531469[/C][C]741.871724685314[/C][/ROW]
[ROW][C]140[/C][C]3315[/C][C]3310.02448855685[/C][C]4.97551144314639[/C][/ROW]
[ROW][C]141[/C][C]3333[/C][C]3310.60727543087[/C][C]22.3927245691275[/C][/ROW]
[ROW][C]142[/C][C]3583[/C][C]3313.2301587468[/C][C]269.769841253205[/C][/ROW]
[ROW][C]143[/C][C]4021[/C][C]3344.82858320729[/C][C]676.171416792712[/C][/ROW]
[ROW][C]144[/C][C]4904[/C][C]3424.02925047467[/C][C]1479.97074952533[/C][/ROW]
[ROW][C]145[/C][C]2252[/C][C]3597.37977666904[/C][C]-1345.37977666904[/C][/ROW]
[ROW][C]146[/C][C]2952[/C][C]3439.79403229426[/C][C]-487.794032294263[/C][/ROW]
[ROW][C]147[/C][C]3573[/C][C]3382.65820565728[/C][C]190.341794342719[/C][/ROW]
[ROW][C]148[/C][C]3048[/C][C]3404.95313967315[/C][C]-356.953139673155[/C][/ROW]
[ROW][C]149[/C][C]3059[/C][C]3363.14284402446[/C][C]-304.142844024461[/C][/ROW]
[ROW][C]150[/C][C]2731[/C][C]3327.51827369643[/C][C]-596.518273696431[/C][/ROW]
[ROW][C]151[/C][C]3563[/C][C]3257.64746262601[/C][C]305.35253737399[/C][/ROW]
[ROW][C]152[/C][C]3092[/C][C]3293.41372560489[/C][C]-201.413725604886[/C][/ROW]
[ROW][C]153[/C][C]3478[/C][C]3269.82192466722[/C][C]208.178075332783[/C][/ROW]
[ROW][C]154[/C][C]3478[/C][C]3294.20604098346[/C][C]183.793959016536[/C][/ROW]
[ROW][C]155[/C][C]4308[/C][C]3315.73402017973[/C][C]992.26597982027[/C][/ROW]
[ROW][C]156[/C][C]5029[/C][C]3431.95917515782[/C][C]1597.04082484218[/C][/ROW]
[ROW][C]157[/C][C]2075[/C][C]3619.02224206578[/C][C]-1544.02224206578[/C][/ROW]
[ROW][C]158[/C][C]3264[/C][C]3438.16929736822[/C][C]-174.169297368216[/C][/ROW]
[ROW][C]159[/C][C]3308[/C][C]3417.76866488587[/C][C]-109.768664885873[/C][/ROW]
[ROW][C]160[/C][C]3688[/C][C]3404.91134603432[/C][C]283.08865396568[/C][/ROW]
[ROW][C]161[/C][C]3136[/C][C]3438.06981699758[/C][C]-302.069816997578[/C][/ROW]
[ROW][C]162[/C][C]2824[/C][C]3402.68806249955[/C][C]-578.68806249955[/C][/ROW]
[ROW][C]163[/C][C]3644[/C][C]3334.90572276826[/C][C]309.094277231739[/C][/ROW]
[ROW][C]164[/C][C]4694[/C][C]3371.11025966129[/C][C]1322.88974033871[/C][/ROW]
[ROW][C]165[/C][C]2914[/C][C]3526.06172249148[/C][C]-612.061722491482[/C][/ROW]
[ROW][C]166[/C][C]3686[/C][C]3454.37029096058[/C][C]231.629709039419[/C][/ROW]
[ROW][C]167[/C][C]4358[/C][C]3481.50132173069[/C][C]876.49867826931[/C][/ROW]
[ROW][C]168[/C][C]5587[/C][C]3584.16653125283[/C][C]2002.83346874717[/C][/ROW]
[ROW][C]169[/C][C]2265[/C][C]3818.76051616663[/C][C]-1553.76051616663[/C][/ROW]
[ROW][C]170[/C][C]3685[/C][C]3636.76691720942[/C][C]48.2330827905816[/C][/ROW]
[ROW][C]171[/C][C]3754[/C][C]3642.41650878709[/C][C]111.583491212907[/C][/ROW]
[ROW][C]172[/C][C]3708[/C][C]3655.48640014986[/C][C]52.5135998501441[/C][/ROW]
[ROW][C]173[/C][C]3210[/C][C]3661.63737318044[/C][C]-451.63737318044[/C][/ROW]
[ROW][C]174[/C][C]3517[/C][C]3608.73661394923[/C][C]-91.7366139492301[/C][/ROW]
[ROW][C]175[/C][C]3905[/C][C]3597.99140813723[/C][C]307.008591862769[/C][/ROW]
[ROW][C]176[/C][C]3670[/C][C]3633.95164651537[/C][C]36.0483534846303[/C][/ROW]
[ROW][C]177[/C][C]4221[/C][C]3638.1740279692[/C][C]582.825972030804[/C][/ROW]
[ROW][C]178[/C][C]4404[/C][C]3706.44104538403[/C][C]697.558954615974[/C][/ROW]
[ROW][C]179[/C][C]5086[/C][C]3788.14685738947[/C][C]1297.85314261053[/C][/ROW]
[ROW][C]180[/C][C]5725[/C][C]3940.16575726753[/C][C]1784.83424273247[/C][/ROW]
[ROW][C]181[/C][C]2367[/C][C]4149.22526418457[/C][C]-1782.22526418457[/C][/ROW]
[ROW][C]182[/C][C]3819[/C][C]3940.47134966134[/C][C]-121.471349661338[/C][/ROW]
[ROW][C]183[/C][C]4067[/C][C]3926.2432830674[/C][C]140.756716932605[/C][/ROW]
[ROW][C]184[/C][C]4022[/C][C]3942.73026495774[/C][C]79.2697350422636[/C][/ROW]
[ROW][C]185[/C][C]3937[/C][C]3952.01521216718[/C][C]-15.0152121671808[/C][/ROW]
[ROW][C]186[/C][C]4365[/C][C]3950.25646461698[/C][C]414.743535383023[/C][/ROW]
[ROW][C]187[/C][C]4290[/C][C]3998.83580993[/C][C]291.164190070003[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=160221&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=160221&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
223021954348
330541994.761605008061059.23839499194
424142118.83130922082295.168690779184
522262153.4047275664772.595272433527
627252161.90788796989563.092112030112
725892227.86345766451361.136542335491
834702270.16375965491199.8362403451
924002410.70183696326-10.7018369632601
1031802409.44831957488770.551680425122
1140092499.70384611451509.2961538855
1239242676.489287680221247.51071231978
1320722822.61152589548-750.611525895477
1424342734.69161057062-300.691610570615
1529562699.47128683694256.528713163058
1628282729.5187640759698.4812359240359
1726872741.05397453413-54.0539745341293
1826292734.72257580115-105.722575801152
1931502722.33917960793427.660820392071
2041192772.431540062661346.56845993734
2130302930.1565161554399.8434838445714
2230552941.85128814135113.148711858647
2338212955.10451544007865.895484559931
2440013056.52776176162944.472238238383
2525293167.15478565862-638.154785658616
2624723092.40704627062-620.40704627062
2731343019.73811821228114.261881787722
2827893033.12173227236-244.121732272362
2927583004.52749771842-246.527497718424
3029932975.6514733344417.3485266655557
3132822977.68352445919304.316475540805
3234373013.32843242885423.671567571148
3328043062.95352751645-258.953527516446
3430763032.6220292288943.3779707711128
3537823037.70293644332744.297063556678
3638893124.88323217137764.116767828633
3722713214.38503064915-943.385030649154
3824523103.88535251742-651.885352517425
3930843027.5293374316356.4706625683748
4025223034.14380536885-512.143805368854
4127692974.15586427181-205.155864271807
4234382950.12574270705487.87425729295
4328393007.27096618227-168.270966182274
4437462987.56121141835758.438788581655
4526323076.39794223145-444.39794223145
4628513024.34514514054-173.345145140545
4738713004.04104647306866.958953526939
4836183105.58885803016512.411141969842
4923893165.60811254368-776.608112543681
5023443074.64318975758-730.643189757578
5126782989.06218658881-311.062186588811
5224922952.6271464087-460.627146408702
5328582898.67340561013-40.6734056101286
5422462893.90928694975-647.909286949747
5528002818.01899259428-18.0189925942805
5638692815.908409092061053.09159090794
5730072939.2581316952467.7418683047649
5830232947.1928077824475.8071922175604
5939072956.07218371906950.927816280944
6042093067.455356243271141.54464375673
6123533201.1656777027-848.165677702702
6225703101.81914225467-531.819142254671
6329033039.52660831124-136.526608311244
6429103023.53510348057-113.535103480573
6537823010.2366177259771.763382274096
6627593100.63407217402-341.63407217402
6729313060.61811496927-129.618114969267
6836413045.43580920988595.564190790121
6927943115.19486754877-321.194867548772
7030703077.57297581992-7.57297581991907
7135763076.68594521904499.314054780963
7241063135.17112417293970.828875827065
7324523248.88532867548-796.885328675481
7422063155.54531429562-949.54531429562
7524883044.32407567902-556.324075679021
7624162979.16125318102-563.161253181019
7725342913.19758491087-379.197584910871
7825212868.78177405987-347.781774059868
7930932828.04573008506264.954269914937
8039032859.080101623781043.91989837622
8129072981.35553426076-74.3555342607619
8230252972.6461925432352.3538074567691
8338122978.77844892318833.221551076823
8442093076.374563145021132.62543685498
8521383209.04016854493-1071.04016854493
8624193083.58811021734-664.588110217344
8726223005.74420779856-383.744207798564
8829122960.79584623989-48.7958462398929
8927082955.08033758913-247.080337589132
9027982926.13955849124-128.139558491237
9132542911.13043760294342.869562397061
9228952951.29110907339-56.2911090733901
9332632944.69767242536318.302327574643
9437362981.98075791313754.019242086869
9540773070.299822609751006.70017739025
9640973188.21567028886908.784329711137
9721753294.66253202795-1119.66253202795
9831383163.51528526688-25.5152852668834
9928233160.52665314126-337.52665314126
10024983120.99180223598-622.991802235978
10128223048.02011900033-226.020119000331
10227383021.54614539525-283.546145395253
10341372988.3340879811148.665912019
10435153122.87853106131392.121468938695
10537853168.80813000401616.191869995991
10636323240.98333004412391.016669955884
10745043286.783522723171217.21647727683
10844513429.357365413011021.64263458699
10925503549.02343877633-999.023438776328
11028673432.006775543-565.006775542997
11134583365.8269393028792.1730606971287
11229613376.62326658023-415.623266580229
11331633327.94087742935-164.940877429353
11428803308.6211794539-428.621179453897
11533313258.4163311349672.5836688650415
11630623266.91813240023-204.918132400226
11735343242.91585661894291.084143381062
11836223277.01084764368344.989152356322
11944643317.419788909241146.58021109076
12054113451.719931652181959.28006834782
12125643681.21246109519-1117.21246109519
12228203550.35219371229-730.352193712292
12335083464.8052752155343.1947247844723
12430883469.86471863535-381.864718635346
12532993425.13650361371-126.136503613709
12629393410.36200264417-471.362002644168
12733203355.15087687523-35.150876875226
12834183351.03361779866.9663822020011
12936043358.8774603846245.1225396154
13034953387.58892055235107.411079447651
13141633400.17009294871762.829907051287
13248823489.521160073891392.47883992611
13322113652.62366712894-1441.62366712894
13432603483.76477491691-223.764774916908
13529923457.55497212989-465.554972129892
13624253403.02402993593-978.024029935929
13727073288.4670494858-581.467049485803
13832443220.3592040940123.6407959059929
13939653223.12827531469741.871724685314
14033153310.024488556854.97551144314639
14133333310.6072754308722.3927245691275
14235833313.2301587468269.769841253205
14340213344.82858320729676.171416792712
14449043424.029250474671479.97074952533
14522523597.37977666904-1345.37977666904
14629523439.79403229426-487.794032294263
14735733382.65820565728190.341794342719
14830483404.95313967315-356.953139673155
14930593363.14284402446-304.142844024461
15027313327.51827369643-596.518273696431
15135633257.64746262601305.35253737399
15230923293.41372560489-201.413725604886
15334783269.82192466722208.178075332783
15434783294.20604098346183.793959016536
15543083315.73402017973992.26597982027
15650293431.959175157821597.04082484218
15720753619.02224206578-1544.02224206578
15832643438.16929736822-174.169297368216
15933083417.76866488587-109.768664885873
16036883404.91134603432283.08865396568
16131363438.06981699758-302.069816997578
16228243402.68806249955-578.68806249955
16336443334.90572276826309.094277231739
16446943371.110259661291322.88974033871
16529143526.06172249148-612.061722491482
16636863454.37029096058231.629709039419
16743583481.50132173069876.49867826931
16855873584.166531252832002.83346874717
16922653818.76051616663-1553.76051616663
17036853636.7669172094248.2330827905816
17137543642.41650878709111.583491212907
17237083655.4864001498652.5135998501441
17332103661.63737318044-451.63737318044
17435173608.73661394923-91.7366139492301
17539053597.99140813723307.008591862769
17636703633.9516465153736.0483534846303
17742213638.1740279692582.825972030804
17844043706.44104538403697.558954615974
17950863788.146857389471297.85314261053
18057253940.165757267531784.83424273247
18123674149.22526418457-1782.22526418457
18238193940.47134966134-121.471349661338
18340673926.2432830674140.756716932605
18440223942.7302649577479.2697350422636
18539373952.01521216718-15.0152121671808
18643653950.25646461698414.743535383023
18742903998.83580993291.164190070003







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
1884032.940176907372676.489090346275389.39126346848
1894032.940176907372667.215749624285398.66460419046
1904032.940176907372658.004952133985407.87540168076
1914032.940176907372648.855449238015417.02490457673
1924032.940176907372639.766033301315426.11432051343
1934032.940176907372630.735535830545435.1448179842
1944032.940176907372621.762825720675444.11752809408
1954032.940176907372612.846807601245453.0335462135
1964032.940176907372603.986420275565461.89393353918
1974032.940176907372595.180635246435470.69971856831
1984032.940176907372586.428455322655479.45189849209
1994032.940176907372577.728913300985488.15144051377

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
188 & 4032.94017690737 & 2676.48909034627 & 5389.39126346848 \tabularnewline
189 & 4032.94017690737 & 2667.21574962428 & 5398.66460419046 \tabularnewline
190 & 4032.94017690737 & 2658.00495213398 & 5407.87540168076 \tabularnewline
191 & 4032.94017690737 & 2648.85544923801 & 5417.02490457673 \tabularnewline
192 & 4032.94017690737 & 2639.76603330131 & 5426.11432051343 \tabularnewline
193 & 4032.94017690737 & 2630.73553583054 & 5435.1448179842 \tabularnewline
194 & 4032.94017690737 & 2621.76282572067 & 5444.11752809408 \tabularnewline
195 & 4032.94017690737 & 2612.84680760124 & 5453.0335462135 \tabularnewline
196 & 4032.94017690737 & 2603.98642027556 & 5461.89393353918 \tabularnewline
197 & 4032.94017690737 & 2595.18063524643 & 5470.69971856831 \tabularnewline
198 & 4032.94017690737 & 2586.42845532265 & 5479.45189849209 \tabularnewline
199 & 4032.94017690737 & 2577.72891330098 & 5488.15144051377 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=160221&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]4032.94017690737[/C][C]2676.48909034627[/C][C]5389.39126346848[/C][/ROW]
[ROW][C]189[/C][C]4032.94017690737[/C][C]2667.21574962428[/C][C]5398.66460419046[/C][/ROW]
[ROW][C]190[/C][C]4032.94017690737[/C][C]2658.00495213398[/C][C]5407.87540168076[/C][/ROW]
[ROW][C]191[/C][C]4032.94017690737[/C][C]2648.85544923801[/C][C]5417.02490457673[/C][/ROW]
[ROW][C]192[/C][C]4032.94017690737[/C][C]2639.76603330131[/C][C]5426.11432051343[/C][/ROW]
[ROW][C]193[/C][C]4032.94017690737[/C][C]2630.73553583054[/C][C]5435.1448179842[/C][/ROW]
[ROW][C]194[/C][C]4032.94017690737[/C][C]2621.76282572067[/C][C]5444.11752809408[/C][/ROW]
[ROW][C]195[/C][C]4032.94017690737[/C][C]2612.84680760124[/C][C]5453.0335462135[/C][/ROW]
[ROW][C]196[/C][C]4032.94017690737[/C][C]2603.98642027556[/C][C]5461.89393353918[/C][/ROW]
[ROW][C]197[/C][C]4032.94017690737[/C][C]2595.18063524643[/C][C]5470.69971856831[/C][/ROW]
[ROW][C]198[/C][C]4032.94017690737[/C][C]2586.42845532265[/C][C]5479.45189849209[/C][/ROW]
[ROW][C]199[/C][C]4032.94017690737[/C][C]2577.72891330098[/C][C]5488.15144051377[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=160221&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=160221&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
1884032.940176907372676.489090346275389.39126346848
1894032.940176907372667.215749624285398.66460419046
1904032.940176907372658.004952133985407.87540168076
1914032.940176907372648.855449238015417.02490457673
1924032.940176907372639.766033301315426.11432051343
1934032.940176907372630.735535830545435.1448179842
1944032.940176907372621.762825720675444.11752809408
1954032.940176907372612.846807601245453.0335462135
1964032.940176907372603.986420275565461.89393353918
1974032.940176907372595.180635246435470.69971856831
1984032.940176907372586.428455322655479.45189849209
1994032.940176907372577.728913300985488.15144051377



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')