Free Statistics

of Irreproducible Research!

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 05:07:38 -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/t1324635194zw0x0y4t6w98gl8.htm/, Retrieved Mon, 29 Apr 2024 19:28:13 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=160235, Retrieved Mon, 29 Apr 2024 19:28:13 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact77
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [] [2011-12-23 10:07:38] [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=160235&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=160235&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=160235&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
alpha0.187283900137838
beta0.168376534148886
gammaFALSE

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.187283900137838 \tabularnewline
beta & 0.168376534148886 \tabularnewline
gamma & FALSE \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=160235&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]0.187283900137838[/C][/ROW]
[ROW][C]beta[/C][C]0.168376534148886[/C][/ROW]
[ROW][C]gamma[/C][C]FALSE[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=160235&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=160235&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
alpha0.187283900137838
beta0.168376534148886
gammaFALSE







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
330542650404
424143086.40251811455-672.402518114553
522263300.00848961329-1074.00848961329
627253404.53211489419-679.532114894193
725893561.50630300896-972.506303008957
834703632.94392065154-162.943920651538
924003850.86123020192-1450.86123020192
1031803781.82059443688-601.820594436882
1140093852.81366089458156.186339105416
1239244070.69443563995-146.694435639946
1320724227.22462388711-2155.22462388711
1424343939.62613041173-1505.62613041173
1529563726.20823970702-770.208239707016
1628283626.23436834367-798.234368343671
1726873495.83996090432-808.83996090432
1826293337.95316430229-708.953164302291
1931503176.41727573605-26.4172757360493
2041193141.87632233799977.123677662007
2130303326.09525980316-296.095259803163
2230553262.52365764138-207.523657641382
2338213208.99599514232612.004004857682
2440013328.25173480931672.748265190694
2525293480.09848422987-951.098484229874
2624723297.83273804928-825.832738049278
2731343112.9852630713521.0147369286497
2827893087.40136924078-298.401369240779
2927582992.58612864231-234.586128642307
3029932902.3249660076590.6750339923515
3132822875.83934840159406.160651598408
3234372921.24706460696515.752935393042
3328043003.44351458587-199.443514585868
3430762945.40588957671130.594110423287
3537822953.29718079766828.702819202344
3638893118.06548576794770.934514232059
3722713296.32553123629-1025.32553123629
3824523105.84215499861-653.84215499861
3930842964.31323585651119.686764143491
4025222971.42805759507-449.428057595065
4127692857.78447534318-88.7844753431777
4234382808.88388108913629.116118910874
4328392914.27319236729-75.2731923672932
4437462885.36804525677860.631954743229
4526323058.8822164984-426.882216498404
4628512977.80431709628-126.804317096282
4738712948.92750256702922.072497432977
4836183145.56526009106472.434739908937
4923893272.89096292944-883.890962929444
5023443118.3258914991-774.325891499105
5126782959.86283559135-281.862835591352
5224922884.74185848962-392.741858489617
5328582776.4702197208781.5297802791338
5422462759.59300072477-513.593000724765
5528002615.06311464398184.936885356024
5638692607.188469311861261.81153068814
5730072840.78534236243166.214657637566
5830232874.43600863433148.563991365665
5939072909.46583798428997.534162015724
6042093134.950567738641074.04943226136
6123533408.63468037583-1055.63468037583
6225703250.17463641246-680.174636412461
6329033140.58344128164-237.583441281644
6429103106.39044425968-196.390444259676
6537823073.71921408012708.280785919885
6627593232.81341811139-473.81341811139
6729313155.5790755552-224.579075555196
6836413117.94038809114523.059611908857
6927943236.81666364969-442.816663649694
7030703160.83598783359-90.8359878335932
7135763147.91118427759428.088815722407
7241063245.67208613886860.327913861143
7324523451.51417664358-999.51417664358
7422063277.51889284866-1071.51889284866
7524883056.24877889481-568.248778894806
7624162911.3137761021-495.313776102101
7725342764.41899447271-230.418994472713
7825212659.86865879003-138.868658790035
7930932568.08511302777524.914886972227
8039032617.170316944481285.82968305552
8129072849.3102399464157.6897600535904
8230252853.2585294931171.741470506902
8338122883.98260047573928.017399524269
8442093085.609276304011123.39072369599
8521383359.25147376068-1221.25147376068
8624193155.26873071986-736.268730719862
8726223018.89779157402-396.897791574023
8829122933.56970560642-21.5697056064187
8927082917.85434369743-209.854343697435
9027982860.25870864625-62.2587086462504
9132542828.34208032852425.657919671483
9228952901.22716903697-6.22716903696755
9332632893.03076503965369.969234960346
9437362966.95657983207769.043420167933
9540773139.87374426681937.126255733188
9640973373.8216575924723.178342407597
9721753590.5054318988-1415.5054318988
9831383362.01131657388-224.011316573884
9928233349.60084536145-526.600845361448
10024983263.91428330286-765.914283302861
10128223109.25566231045-287.255662310448
10227383035.18371316205-297.183713162046
10341372949.880945119121187.11905488088
10435153179.99905478917335.000945210832
10537853261.09315300099523.906846999011
10636323394.0872758918237.912724108196
10745043481.021694788171022.97830521183
10844513747.24507437876703.754925621238
10925503975.87541285754-1425.87541285754
11028673760.69641527764-893.696415277637
11134583617.00396191921-159.003961919207
11229613605.89351166444-644.893511664445
11331633483.44756148856-320.447561488562
11428803411.66005226351-531.660052263513
11533313283.550362141247.4496378587969
11630623265.39488042741-203.394880427413
11735343193.84636131344340.153638686561
11836223234.82220641091387.17779358909
11944643296.814266041051167.18573395895
12054113541.695539602821869.30446039718
12125643977.01939351034-1413.01939351034
12228203753.05837859147-933.058378591473
12335083589.56307186911-81.5630718691068
12430883582.96709977537-494.967099775374
12532993483.33881055188-184.338810551876
12629393436.07321932554-497.073219325543
12733203314.562695041375.4373049586311
12834183287.33576274363130.664237256368
12936043287.68221274963316.317787250372
13034953332.77341647034162.226583529658
13141633354.12150638397808.878493616031
13248823522.084435573581359.91556442642
13322113836.13160494529-1625.13160494529
13432603539.88025052162-279.880250521619
13529923486.74701270381-494.747012703811
13624253377.77123147656-952.77123147656
13727073152.96999628678-445.969996286777
13832443009.02115971436234.978840285641
13939653000.01295008625964.987049913746
14033153158.153633236156.846366764004
14133333169.88860428117163.111395718831
14235833187.94050404307395.059495956928
14340213261.89043933817759.109560661831
14449043427.959013937381476.04098606262
14522523774.84309435476-1522.84309435476
14629523512.0628080937-560.062808093699
14735733411.93462837159161.06537162841
14830483451.9412165452-403.9412165452
14930593373.39319851326-314.39319851326
15027313301.70194014366-570.701940143663
15135633164.01154388735398.988456112652
15230923220.51033432954-128.510334329538
15334783174.16462159485303.835378405148
15434783218.37150999455259.628490005454
15543083262.486340287961045.51365971204
15650293486.754261717211542.24573828279
15720753852.6856113073-1777.6856113073
15832643540.78935105199-276.789351051989
15933083501.25846148863-193.258461488628
16036883471.27730902141216.722690978588
16131363524.91320548877-388.913205488775
16228243452.85917695018-628.859176950185
16336443316.03655118767327.963448812333
16446943368.753468099431325.24653190057
16529143650.03605810257-736.036058102566
16636863522.06328679054163.936713209458
16743583567.81054150566790.189458494341
16855873755.762856320071831.23714367993
16922654196.43326583205-1931.43326583205
17036853871.50985617222-186.509856172218
17137543867.50106639633-113.501066396328
17237083873.58648059623-165.586480596234
17332103864.69549576868-654.695495768684
17435173743.55695911401-226.556959114009
17539053695.45758176983209.542418230169
17636703735.64035212239-65.6403521223879
17742213722.21590308125498.784096918746
17844043830.22783064527573.772169354734
17950863970.377271258661115.62272874134
18057254247.186883805151477.81311619485
18123674638.43059977495-2271.43059977495
18238194255.87355141508-436.873551415077
18340674203.12303803304-136.123038033039
18440224202.40572075302-180.405720753017
18539374187.7060173383-250.7060173383
18643654151.93438299463213.065617005367
18742904209.7385658683580.2614341316521

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
3 & 3054 & 2650 & 404 \tabularnewline
4 & 2414 & 3086.40251811455 & -672.402518114553 \tabularnewline
5 & 2226 & 3300.00848961329 & -1074.00848961329 \tabularnewline
6 & 2725 & 3404.53211489419 & -679.532114894193 \tabularnewline
7 & 2589 & 3561.50630300896 & -972.506303008957 \tabularnewline
8 & 3470 & 3632.94392065154 & -162.943920651538 \tabularnewline
9 & 2400 & 3850.86123020192 & -1450.86123020192 \tabularnewline
10 & 3180 & 3781.82059443688 & -601.820594436882 \tabularnewline
11 & 4009 & 3852.81366089458 & 156.186339105416 \tabularnewline
12 & 3924 & 4070.69443563995 & -146.694435639946 \tabularnewline
13 & 2072 & 4227.22462388711 & -2155.22462388711 \tabularnewline
14 & 2434 & 3939.62613041173 & -1505.62613041173 \tabularnewline
15 & 2956 & 3726.20823970702 & -770.208239707016 \tabularnewline
16 & 2828 & 3626.23436834367 & -798.234368343671 \tabularnewline
17 & 2687 & 3495.83996090432 & -808.83996090432 \tabularnewline
18 & 2629 & 3337.95316430229 & -708.953164302291 \tabularnewline
19 & 3150 & 3176.41727573605 & -26.4172757360493 \tabularnewline
20 & 4119 & 3141.87632233799 & 977.123677662007 \tabularnewline
21 & 3030 & 3326.09525980316 & -296.095259803163 \tabularnewline
22 & 3055 & 3262.52365764138 & -207.523657641382 \tabularnewline
23 & 3821 & 3208.99599514232 & 612.004004857682 \tabularnewline
24 & 4001 & 3328.25173480931 & 672.748265190694 \tabularnewline
25 & 2529 & 3480.09848422987 & -951.098484229874 \tabularnewline
26 & 2472 & 3297.83273804928 & -825.832738049278 \tabularnewline
27 & 3134 & 3112.98526307135 & 21.0147369286497 \tabularnewline
28 & 2789 & 3087.40136924078 & -298.401369240779 \tabularnewline
29 & 2758 & 2992.58612864231 & -234.586128642307 \tabularnewline
30 & 2993 & 2902.32496600765 & 90.6750339923515 \tabularnewline
31 & 3282 & 2875.83934840159 & 406.160651598408 \tabularnewline
32 & 3437 & 2921.24706460696 & 515.752935393042 \tabularnewline
33 & 2804 & 3003.44351458587 & -199.443514585868 \tabularnewline
34 & 3076 & 2945.40588957671 & 130.594110423287 \tabularnewline
35 & 3782 & 2953.29718079766 & 828.702819202344 \tabularnewline
36 & 3889 & 3118.06548576794 & 770.934514232059 \tabularnewline
37 & 2271 & 3296.32553123629 & -1025.32553123629 \tabularnewline
38 & 2452 & 3105.84215499861 & -653.84215499861 \tabularnewline
39 & 3084 & 2964.31323585651 & 119.686764143491 \tabularnewline
40 & 2522 & 2971.42805759507 & -449.428057595065 \tabularnewline
41 & 2769 & 2857.78447534318 & -88.7844753431777 \tabularnewline
42 & 3438 & 2808.88388108913 & 629.116118910874 \tabularnewline
43 & 2839 & 2914.27319236729 & -75.2731923672932 \tabularnewline
44 & 3746 & 2885.36804525677 & 860.631954743229 \tabularnewline
45 & 2632 & 3058.8822164984 & -426.882216498404 \tabularnewline
46 & 2851 & 2977.80431709628 & -126.804317096282 \tabularnewline
47 & 3871 & 2948.92750256702 & 922.072497432977 \tabularnewline
48 & 3618 & 3145.56526009106 & 472.434739908937 \tabularnewline
49 & 2389 & 3272.89096292944 & -883.890962929444 \tabularnewline
50 & 2344 & 3118.3258914991 & -774.325891499105 \tabularnewline
51 & 2678 & 2959.86283559135 & -281.862835591352 \tabularnewline
52 & 2492 & 2884.74185848962 & -392.741858489617 \tabularnewline
53 & 2858 & 2776.47021972087 & 81.5297802791338 \tabularnewline
54 & 2246 & 2759.59300072477 & -513.593000724765 \tabularnewline
55 & 2800 & 2615.06311464398 & 184.936885356024 \tabularnewline
56 & 3869 & 2607.18846931186 & 1261.81153068814 \tabularnewline
57 & 3007 & 2840.78534236243 & 166.214657637566 \tabularnewline
58 & 3023 & 2874.43600863433 & 148.563991365665 \tabularnewline
59 & 3907 & 2909.46583798428 & 997.534162015724 \tabularnewline
60 & 4209 & 3134.95056773864 & 1074.04943226136 \tabularnewline
61 & 2353 & 3408.63468037583 & -1055.63468037583 \tabularnewline
62 & 2570 & 3250.17463641246 & -680.174636412461 \tabularnewline
63 & 2903 & 3140.58344128164 & -237.583441281644 \tabularnewline
64 & 2910 & 3106.39044425968 & -196.390444259676 \tabularnewline
65 & 3782 & 3073.71921408012 & 708.280785919885 \tabularnewline
66 & 2759 & 3232.81341811139 & -473.81341811139 \tabularnewline
67 & 2931 & 3155.5790755552 & -224.579075555196 \tabularnewline
68 & 3641 & 3117.94038809114 & 523.059611908857 \tabularnewline
69 & 2794 & 3236.81666364969 & -442.816663649694 \tabularnewline
70 & 3070 & 3160.83598783359 & -90.8359878335932 \tabularnewline
71 & 3576 & 3147.91118427759 & 428.088815722407 \tabularnewline
72 & 4106 & 3245.67208613886 & 860.327913861143 \tabularnewline
73 & 2452 & 3451.51417664358 & -999.51417664358 \tabularnewline
74 & 2206 & 3277.51889284866 & -1071.51889284866 \tabularnewline
75 & 2488 & 3056.24877889481 & -568.248778894806 \tabularnewline
76 & 2416 & 2911.3137761021 & -495.313776102101 \tabularnewline
77 & 2534 & 2764.41899447271 & -230.418994472713 \tabularnewline
78 & 2521 & 2659.86865879003 & -138.868658790035 \tabularnewline
79 & 3093 & 2568.08511302777 & 524.914886972227 \tabularnewline
80 & 3903 & 2617.17031694448 & 1285.82968305552 \tabularnewline
81 & 2907 & 2849.31023994641 & 57.6897600535904 \tabularnewline
82 & 3025 & 2853.2585294931 & 171.741470506902 \tabularnewline
83 & 3812 & 2883.98260047573 & 928.017399524269 \tabularnewline
84 & 4209 & 3085.60927630401 & 1123.39072369599 \tabularnewline
85 & 2138 & 3359.25147376068 & -1221.25147376068 \tabularnewline
86 & 2419 & 3155.26873071986 & -736.268730719862 \tabularnewline
87 & 2622 & 3018.89779157402 & -396.897791574023 \tabularnewline
88 & 2912 & 2933.56970560642 & -21.5697056064187 \tabularnewline
89 & 2708 & 2917.85434369743 & -209.854343697435 \tabularnewline
90 & 2798 & 2860.25870864625 & -62.2587086462504 \tabularnewline
91 & 3254 & 2828.34208032852 & 425.657919671483 \tabularnewline
92 & 2895 & 2901.22716903697 & -6.22716903696755 \tabularnewline
93 & 3263 & 2893.03076503965 & 369.969234960346 \tabularnewline
94 & 3736 & 2966.95657983207 & 769.043420167933 \tabularnewline
95 & 4077 & 3139.87374426681 & 937.126255733188 \tabularnewline
96 & 4097 & 3373.8216575924 & 723.178342407597 \tabularnewline
97 & 2175 & 3590.5054318988 & -1415.5054318988 \tabularnewline
98 & 3138 & 3362.01131657388 & -224.011316573884 \tabularnewline
99 & 2823 & 3349.60084536145 & -526.600845361448 \tabularnewline
100 & 2498 & 3263.91428330286 & -765.914283302861 \tabularnewline
101 & 2822 & 3109.25566231045 & -287.255662310448 \tabularnewline
102 & 2738 & 3035.18371316205 & -297.183713162046 \tabularnewline
103 & 4137 & 2949.88094511912 & 1187.11905488088 \tabularnewline
104 & 3515 & 3179.99905478917 & 335.000945210832 \tabularnewline
105 & 3785 & 3261.09315300099 & 523.906846999011 \tabularnewline
106 & 3632 & 3394.0872758918 & 237.912724108196 \tabularnewline
107 & 4504 & 3481.02169478817 & 1022.97830521183 \tabularnewline
108 & 4451 & 3747.24507437876 & 703.754925621238 \tabularnewline
109 & 2550 & 3975.87541285754 & -1425.87541285754 \tabularnewline
110 & 2867 & 3760.69641527764 & -893.696415277637 \tabularnewline
111 & 3458 & 3617.00396191921 & -159.003961919207 \tabularnewline
112 & 2961 & 3605.89351166444 & -644.893511664445 \tabularnewline
113 & 3163 & 3483.44756148856 & -320.447561488562 \tabularnewline
114 & 2880 & 3411.66005226351 & -531.660052263513 \tabularnewline
115 & 3331 & 3283.5503621412 & 47.4496378587969 \tabularnewline
116 & 3062 & 3265.39488042741 & -203.394880427413 \tabularnewline
117 & 3534 & 3193.84636131344 & 340.153638686561 \tabularnewline
118 & 3622 & 3234.82220641091 & 387.17779358909 \tabularnewline
119 & 4464 & 3296.81426604105 & 1167.18573395895 \tabularnewline
120 & 5411 & 3541.69553960282 & 1869.30446039718 \tabularnewline
121 & 2564 & 3977.01939351034 & -1413.01939351034 \tabularnewline
122 & 2820 & 3753.05837859147 & -933.058378591473 \tabularnewline
123 & 3508 & 3589.56307186911 & -81.5630718691068 \tabularnewline
124 & 3088 & 3582.96709977537 & -494.967099775374 \tabularnewline
125 & 3299 & 3483.33881055188 & -184.338810551876 \tabularnewline
126 & 2939 & 3436.07321932554 & -497.073219325543 \tabularnewline
127 & 3320 & 3314.56269504137 & 5.4373049586311 \tabularnewline
128 & 3418 & 3287.33576274363 & 130.664237256368 \tabularnewline
129 & 3604 & 3287.68221274963 & 316.317787250372 \tabularnewline
130 & 3495 & 3332.77341647034 & 162.226583529658 \tabularnewline
131 & 4163 & 3354.12150638397 & 808.878493616031 \tabularnewline
132 & 4882 & 3522.08443557358 & 1359.91556442642 \tabularnewline
133 & 2211 & 3836.13160494529 & -1625.13160494529 \tabularnewline
134 & 3260 & 3539.88025052162 & -279.880250521619 \tabularnewline
135 & 2992 & 3486.74701270381 & -494.747012703811 \tabularnewline
136 & 2425 & 3377.77123147656 & -952.77123147656 \tabularnewline
137 & 2707 & 3152.96999628678 & -445.969996286777 \tabularnewline
138 & 3244 & 3009.02115971436 & 234.978840285641 \tabularnewline
139 & 3965 & 3000.01295008625 & 964.987049913746 \tabularnewline
140 & 3315 & 3158.153633236 & 156.846366764004 \tabularnewline
141 & 3333 & 3169.88860428117 & 163.111395718831 \tabularnewline
142 & 3583 & 3187.94050404307 & 395.059495956928 \tabularnewline
143 & 4021 & 3261.89043933817 & 759.109560661831 \tabularnewline
144 & 4904 & 3427.95901393738 & 1476.04098606262 \tabularnewline
145 & 2252 & 3774.84309435476 & -1522.84309435476 \tabularnewline
146 & 2952 & 3512.0628080937 & -560.062808093699 \tabularnewline
147 & 3573 & 3411.93462837159 & 161.06537162841 \tabularnewline
148 & 3048 & 3451.9412165452 & -403.9412165452 \tabularnewline
149 & 3059 & 3373.39319851326 & -314.39319851326 \tabularnewline
150 & 2731 & 3301.70194014366 & -570.701940143663 \tabularnewline
151 & 3563 & 3164.01154388735 & 398.988456112652 \tabularnewline
152 & 3092 & 3220.51033432954 & -128.510334329538 \tabularnewline
153 & 3478 & 3174.16462159485 & 303.835378405148 \tabularnewline
154 & 3478 & 3218.37150999455 & 259.628490005454 \tabularnewline
155 & 4308 & 3262.48634028796 & 1045.51365971204 \tabularnewline
156 & 5029 & 3486.75426171721 & 1542.24573828279 \tabularnewline
157 & 2075 & 3852.6856113073 & -1777.6856113073 \tabularnewline
158 & 3264 & 3540.78935105199 & -276.789351051989 \tabularnewline
159 & 3308 & 3501.25846148863 & -193.258461488628 \tabularnewline
160 & 3688 & 3471.27730902141 & 216.722690978588 \tabularnewline
161 & 3136 & 3524.91320548877 & -388.913205488775 \tabularnewline
162 & 2824 & 3452.85917695018 & -628.859176950185 \tabularnewline
163 & 3644 & 3316.03655118767 & 327.963448812333 \tabularnewline
164 & 4694 & 3368.75346809943 & 1325.24653190057 \tabularnewline
165 & 2914 & 3650.03605810257 & -736.036058102566 \tabularnewline
166 & 3686 & 3522.06328679054 & 163.936713209458 \tabularnewline
167 & 4358 & 3567.81054150566 & 790.189458494341 \tabularnewline
168 & 5587 & 3755.76285632007 & 1831.23714367993 \tabularnewline
169 & 2265 & 4196.43326583205 & -1931.43326583205 \tabularnewline
170 & 3685 & 3871.50985617222 & -186.509856172218 \tabularnewline
171 & 3754 & 3867.50106639633 & -113.501066396328 \tabularnewline
172 & 3708 & 3873.58648059623 & -165.586480596234 \tabularnewline
173 & 3210 & 3864.69549576868 & -654.695495768684 \tabularnewline
174 & 3517 & 3743.55695911401 & -226.556959114009 \tabularnewline
175 & 3905 & 3695.45758176983 & 209.542418230169 \tabularnewline
176 & 3670 & 3735.64035212239 & -65.6403521223879 \tabularnewline
177 & 4221 & 3722.21590308125 & 498.784096918746 \tabularnewline
178 & 4404 & 3830.22783064527 & 573.772169354734 \tabularnewline
179 & 5086 & 3970.37727125866 & 1115.62272874134 \tabularnewline
180 & 5725 & 4247.18688380515 & 1477.81311619485 \tabularnewline
181 & 2367 & 4638.43059977495 & -2271.43059977495 \tabularnewline
182 & 3819 & 4255.87355141508 & -436.873551415077 \tabularnewline
183 & 4067 & 4203.12303803304 & -136.123038033039 \tabularnewline
184 & 4022 & 4202.40572075302 & -180.405720753017 \tabularnewline
185 & 3937 & 4187.7060173383 & -250.7060173383 \tabularnewline
186 & 4365 & 4151.93438299463 & 213.065617005367 \tabularnewline
187 & 4290 & 4209.73856586835 & 80.2614341316521 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=160235&T=2

[TABLE]
[ROW][C]Interpolation Forecasts of Exponential Smoothing[/C][/ROW]
[ROW][C]t[/C][C]Observed[/C][C]Fitted[/C][C]Residuals[/C][/ROW]
[ROW][C]3[/C][C]3054[/C][C]2650[/C][C]404[/C][/ROW]
[ROW][C]4[/C][C]2414[/C][C]3086.40251811455[/C][C]-672.402518114553[/C][/ROW]
[ROW][C]5[/C][C]2226[/C][C]3300.00848961329[/C][C]-1074.00848961329[/C][/ROW]
[ROW][C]6[/C][C]2725[/C][C]3404.53211489419[/C][C]-679.532114894193[/C][/ROW]
[ROW][C]7[/C][C]2589[/C][C]3561.50630300896[/C][C]-972.506303008957[/C][/ROW]
[ROW][C]8[/C][C]3470[/C][C]3632.94392065154[/C][C]-162.943920651538[/C][/ROW]
[ROW][C]9[/C][C]2400[/C][C]3850.86123020192[/C][C]-1450.86123020192[/C][/ROW]
[ROW][C]10[/C][C]3180[/C][C]3781.82059443688[/C][C]-601.820594436882[/C][/ROW]
[ROW][C]11[/C][C]4009[/C][C]3852.81366089458[/C][C]156.186339105416[/C][/ROW]
[ROW][C]12[/C][C]3924[/C][C]4070.69443563995[/C][C]-146.694435639946[/C][/ROW]
[ROW][C]13[/C][C]2072[/C][C]4227.22462388711[/C][C]-2155.22462388711[/C][/ROW]
[ROW][C]14[/C][C]2434[/C][C]3939.62613041173[/C][C]-1505.62613041173[/C][/ROW]
[ROW][C]15[/C][C]2956[/C][C]3726.20823970702[/C][C]-770.208239707016[/C][/ROW]
[ROW][C]16[/C][C]2828[/C][C]3626.23436834367[/C][C]-798.234368343671[/C][/ROW]
[ROW][C]17[/C][C]2687[/C][C]3495.83996090432[/C][C]-808.83996090432[/C][/ROW]
[ROW][C]18[/C][C]2629[/C][C]3337.95316430229[/C][C]-708.953164302291[/C][/ROW]
[ROW][C]19[/C][C]3150[/C][C]3176.41727573605[/C][C]-26.4172757360493[/C][/ROW]
[ROW][C]20[/C][C]4119[/C][C]3141.87632233799[/C][C]977.123677662007[/C][/ROW]
[ROW][C]21[/C][C]3030[/C][C]3326.09525980316[/C][C]-296.095259803163[/C][/ROW]
[ROW][C]22[/C][C]3055[/C][C]3262.52365764138[/C][C]-207.523657641382[/C][/ROW]
[ROW][C]23[/C][C]3821[/C][C]3208.99599514232[/C][C]612.004004857682[/C][/ROW]
[ROW][C]24[/C][C]4001[/C][C]3328.25173480931[/C][C]672.748265190694[/C][/ROW]
[ROW][C]25[/C][C]2529[/C][C]3480.09848422987[/C][C]-951.098484229874[/C][/ROW]
[ROW][C]26[/C][C]2472[/C][C]3297.83273804928[/C][C]-825.832738049278[/C][/ROW]
[ROW][C]27[/C][C]3134[/C][C]3112.98526307135[/C][C]21.0147369286497[/C][/ROW]
[ROW][C]28[/C][C]2789[/C][C]3087.40136924078[/C][C]-298.401369240779[/C][/ROW]
[ROW][C]29[/C][C]2758[/C][C]2992.58612864231[/C][C]-234.586128642307[/C][/ROW]
[ROW][C]30[/C][C]2993[/C][C]2902.32496600765[/C][C]90.6750339923515[/C][/ROW]
[ROW][C]31[/C][C]3282[/C][C]2875.83934840159[/C][C]406.160651598408[/C][/ROW]
[ROW][C]32[/C][C]3437[/C][C]2921.24706460696[/C][C]515.752935393042[/C][/ROW]
[ROW][C]33[/C][C]2804[/C][C]3003.44351458587[/C][C]-199.443514585868[/C][/ROW]
[ROW][C]34[/C][C]3076[/C][C]2945.40588957671[/C][C]130.594110423287[/C][/ROW]
[ROW][C]35[/C][C]3782[/C][C]2953.29718079766[/C][C]828.702819202344[/C][/ROW]
[ROW][C]36[/C][C]3889[/C][C]3118.06548576794[/C][C]770.934514232059[/C][/ROW]
[ROW][C]37[/C][C]2271[/C][C]3296.32553123629[/C][C]-1025.32553123629[/C][/ROW]
[ROW][C]38[/C][C]2452[/C][C]3105.84215499861[/C][C]-653.84215499861[/C][/ROW]
[ROW][C]39[/C][C]3084[/C][C]2964.31323585651[/C][C]119.686764143491[/C][/ROW]
[ROW][C]40[/C][C]2522[/C][C]2971.42805759507[/C][C]-449.428057595065[/C][/ROW]
[ROW][C]41[/C][C]2769[/C][C]2857.78447534318[/C][C]-88.7844753431777[/C][/ROW]
[ROW][C]42[/C][C]3438[/C][C]2808.88388108913[/C][C]629.116118910874[/C][/ROW]
[ROW][C]43[/C][C]2839[/C][C]2914.27319236729[/C][C]-75.2731923672932[/C][/ROW]
[ROW][C]44[/C][C]3746[/C][C]2885.36804525677[/C][C]860.631954743229[/C][/ROW]
[ROW][C]45[/C][C]2632[/C][C]3058.8822164984[/C][C]-426.882216498404[/C][/ROW]
[ROW][C]46[/C][C]2851[/C][C]2977.80431709628[/C][C]-126.804317096282[/C][/ROW]
[ROW][C]47[/C][C]3871[/C][C]2948.92750256702[/C][C]922.072497432977[/C][/ROW]
[ROW][C]48[/C][C]3618[/C][C]3145.56526009106[/C][C]472.434739908937[/C][/ROW]
[ROW][C]49[/C][C]2389[/C][C]3272.89096292944[/C][C]-883.890962929444[/C][/ROW]
[ROW][C]50[/C][C]2344[/C][C]3118.3258914991[/C][C]-774.325891499105[/C][/ROW]
[ROW][C]51[/C][C]2678[/C][C]2959.86283559135[/C][C]-281.862835591352[/C][/ROW]
[ROW][C]52[/C][C]2492[/C][C]2884.74185848962[/C][C]-392.741858489617[/C][/ROW]
[ROW][C]53[/C][C]2858[/C][C]2776.47021972087[/C][C]81.5297802791338[/C][/ROW]
[ROW][C]54[/C][C]2246[/C][C]2759.59300072477[/C][C]-513.593000724765[/C][/ROW]
[ROW][C]55[/C][C]2800[/C][C]2615.06311464398[/C][C]184.936885356024[/C][/ROW]
[ROW][C]56[/C][C]3869[/C][C]2607.18846931186[/C][C]1261.81153068814[/C][/ROW]
[ROW][C]57[/C][C]3007[/C][C]2840.78534236243[/C][C]166.214657637566[/C][/ROW]
[ROW][C]58[/C][C]3023[/C][C]2874.43600863433[/C][C]148.563991365665[/C][/ROW]
[ROW][C]59[/C][C]3907[/C][C]2909.46583798428[/C][C]997.534162015724[/C][/ROW]
[ROW][C]60[/C][C]4209[/C][C]3134.95056773864[/C][C]1074.04943226136[/C][/ROW]
[ROW][C]61[/C][C]2353[/C][C]3408.63468037583[/C][C]-1055.63468037583[/C][/ROW]
[ROW][C]62[/C][C]2570[/C][C]3250.17463641246[/C][C]-680.174636412461[/C][/ROW]
[ROW][C]63[/C][C]2903[/C][C]3140.58344128164[/C][C]-237.583441281644[/C][/ROW]
[ROW][C]64[/C][C]2910[/C][C]3106.39044425968[/C][C]-196.390444259676[/C][/ROW]
[ROW][C]65[/C][C]3782[/C][C]3073.71921408012[/C][C]708.280785919885[/C][/ROW]
[ROW][C]66[/C][C]2759[/C][C]3232.81341811139[/C][C]-473.81341811139[/C][/ROW]
[ROW][C]67[/C][C]2931[/C][C]3155.5790755552[/C][C]-224.579075555196[/C][/ROW]
[ROW][C]68[/C][C]3641[/C][C]3117.94038809114[/C][C]523.059611908857[/C][/ROW]
[ROW][C]69[/C][C]2794[/C][C]3236.81666364969[/C][C]-442.816663649694[/C][/ROW]
[ROW][C]70[/C][C]3070[/C][C]3160.83598783359[/C][C]-90.8359878335932[/C][/ROW]
[ROW][C]71[/C][C]3576[/C][C]3147.91118427759[/C][C]428.088815722407[/C][/ROW]
[ROW][C]72[/C][C]4106[/C][C]3245.67208613886[/C][C]860.327913861143[/C][/ROW]
[ROW][C]73[/C][C]2452[/C][C]3451.51417664358[/C][C]-999.51417664358[/C][/ROW]
[ROW][C]74[/C][C]2206[/C][C]3277.51889284866[/C][C]-1071.51889284866[/C][/ROW]
[ROW][C]75[/C][C]2488[/C][C]3056.24877889481[/C][C]-568.248778894806[/C][/ROW]
[ROW][C]76[/C][C]2416[/C][C]2911.3137761021[/C][C]-495.313776102101[/C][/ROW]
[ROW][C]77[/C][C]2534[/C][C]2764.41899447271[/C][C]-230.418994472713[/C][/ROW]
[ROW][C]78[/C][C]2521[/C][C]2659.86865879003[/C][C]-138.868658790035[/C][/ROW]
[ROW][C]79[/C][C]3093[/C][C]2568.08511302777[/C][C]524.914886972227[/C][/ROW]
[ROW][C]80[/C][C]3903[/C][C]2617.17031694448[/C][C]1285.82968305552[/C][/ROW]
[ROW][C]81[/C][C]2907[/C][C]2849.31023994641[/C][C]57.6897600535904[/C][/ROW]
[ROW][C]82[/C][C]3025[/C][C]2853.2585294931[/C][C]171.741470506902[/C][/ROW]
[ROW][C]83[/C][C]3812[/C][C]2883.98260047573[/C][C]928.017399524269[/C][/ROW]
[ROW][C]84[/C][C]4209[/C][C]3085.60927630401[/C][C]1123.39072369599[/C][/ROW]
[ROW][C]85[/C][C]2138[/C][C]3359.25147376068[/C][C]-1221.25147376068[/C][/ROW]
[ROW][C]86[/C][C]2419[/C][C]3155.26873071986[/C][C]-736.268730719862[/C][/ROW]
[ROW][C]87[/C][C]2622[/C][C]3018.89779157402[/C][C]-396.897791574023[/C][/ROW]
[ROW][C]88[/C][C]2912[/C][C]2933.56970560642[/C][C]-21.5697056064187[/C][/ROW]
[ROW][C]89[/C][C]2708[/C][C]2917.85434369743[/C][C]-209.854343697435[/C][/ROW]
[ROW][C]90[/C][C]2798[/C][C]2860.25870864625[/C][C]-62.2587086462504[/C][/ROW]
[ROW][C]91[/C][C]3254[/C][C]2828.34208032852[/C][C]425.657919671483[/C][/ROW]
[ROW][C]92[/C][C]2895[/C][C]2901.22716903697[/C][C]-6.22716903696755[/C][/ROW]
[ROW][C]93[/C][C]3263[/C][C]2893.03076503965[/C][C]369.969234960346[/C][/ROW]
[ROW][C]94[/C][C]3736[/C][C]2966.95657983207[/C][C]769.043420167933[/C][/ROW]
[ROW][C]95[/C][C]4077[/C][C]3139.87374426681[/C][C]937.126255733188[/C][/ROW]
[ROW][C]96[/C][C]4097[/C][C]3373.8216575924[/C][C]723.178342407597[/C][/ROW]
[ROW][C]97[/C][C]2175[/C][C]3590.5054318988[/C][C]-1415.5054318988[/C][/ROW]
[ROW][C]98[/C][C]3138[/C][C]3362.01131657388[/C][C]-224.011316573884[/C][/ROW]
[ROW][C]99[/C][C]2823[/C][C]3349.60084536145[/C][C]-526.600845361448[/C][/ROW]
[ROW][C]100[/C][C]2498[/C][C]3263.91428330286[/C][C]-765.914283302861[/C][/ROW]
[ROW][C]101[/C][C]2822[/C][C]3109.25566231045[/C][C]-287.255662310448[/C][/ROW]
[ROW][C]102[/C][C]2738[/C][C]3035.18371316205[/C][C]-297.183713162046[/C][/ROW]
[ROW][C]103[/C][C]4137[/C][C]2949.88094511912[/C][C]1187.11905488088[/C][/ROW]
[ROW][C]104[/C][C]3515[/C][C]3179.99905478917[/C][C]335.000945210832[/C][/ROW]
[ROW][C]105[/C][C]3785[/C][C]3261.09315300099[/C][C]523.906846999011[/C][/ROW]
[ROW][C]106[/C][C]3632[/C][C]3394.0872758918[/C][C]237.912724108196[/C][/ROW]
[ROW][C]107[/C][C]4504[/C][C]3481.02169478817[/C][C]1022.97830521183[/C][/ROW]
[ROW][C]108[/C][C]4451[/C][C]3747.24507437876[/C][C]703.754925621238[/C][/ROW]
[ROW][C]109[/C][C]2550[/C][C]3975.87541285754[/C][C]-1425.87541285754[/C][/ROW]
[ROW][C]110[/C][C]2867[/C][C]3760.69641527764[/C][C]-893.696415277637[/C][/ROW]
[ROW][C]111[/C][C]3458[/C][C]3617.00396191921[/C][C]-159.003961919207[/C][/ROW]
[ROW][C]112[/C][C]2961[/C][C]3605.89351166444[/C][C]-644.893511664445[/C][/ROW]
[ROW][C]113[/C][C]3163[/C][C]3483.44756148856[/C][C]-320.447561488562[/C][/ROW]
[ROW][C]114[/C][C]2880[/C][C]3411.66005226351[/C][C]-531.660052263513[/C][/ROW]
[ROW][C]115[/C][C]3331[/C][C]3283.5503621412[/C][C]47.4496378587969[/C][/ROW]
[ROW][C]116[/C][C]3062[/C][C]3265.39488042741[/C][C]-203.394880427413[/C][/ROW]
[ROW][C]117[/C][C]3534[/C][C]3193.84636131344[/C][C]340.153638686561[/C][/ROW]
[ROW][C]118[/C][C]3622[/C][C]3234.82220641091[/C][C]387.17779358909[/C][/ROW]
[ROW][C]119[/C][C]4464[/C][C]3296.81426604105[/C][C]1167.18573395895[/C][/ROW]
[ROW][C]120[/C][C]5411[/C][C]3541.69553960282[/C][C]1869.30446039718[/C][/ROW]
[ROW][C]121[/C][C]2564[/C][C]3977.01939351034[/C][C]-1413.01939351034[/C][/ROW]
[ROW][C]122[/C][C]2820[/C][C]3753.05837859147[/C][C]-933.058378591473[/C][/ROW]
[ROW][C]123[/C][C]3508[/C][C]3589.56307186911[/C][C]-81.5630718691068[/C][/ROW]
[ROW][C]124[/C][C]3088[/C][C]3582.96709977537[/C][C]-494.967099775374[/C][/ROW]
[ROW][C]125[/C][C]3299[/C][C]3483.33881055188[/C][C]-184.338810551876[/C][/ROW]
[ROW][C]126[/C][C]2939[/C][C]3436.07321932554[/C][C]-497.073219325543[/C][/ROW]
[ROW][C]127[/C][C]3320[/C][C]3314.56269504137[/C][C]5.4373049586311[/C][/ROW]
[ROW][C]128[/C][C]3418[/C][C]3287.33576274363[/C][C]130.664237256368[/C][/ROW]
[ROW][C]129[/C][C]3604[/C][C]3287.68221274963[/C][C]316.317787250372[/C][/ROW]
[ROW][C]130[/C][C]3495[/C][C]3332.77341647034[/C][C]162.226583529658[/C][/ROW]
[ROW][C]131[/C][C]4163[/C][C]3354.12150638397[/C][C]808.878493616031[/C][/ROW]
[ROW][C]132[/C][C]4882[/C][C]3522.08443557358[/C][C]1359.91556442642[/C][/ROW]
[ROW][C]133[/C][C]2211[/C][C]3836.13160494529[/C][C]-1625.13160494529[/C][/ROW]
[ROW][C]134[/C][C]3260[/C][C]3539.88025052162[/C][C]-279.880250521619[/C][/ROW]
[ROW][C]135[/C][C]2992[/C][C]3486.74701270381[/C][C]-494.747012703811[/C][/ROW]
[ROW][C]136[/C][C]2425[/C][C]3377.77123147656[/C][C]-952.77123147656[/C][/ROW]
[ROW][C]137[/C][C]2707[/C][C]3152.96999628678[/C][C]-445.969996286777[/C][/ROW]
[ROW][C]138[/C][C]3244[/C][C]3009.02115971436[/C][C]234.978840285641[/C][/ROW]
[ROW][C]139[/C][C]3965[/C][C]3000.01295008625[/C][C]964.987049913746[/C][/ROW]
[ROW][C]140[/C][C]3315[/C][C]3158.153633236[/C][C]156.846366764004[/C][/ROW]
[ROW][C]141[/C][C]3333[/C][C]3169.88860428117[/C][C]163.111395718831[/C][/ROW]
[ROW][C]142[/C][C]3583[/C][C]3187.94050404307[/C][C]395.059495956928[/C][/ROW]
[ROW][C]143[/C][C]4021[/C][C]3261.89043933817[/C][C]759.109560661831[/C][/ROW]
[ROW][C]144[/C][C]4904[/C][C]3427.95901393738[/C][C]1476.04098606262[/C][/ROW]
[ROW][C]145[/C][C]2252[/C][C]3774.84309435476[/C][C]-1522.84309435476[/C][/ROW]
[ROW][C]146[/C][C]2952[/C][C]3512.0628080937[/C][C]-560.062808093699[/C][/ROW]
[ROW][C]147[/C][C]3573[/C][C]3411.93462837159[/C][C]161.06537162841[/C][/ROW]
[ROW][C]148[/C][C]3048[/C][C]3451.9412165452[/C][C]-403.9412165452[/C][/ROW]
[ROW][C]149[/C][C]3059[/C][C]3373.39319851326[/C][C]-314.39319851326[/C][/ROW]
[ROW][C]150[/C][C]2731[/C][C]3301.70194014366[/C][C]-570.701940143663[/C][/ROW]
[ROW][C]151[/C][C]3563[/C][C]3164.01154388735[/C][C]398.988456112652[/C][/ROW]
[ROW][C]152[/C][C]3092[/C][C]3220.51033432954[/C][C]-128.510334329538[/C][/ROW]
[ROW][C]153[/C][C]3478[/C][C]3174.16462159485[/C][C]303.835378405148[/C][/ROW]
[ROW][C]154[/C][C]3478[/C][C]3218.37150999455[/C][C]259.628490005454[/C][/ROW]
[ROW][C]155[/C][C]4308[/C][C]3262.48634028796[/C][C]1045.51365971204[/C][/ROW]
[ROW][C]156[/C][C]5029[/C][C]3486.75426171721[/C][C]1542.24573828279[/C][/ROW]
[ROW][C]157[/C][C]2075[/C][C]3852.6856113073[/C][C]-1777.6856113073[/C][/ROW]
[ROW][C]158[/C][C]3264[/C][C]3540.78935105199[/C][C]-276.789351051989[/C][/ROW]
[ROW][C]159[/C][C]3308[/C][C]3501.25846148863[/C][C]-193.258461488628[/C][/ROW]
[ROW][C]160[/C][C]3688[/C][C]3471.27730902141[/C][C]216.722690978588[/C][/ROW]
[ROW][C]161[/C][C]3136[/C][C]3524.91320548877[/C][C]-388.913205488775[/C][/ROW]
[ROW][C]162[/C][C]2824[/C][C]3452.85917695018[/C][C]-628.859176950185[/C][/ROW]
[ROW][C]163[/C][C]3644[/C][C]3316.03655118767[/C][C]327.963448812333[/C][/ROW]
[ROW][C]164[/C][C]4694[/C][C]3368.75346809943[/C][C]1325.24653190057[/C][/ROW]
[ROW][C]165[/C][C]2914[/C][C]3650.03605810257[/C][C]-736.036058102566[/C][/ROW]
[ROW][C]166[/C][C]3686[/C][C]3522.06328679054[/C][C]163.936713209458[/C][/ROW]
[ROW][C]167[/C][C]4358[/C][C]3567.81054150566[/C][C]790.189458494341[/C][/ROW]
[ROW][C]168[/C][C]5587[/C][C]3755.76285632007[/C][C]1831.23714367993[/C][/ROW]
[ROW][C]169[/C][C]2265[/C][C]4196.43326583205[/C][C]-1931.43326583205[/C][/ROW]
[ROW][C]170[/C][C]3685[/C][C]3871.50985617222[/C][C]-186.509856172218[/C][/ROW]
[ROW][C]171[/C][C]3754[/C][C]3867.50106639633[/C][C]-113.501066396328[/C][/ROW]
[ROW][C]172[/C][C]3708[/C][C]3873.58648059623[/C][C]-165.586480596234[/C][/ROW]
[ROW][C]173[/C][C]3210[/C][C]3864.69549576868[/C][C]-654.695495768684[/C][/ROW]
[ROW][C]174[/C][C]3517[/C][C]3743.55695911401[/C][C]-226.556959114009[/C][/ROW]
[ROW][C]175[/C][C]3905[/C][C]3695.45758176983[/C][C]209.542418230169[/C][/ROW]
[ROW][C]176[/C][C]3670[/C][C]3735.64035212239[/C][C]-65.6403521223879[/C][/ROW]
[ROW][C]177[/C][C]4221[/C][C]3722.21590308125[/C][C]498.784096918746[/C][/ROW]
[ROW][C]178[/C][C]4404[/C][C]3830.22783064527[/C][C]573.772169354734[/C][/ROW]
[ROW][C]179[/C][C]5086[/C][C]3970.37727125866[/C][C]1115.62272874134[/C][/ROW]
[ROW][C]180[/C][C]5725[/C][C]4247.18688380515[/C][C]1477.81311619485[/C][/ROW]
[ROW][C]181[/C][C]2367[/C][C]4638.43059977495[/C][C]-2271.43059977495[/C][/ROW]
[ROW][C]182[/C][C]3819[/C][C]4255.87355141508[/C][C]-436.873551415077[/C][/ROW]
[ROW][C]183[/C][C]4067[/C][C]4203.12303803304[/C][C]-136.123038033039[/C][/ROW]
[ROW][C]184[/C][C]4022[/C][C]4202.40572075302[/C][C]-180.405720753017[/C][/ROW]
[ROW][C]185[/C][C]3937[/C][C]4187.7060173383[/C][C]-250.7060173383[/C][/ROW]
[ROW][C]186[/C][C]4365[/C][C]4151.93438299463[/C][C]213.065617005367[/C][/ROW]
[ROW][C]187[/C][C]4290[/C][C]4209.73856586835[/C][C]80.2614341316521[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=160235&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=160235&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
330542650404
424143086.40251811455-672.402518114553
522263300.00848961329-1074.00848961329
627253404.53211489419-679.532114894193
725893561.50630300896-972.506303008957
834703632.94392065154-162.943920651538
924003850.86123020192-1450.86123020192
1031803781.82059443688-601.820594436882
1140093852.81366089458156.186339105416
1239244070.69443563995-146.694435639946
1320724227.22462388711-2155.22462388711
1424343939.62613041173-1505.62613041173
1529563726.20823970702-770.208239707016
1628283626.23436834367-798.234368343671
1726873495.83996090432-808.83996090432
1826293337.95316430229-708.953164302291
1931503176.41727573605-26.4172757360493
2041193141.87632233799977.123677662007
2130303326.09525980316-296.095259803163
2230553262.52365764138-207.523657641382
2338213208.99599514232612.004004857682
2440013328.25173480931672.748265190694
2525293480.09848422987-951.098484229874
2624723297.83273804928-825.832738049278
2731343112.9852630713521.0147369286497
2827893087.40136924078-298.401369240779
2927582992.58612864231-234.586128642307
3029932902.3249660076590.6750339923515
3132822875.83934840159406.160651598408
3234372921.24706460696515.752935393042
3328043003.44351458587-199.443514585868
3430762945.40588957671130.594110423287
3537822953.29718079766828.702819202344
3638893118.06548576794770.934514232059
3722713296.32553123629-1025.32553123629
3824523105.84215499861-653.84215499861
3930842964.31323585651119.686764143491
4025222971.42805759507-449.428057595065
4127692857.78447534318-88.7844753431777
4234382808.88388108913629.116118910874
4328392914.27319236729-75.2731923672932
4437462885.36804525677860.631954743229
4526323058.8822164984-426.882216498404
4628512977.80431709628-126.804317096282
4738712948.92750256702922.072497432977
4836183145.56526009106472.434739908937
4923893272.89096292944-883.890962929444
5023443118.3258914991-774.325891499105
5126782959.86283559135-281.862835591352
5224922884.74185848962-392.741858489617
5328582776.4702197208781.5297802791338
5422462759.59300072477-513.593000724765
5528002615.06311464398184.936885356024
5638692607.188469311861261.81153068814
5730072840.78534236243166.214657637566
5830232874.43600863433148.563991365665
5939072909.46583798428997.534162015724
6042093134.950567738641074.04943226136
6123533408.63468037583-1055.63468037583
6225703250.17463641246-680.174636412461
6329033140.58344128164-237.583441281644
6429103106.39044425968-196.390444259676
6537823073.71921408012708.280785919885
6627593232.81341811139-473.81341811139
6729313155.5790755552-224.579075555196
6836413117.94038809114523.059611908857
6927943236.81666364969-442.816663649694
7030703160.83598783359-90.8359878335932
7135763147.91118427759428.088815722407
7241063245.67208613886860.327913861143
7324523451.51417664358-999.51417664358
7422063277.51889284866-1071.51889284866
7524883056.24877889481-568.248778894806
7624162911.3137761021-495.313776102101
7725342764.41899447271-230.418994472713
7825212659.86865879003-138.868658790035
7930932568.08511302777524.914886972227
8039032617.170316944481285.82968305552
8129072849.3102399464157.6897600535904
8230252853.2585294931171.741470506902
8338122883.98260047573928.017399524269
8442093085.609276304011123.39072369599
8521383359.25147376068-1221.25147376068
8624193155.26873071986-736.268730719862
8726223018.89779157402-396.897791574023
8829122933.56970560642-21.5697056064187
8927082917.85434369743-209.854343697435
9027982860.25870864625-62.2587086462504
9132542828.34208032852425.657919671483
9228952901.22716903697-6.22716903696755
9332632893.03076503965369.969234960346
9437362966.95657983207769.043420167933
9540773139.87374426681937.126255733188
9640973373.8216575924723.178342407597
9721753590.5054318988-1415.5054318988
9831383362.01131657388-224.011316573884
9928233349.60084536145-526.600845361448
10024983263.91428330286-765.914283302861
10128223109.25566231045-287.255662310448
10227383035.18371316205-297.183713162046
10341372949.880945119121187.11905488088
10435153179.99905478917335.000945210832
10537853261.09315300099523.906846999011
10636323394.0872758918237.912724108196
10745043481.021694788171022.97830521183
10844513747.24507437876703.754925621238
10925503975.87541285754-1425.87541285754
11028673760.69641527764-893.696415277637
11134583617.00396191921-159.003961919207
11229613605.89351166444-644.893511664445
11331633483.44756148856-320.447561488562
11428803411.66005226351-531.660052263513
11533313283.550362141247.4496378587969
11630623265.39488042741-203.394880427413
11735343193.84636131344340.153638686561
11836223234.82220641091387.17779358909
11944643296.814266041051167.18573395895
12054113541.695539602821869.30446039718
12125643977.01939351034-1413.01939351034
12228203753.05837859147-933.058378591473
12335083589.56307186911-81.5630718691068
12430883582.96709977537-494.967099775374
12532993483.33881055188-184.338810551876
12629393436.07321932554-497.073219325543
12733203314.562695041375.4373049586311
12834183287.33576274363130.664237256368
12936043287.68221274963316.317787250372
13034953332.77341647034162.226583529658
13141633354.12150638397808.878493616031
13248823522.084435573581359.91556442642
13322113836.13160494529-1625.13160494529
13432603539.88025052162-279.880250521619
13529923486.74701270381-494.747012703811
13624253377.77123147656-952.77123147656
13727073152.96999628678-445.969996286777
13832443009.02115971436234.978840285641
13939653000.01295008625964.987049913746
14033153158.153633236156.846366764004
14133333169.88860428117163.111395718831
14235833187.94050404307395.059495956928
14340213261.89043933817759.109560661831
14449043427.959013937381476.04098606262
14522523774.84309435476-1522.84309435476
14629523512.0628080937-560.062808093699
14735733411.93462837159161.06537162841
14830483451.9412165452-403.9412165452
14930593373.39319851326-314.39319851326
15027313301.70194014366-570.701940143663
15135633164.01154388735398.988456112652
15230923220.51033432954-128.510334329538
15334783174.16462159485303.835378405148
15434783218.37150999455259.628490005454
15543083262.486340287961045.51365971204
15650293486.754261717211542.24573828279
15720753852.6856113073-1777.6856113073
15832643540.78935105199-276.789351051989
15933083501.25846148863-193.258461488628
16036883471.27730902141216.722690978588
16131363524.91320548877-388.913205488775
16228243452.85917695018-628.859176950185
16336443316.03655118767327.963448812333
16446943368.753468099431325.24653190057
16529143650.03605810257-736.036058102566
16636863522.06328679054163.936713209458
16743583567.81054150566790.189458494341
16855873755.762856320071831.23714367993
16922654196.43326583205-1931.43326583205
17036853871.50985617222-186.509856172218
17137543867.50106639633-113.501066396328
17237083873.58648059623-165.586480596234
17332103864.69549576868-654.695495768684
17435173743.55695911401-226.556959114009
17539053695.45758176983209.542418230169
17636703735.64035212239-65.6403521223879
17742213722.21590308125498.784096918746
17844043830.22783064527573.772169354734
17950863970.377271258661115.62272874134
18057254247.186883805151477.81311619485
18123674638.43059977495-2271.43059977495
18238194255.87355141508-436.873551415077
18340674203.12303803304-136.123038033039
18440224202.40572075302-180.405720753017
18539374187.7060173383-250.7060173383
18643654151.93438299463213.065617005367
18742904209.7385658683580.2614341316521







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
1884245.201644659282760.993443476635729.40984584193
1894265.633049035382746.30734256755784.95875550325
1904286.064453411482721.961334343945850.16757247902
1914306.495857787582687.403833294265925.58788228089
1924326.927262163672642.334445626336011.52007870102
1934347.358666539772586.682207498326108.03512558123
1944367.790070915872520.5689156266215.01122620575
1954388.221475291972444.264872894626332.17807768932
1964408.652879668072358.144034313826459.16172502232
1974429.084284044172262.643687060786595.52488102756
1984449.515688420272158.231467019246740.7999098213
1994469.947092796372045.3804925736894.51369301973

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
188 & 4245.20164465928 & 2760.99344347663 & 5729.40984584193 \tabularnewline
189 & 4265.63304903538 & 2746.3073425675 & 5784.95875550325 \tabularnewline
190 & 4286.06445341148 & 2721.96133434394 & 5850.16757247902 \tabularnewline
191 & 4306.49585778758 & 2687.40383329426 & 5925.58788228089 \tabularnewline
192 & 4326.92726216367 & 2642.33444562633 & 6011.52007870102 \tabularnewline
193 & 4347.35866653977 & 2586.68220749832 & 6108.03512558123 \tabularnewline
194 & 4367.79007091587 & 2520.568915626 & 6215.01122620575 \tabularnewline
195 & 4388.22147529197 & 2444.26487289462 & 6332.17807768932 \tabularnewline
196 & 4408.65287966807 & 2358.14403431382 & 6459.16172502232 \tabularnewline
197 & 4429.08428404417 & 2262.64368706078 & 6595.52488102756 \tabularnewline
198 & 4449.51568842027 & 2158.23146701924 & 6740.7999098213 \tabularnewline
199 & 4469.94709279637 & 2045.380492573 & 6894.51369301973 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=160235&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]4245.20164465928[/C][C]2760.99344347663[/C][C]5729.40984584193[/C][/ROW]
[ROW][C]189[/C][C]4265.63304903538[/C][C]2746.3073425675[/C][C]5784.95875550325[/C][/ROW]
[ROW][C]190[/C][C]4286.06445341148[/C][C]2721.96133434394[/C][C]5850.16757247902[/C][/ROW]
[ROW][C]191[/C][C]4306.49585778758[/C][C]2687.40383329426[/C][C]5925.58788228089[/C][/ROW]
[ROW][C]192[/C][C]4326.92726216367[/C][C]2642.33444562633[/C][C]6011.52007870102[/C][/ROW]
[ROW][C]193[/C][C]4347.35866653977[/C][C]2586.68220749832[/C][C]6108.03512558123[/C][/ROW]
[ROW][C]194[/C][C]4367.79007091587[/C][C]2520.568915626[/C][C]6215.01122620575[/C][/ROW]
[ROW][C]195[/C][C]4388.22147529197[/C][C]2444.26487289462[/C][C]6332.17807768932[/C][/ROW]
[ROW][C]196[/C][C]4408.65287966807[/C][C]2358.14403431382[/C][C]6459.16172502232[/C][/ROW]
[ROW][C]197[/C][C]4429.08428404417[/C][C]2262.64368706078[/C][C]6595.52488102756[/C][/ROW]
[ROW][C]198[/C][C]4449.51568842027[/C][C]2158.23146701924[/C][C]6740.7999098213[/C][/ROW]
[ROW][C]199[/C][C]4469.94709279637[/C][C]2045.380492573[/C][C]6894.51369301973[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=160235&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=160235&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
1884245.201644659282760.993443476635729.40984584193
1894265.633049035382746.30734256755784.95875550325
1904286.064453411482721.961334343945850.16757247902
1914306.495857787582687.403833294265925.58788228089
1924326.927262163672642.334445626336011.52007870102
1934347.358666539772586.682207498326108.03512558123
1944367.790070915872520.5689156266215.01122620575
1954388.221475291972444.264872894626332.17807768932
1964408.652879668072358.144034313826459.16172502232
1974429.084284044172262.643687060786595.52488102756
1984449.515688420272158.231467019246740.7999098213
1994469.947092796372045.3804925736894.51369301973



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