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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, 16 Dec 2016 13:10:12 +0100
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2016/Dec/16/t1481890254hfvu7c71e3s9l7x.htm/, Retrieved Sat, 18 May 2024 08:15:43 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=300203, Retrieved Sat, 18 May 2024 08:15:43 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact67
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [Exponential Smoot...] [2016-12-16 12:10:12] [d5bfc1731fe289380efec318f4354749] [Current]
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Dataseries X:
3280
3444
3855
3811
3785
4075
3547
3863
4064
4176
4191
4307
4179
4622
4798
4673
4635
4875
4097
4262
4135
4238
3891
3573
3963
4192
4306
4316
4249
4408
3731
4096
4102
3962
3845
3734
3933
4176
4150
4137
4016
4113
3611
3474
3654
3712
3394
3348
3476
3908
4009
4102
4253
4532
4080
4402
4597
4844
4877
4735
4768
5251
5553
5548
5519
5798
4918
5271
5492
5547
5244
5149
5453
5584
5773
5811
5687
5647
4892
5235
5311
5378
4994
4559
4895
5104
5477
5302
5360
5540
4877
5241
5233
5561
5049
4482
4846
4636
4431
4702
4775
4834
4344
4800
4981
5069
4655
4254
4753
4888
5048
4991
4962
5150
4444
4815




Summary of computational transaction
Raw Input view raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R ServerBig Analytics Cloud Computing Center

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input view raw input (R code)  \tabularnewline
Raw Outputview raw output of R engine  \tabularnewline
Computing time2 seconds \tabularnewline
R ServerBig Analytics Cloud Computing Center \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=300203&T=0

[TABLE]
[ROW]
Summary of computational transaction[/C][/ROW] [ROW]Raw Input[/C] view raw input (R code) [/C][/ROW] [ROW]Raw Output[/C]view raw output of R engine [/C][/ROW] [ROW]Computing time[/C]2 seconds[/C][/ROW] [ROW]R Server[/C]Big Analytics Cloud Computing Center[/C][/ROW] [/TABLE] Source: https://freestatistics.org/blog/index.php?pk=300203&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=300203&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 Input view raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R ServerBig Analytics Cloud Computing Center







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.777338307029229
beta0.0170416067528951
gamma1

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.777338307029229 \tabularnewline
beta & 0.0170416067528951 \tabularnewline
gamma & 1 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=300203&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]0.777338307029229[/C][/ROW]
[ROW][C]beta[/C][C]0.0170416067528951[/C][/ROW]
[ROW][C]gamma[/C][C]1[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=300203&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=300203&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
alpha0.777338307029229
beta0.0170416067528951
gamma1







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
1341793748.54807692308430.451923076921
1446224537.6021296617984.3978703382081
1547984811.73147073735-13.731470737348
1646734722.44088053793-49.4408805379262
1746354707.19538353325-72.1953835332524
1848754984.47222734614-109.472227346138
1940974078.3638303069518.6361696930508
2042624371.41920615869-109.419206158688
2141354446.64941312531-311.649413125313
2242384284.71655105458-46.7165510545783
2338914234.98229293118-343.982292931177
2435734053.1985539328-480.198553932796
2539633623.51261589351339.487384106494
2641924250.30737658325-58.3073765832523
2743064375.27029753141-69.2702975314069
2843164217.7338841841498.2661158158589
2942494297.07457801677-48.0745780167663
3044084569.95529388877-161.955293888775
3137313636.0333543085194.9666456914879
3240963945.38018632177150.619813678232
3341024166.63440570471-64.6344057047099
3439624247.89304309221-285.893043092213
3538453935.06652099447-90.0665209944736
3637343912.71321980597-178.713219805971
3739333896.271968951636.7280310483952
3841764191.51187958896-15.5118795889612
3941504340.23252090248-190.232520902483
4041374117.301244864919.6987551351012
4140164093.27302953616-77.2730295361634
4241134308.00197953628-195.001979536279
4336113395.06266876034215.937331239657
4434743801.90339674264-327.903396742635
4536543587.9822025913366.0177974086741
4637123707.994619189214.00538081078867
4733943654.41926329243-260.419263292431
4833483467.94829824302-119.948298243018
4934763533.97852257319-57.9785225731916
5039083731.53372450989176.466275490111
5140093980.6920490034628.3079509965442
5241023967.38863577311134.611364226891
5342534005.62107884545247.37892115455
5445324445.3279812136286.6720187863848
5540803845.40374589724234.59625410276
5644024148.46209251389253.537907486114
5745974484.73688520217112.263114797834
5848444638.01061270382205.989387296176
5948774696.36446844587180.635531554126
6047354903.65903294331-168.659032943309
6147684964.6167958448-196.6167958448
6252515123.76244204348127.237557956524
6355535318.16948704825234.830512951748
6455485508.3147660035139.685233996488
6555195515.850107055213.14989294478528
6657985744.6734345305353.3265654694669
6749185166.07210668315-248.072106683153
6852715106.06401948865164.935980511353
6954925348.74752972512143.252470274876
7055475554.12911373293-7.12911373292536
7152445445.49865435756-201.498654357555
7251495277.235183373-128.235183373004
7354535363.1903534975289.8096465024755
7455845820.69004535802-236.690045358023
7557735754.9319109413218.0680890586818
7658115729.0294620527281.9705379472834
7756875757.76131214343-70.7613121434297
7856475935.78548612007-288.785486120075
7948925015.08786094045-123.087860940449
8052355136.8020179272398.1979820727702
8153115314.50147610762-3.50147610762451
8253785362.0993522764915.9006477235098
8349945218.1752095931-224.175209593097
8445595038.38000546945-479.380005469446
8548954885.05809008629.94190991380037
8651045191.84754632209-87.8475463220911
8754775284.55998583043192.440014169565
8853025396.78678289661-94.7867828966055
8953605240.12398477802119.876015221978
9055405506.3307355679533.6692644320528
9148774865.9941535166811.0058464833201
9252415135.80281786072105.197182139282
9352335290.97761930752-57.977619307524
9455615294.50673218048266.493267819515
9550495289.19927954769-240.199279547685
9644825037.18849157558-555.188491575579
9748464929.95161137501-83.9516113750105
9846365136.79688391669-500.796883916692
9944314960.26372166779-529.263721667791
10047024427.31411107698274.685888923024
10147754590.33415276681184.665847233193
10248344873.2482543425-39.2482543425003
10343444155.75654501247188.243454987529
10448004571.23220569513228.767794304868
10549814774.68796308586206.312036914143
10650695047.9654198149121.0345801850854
10746554727.8395247093-72.839524709304
10842544526.81190300248-272.811903002479
10947534738.7682817752614.2317182247416
11048884925.18510533818-37.185105338177
11150485104.90353447468-56.9035344746799
11249915126.61064373537-135.610643735369
11349624953.676492107788.32350789222437
11451505050.3488553688999.6511446311115
11544444494.01568232276-50.0156823227562
11648154732.6833889485382.3166110514703

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 4179 & 3748.54807692308 & 430.451923076921 \tabularnewline
14 & 4622 & 4537.60212966179 & 84.3978703382081 \tabularnewline
15 & 4798 & 4811.73147073735 & -13.731470737348 \tabularnewline
16 & 4673 & 4722.44088053793 & -49.4408805379262 \tabularnewline
17 & 4635 & 4707.19538353325 & -72.1953835332524 \tabularnewline
18 & 4875 & 4984.47222734614 & -109.472227346138 \tabularnewline
19 & 4097 & 4078.36383030695 & 18.6361696930508 \tabularnewline
20 & 4262 & 4371.41920615869 & -109.419206158688 \tabularnewline
21 & 4135 & 4446.64941312531 & -311.649413125313 \tabularnewline
22 & 4238 & 4284.71655105458 & -46.7165510545783 \tabularnewline
23 & 3891 & 4234.98229293118 & -343.982292931177 \tabularnewline
24 & 3573 & 4053.1985539328 & -480.198553932796 \tabularnewline
25 & 3963 & 3623.51261589351 & 339.487384106494 \tabularnewline
26 & 4192 & 4250.30737658325 & -58.3073765832523 \tabularnewline
27 & 4306 & 4375.27029753141 & -69.2702975314069 \tabularnewline
28 & 4316 & 4217.73388418414 & 98.2661158158589 \tabularnewline
29 & 4249 & 4297.07457801677 & -48.0745780167663 \tabularnewline
30 & 4408 & 4569.95529388877 & -161.955293888775 \tabularnewline
31 & 3731 & 3636.03335430851 & 94.9666456914879 \tabularnewline
32 & 4096 & 3945.38018632177 & 150.619813678232 \tabularnewline
33 & 4102 & 4166.63440570471 & -64.6344057047099 \tabularnewline
34 & 3962 & 4247.89304309221 & -285.893043092213 \tabularnewline
35 & 3845 & 3935.06652099447 & -90.0665209944736 \tabularnewline
36 & 3734 & 3912.71321980597 & -178.713219805971 \tabularnewline
37 & 3933 & 3896.2719689516 & 36.7280310483952 \tabularnewline
38 & 4176 & 4191.51187958896 & -15.5118795889612 \tabularnewline
39 & 4150 & 4340.23252090248 & -190.232520902483 \tabularnewline
40 & 4137 & 4117.3012448649 & 19.6987551351012 \tabularnewline
41 & 4016 & 4093.27302953616 & -77.2730295361634 \tabularnewline
42 & 4113 & 4308.00197953628 & -195.001979536279 \tabularnewline
43 & 3611 & 3395.06266876034 & 215.937331239657 \tabularnewline
44 & 3474 & 3801.90339674264 & -327.903396742635 \tabularnewline
45 & 3654 & 3587.98220259133 & 66.0177974086741 \tabularnewline
46 & 3712 & 3707.99461918921 & 4.00538081078867 \tabularnewline
47 & 3394 & 3654.41926329243 & -260.419263292431 \tabularnewline
48 & 3348 & 3467.94829824302 & -119.948298243018 \tabularnewline
49 & 3476 & 3533.97852257319 & -57.9785225731916 \tabularnewline
50 & 3908 & 3731.53372450989 & 176.466275490111 \tabularnewline
51 & 4009 & 3980.69204900346 & 28.3079509965442 \tabularnewline
52 & 4102 & 3967.38863577311 & 134.611364226891 \tabularnewline
53 & 4253 & 4005.62107884545 & 247.37892115455 \tabularnewline
54 & 4532 & 4445.32798121362 & 86.6720187863848 \tabularnewline
55 & 4080 & 3845.40374589724 & 234.59625410276 \tabularnewline
56 & 4402 & 4148.46209251389 & 253.537907486114 \tabularnewline
57 & 4597 & 4484.73688520217 & 112.263114797834 \tabularnewline
58 & 4844 & 4638.01061270382 & 205.989387296176 \tabularnewline
59 & 4877 & 4696.36446844587 & 180.635531554126 \tabularnewline
60 & 4735 & 4903.65903294331 & -168.659032943309 \tabularnewline
61 & 4768 & 4964.6167958448 & -196.6167958448 \tabularnewline
62 & 5251 & 5123.76244204348 & 127.237557956524 \tabularnewline
63 & 5553 & 5318.16948704825 & 234.830512951748 \tabularnewline
64 & 5548 & 5508.31476600351 & 39.685233996488 \tabularnewline
65 & 5519 & 5515.85010705521 & 3.14989294478528 \tabularnewline
66 & 5798 & 5744.67343453053 & 53.3265654694669 \tabularnewline
67 & 4918 & 5166.07210668315 & -248.072106683153 \tabularnewline
68 & 5271 & 5106.06401948865 & 164.935980511353 \tabularnewline
69 & 5492 & 5348.74752972512 & 143.252470274876 \tabularnewline
70 & 5547 & 5554.12911373293 & -7.12911373292536 \tabularnewline
71 & 5244 & 5445.49865435756 & -201.498654357555 \tabularnewline
72 & 5149 & 5277.235183373 & -128.235183373004 \tabularnewline
73 & 5453 & 5363.19035349752 & 89.8096465024755 \tabularnewline
74 & 5584 & 5820.69004535802 & -236.690045358023 \tabularnewline
75 & 5773 & 5754.93191094132 & 18.0680890586818 \tabularnewline
76 & 5811 & 5729.02946205272 & 81.9705379472834 \tabularnewline
77 & 5687 & 5757.76131214343 & -70.7613121434297 \tabularnewline
78 & 5647 & 5935.78548612007 & -288.785486120075 \tabularnewline
79 & 4892 & 5015.08786094045 & -123.087860940449 \tabularnewline
80 & 5235 & 5136.80201792723 & 98.1979820727702 \tabularnewline
81 & 5311 & 5314.50147610762 & -3.50147610762451 \tabularnewline
82 & 5378 & 5362.09935227649 & 15.9006477235098 \tabularnewline
83 & 4994 & 5218.1752095931 & -224.175209593097 \tabularnewline
84 & 4559 & 5038.38000546945 & -479.380005469446 \tabularnewline
85 & 4895 & 4885.0580900862 & 9.94190991380037 \tabularnewline
86 & 5104 & 5191.84754632209 & -87.8475463220911 \tabularnewline
87 & 5477 & 5284.55998583043 & 192.440014169565 \tabularnewline
88 & 5302 & 5396.78678289661 & -94.7867828966055 \tabularnewline
89 & 5360 & 5240.12398477802 & 119.876015221978 \tabularnewline
90 & 5540 & 5506.33073556795 & 33.6692644320528 \tabularnewline
91 & 4877 & 4865.99415351668 & 11.0058464833201 \tabularnewline
92 & 5241 & 5135.80281786072 & 105.197182139282 \tabularnewline
93 & 5233 & 5290.97761930752 & -57.977619307524 \tabularnewline
94 & 5561 & 5294.50673218048 & 266.493267819515 \tabularnewline
95 & 5049 & 5289.19927954769 & -240.199279547685 \tabularnewline
96 & 4482 & 5037.18849157558 & -555.188491575579 \tabularnewline
97 & 4846 & 4929.95161137501 & -83.9516113750105 \tabularnewline
98 & 4636 & 5136.79688391669 & -500.796883916692 \tabularnewline
99 & 4431 & 4960.26372166779 & -529.263721667791 \tabularnewline
100 & 4702 & 4427.31411107698 & 274.685888923024 \tabularnewline
101 & 4775 & 4590.33415276681 & 184.665847233193 \tabularnewline
102 & 4834 & 4873.2482543425 & -39.2482543425003 \tabularnewline
103 & 4344 & 4155.75654501247 & 188.243454987529 \tabularnewline
104 & 4800 & 4571.23220569513 & 228.767794304868 \tabularnewline
105 & 4981 & 4774.68796308586 & 206.312036914143 \tabularnewline
106 & 5069 & 5047.96541981491 & 21.0345801850854 \tabularnewline
107 & 4655 & 4727.8395247093 & -72.839524709304 \tabularnewline
108 & 4254 & 4526.81190300248 & -272.811903002479 \tabularnewline
109 & 4753 & 4738.76828177526 & 14.2317182247416 \tabularnewline
110 & 4888 & 4925.18510533818 & -37.185105338177 \tabularnewline
111 & 5048 & 5104.90353447468 & -56.9035344746799 \tabularnewline
112 & 4991 & 5126.61064373537 & -135.610643735369 \tabularnewline
113 & 4962 & 4953.67649210778 & 8.32350789222437 \tabularnewline
114 & 5150 & 5050.34885536889 & 99.6511446311115 \tabularnewline
115 & 4444 & 4494.01568232276 & -50.0156823227562 \tabularnewline
116 & 4815 & 4732.68338894853 & 82.3166110514703 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=300203&T=2

[TABLE]
[ROW][C]Interpolation Forecasts of Exponential Smoothing[/C][/ROW]
[ROW][C]t[/C][C]Observed[/C][C]Fitted[/C][C]Residuals[/C][/ROW]
[ROW][C]13[/C][C]4179[/C][C]3748.54807692308[/C][C]430.451923076921[/C][/ROW]
[ROW][C]14[/C][C]4622[/C][C]4537.60212966179[/C][C]84.3978703382081[/C][/ROW]
[ROW][C]15[/C][C]4798[/C][C]4811.73147073735[/C][C]-13.731470737348[/C][/ROW]
[ROW][C]16[/C][C]4673[/C][C]4722.44088053793[/C][C]-49.4408805379262[/C][/ROW]
[ROW][C]17[/C][C]4635[/C][C]4707.19538353325[/C][C]-72.1953835332524[/C][/ROW]
[ROW][C]18[/C][C]4875[/C][C]4984.47222734614[/C][C]-109.472227346138[/C][/ROW]
[ROW][C]19[/C][C]4097[/C][C]4078.36383030695[/C][C]18.6361696930508[/C][/ROW]
[ROW][C]20[/C][C]4262[/C][C]4371.41920615869[/C][C]-109.419206158688[/C][/ROW]
[ROW][C]21[/C][C]4135[/C][C]4446.64941312531[/C][C]-311.649413125313[/C][/ROW]
[ROW][C]22[/C][C]4238[/C][C]4284.71655105458[/C][C]-46.7165510545783[/C][/ROW]
[ROW][C]23[/C][C]3891[/C][C]4234.98229293118[/C][C]-343.982292931177[/C][/ROW]
[ROW][C]24[/C][C]3573[/C][C]4053.1985539328[/C][C]-480.198553932796[/C][/ROW]
[ROW][C]25[/C][C]3963[/C][C]3623.51261589351[/C][C]339.487384106494[/C][/ROW]
[ROW][C]26[/C][C]4192[/C][C]4250.30737658325[/C][C]-58.3073765832523[/C][/ROW]
[ROW][C]27[/C][C]4306[/C][C]4375.27029753141[/C][C]-69.2702975314069[/C][/ROW]
[ROW][C]28[/C][C]4316[/C][C]4217.73388418414[/C][C]98.2661158158589[/C][/ROW]
[ROW][C]29[/C][C]4249[/C][C]4297.07457801677[/C][C]-48.0745780167663[/C][/ROW]
[ROW][C]30[/C][C]4408[/C][C]4569.95529388877[/C][C]-161.955293888775[/C][/ROW]
[ROW][C]31[/C][C]3731[/C][C]3636.03335430851[/C][C]94.9666456914879[/C][/ROW]
[ROW][C]32[/C][C]4096[/C][C]3945.38018632177[/C][C]150.619813678232[/C][/ROW]
[ROW][C]33[/C][C]4102[/C][C]4166.63440570471[/C][C]-64.6344057047099[/C][/ROW]
[ROW][C]34[/C][C]3962[/C][C]4247.89304309221[/C][C]-285.893043092213[/C][/ROW]
[ROW][C]35[/C][C]3845[/C][C]3935.06652099447[/C][C]-90.0665209944736[/C][/ROW]
[ROW][C]36[/C][C]3734[/C][C]3912.71321980597[/C][C]-178.713219805971[/C][/ROW]
[ROW][C]37[/C][C]3933[/C][C]3896.2719689516[/C][C]36.7280310483952[/C][/ROW]
[ROW][C]38[/C][C]4176[/C][C]4191.51187958896[/C][C]-15.5118795889612[/C][/ROW]
[ROW][C]39[/C][C]4150[/C][C]4340.23252090248[/C][C]-190.232520902483[/C][/ROW]
[ROW][C]40[/C][C]4137[/C][C]4117.3012448649[/C][C]19.6987551351012[/C][/ROW]
[ROW][C]41[/C][C]4016[/C][C]4093.27302953616[/C][C]-77.2730295361634[/C][/ROW]
[ROW][C]42[/C][C]4113[/C][C]4308.00197953628[/C][C]-195.001979536279[/C][/ROW]
[ROW][C]43[/C][C]3611[/C][C]3395.06266876034[/C][C]215.937331239657[/C][/ROW]
[ROW][C]44[/C][C]3474[/C][C]3801.90339674264[/C][C]-327.903396742635[/C][/ROW]
[ROW][C]45[/C][C]3654[/C][C]3587.98220259133[/C][C]66.0177974086741[/C][/ROW]
[ROW][C]46[/C][C]3712[/C][C]3707.99461918921[/C][C]4.00538081078867[/C][/ROW]
[ROW][C]47[/C][C]3394[/C][C]3654.41926329243[/C][C]-260.419263292431[/C][/ROW]
[ROW][C]48[/C][C]3348[/C][C]3467.94829824302[/C][C]-119.948298243018[/C][/ROW]
[ROW][C]49[/C][C]3476[/C][C]3533.97852257319[/C][C]-57.9785225731916[/C][/ROW]
[ROW][C]50[/C][C]3908[/C][C]3731.53372450989[/C][C]176.466275490111[/C][/ROW]
[ROW][C]51[/C][C]4009[/C][C]3980.69204900346[/C][C]28.3079509965442[/C][/ROW]
[ROW][C]52[/C][C]4102[/C][C]3967.38863577311[/C][C]134.611364226891[/C][/ROW]
[ROW][C]53[/C][C]4253[/C][C]4005.62107884545[/C][C]247.37892115455[/C][/ROW]
[ROW][C]54[/C][C]4532[/C][C]4445.32798121362[/C][C]86.6720187863848[/C][/ROW]
[ROW][C]55[/C][C]4080[/C][C]3845.40374589724[/C][C]234.59625410276[/C][/ROW]
[ROW][C]56[/C][C]4402[/C][C]4148.46209251389[/C][C]253.537907486114[/C][/ROW]
[ROW][C]57[/C][C]4597[/C][C]4484.73688520217[/C][C]112.263114797834[/C][/ROW]
[ROW][C]58[/C][C]4844[/C][C]4638.01061270382[/C][C]205.989387296176[/C][/ROW]
[ROW][C]59[/C][C]4877[/C][C]4696.36446844587[/C][C]180.635531554126[/C][/ROW]
[ROW][C]60[/C][C]4735[/C][C]4903.65903294331[/C][C]-168.659032943309[/C][/ROW]
[ROW][C]61[/C][C]4768[/C][C]4964.6167958448[/C][C]-196.6167958448[/C][/ROW]
[ROW][C]62[/C][C]5251[/C][C]5123.76244204348[/C][C]127.237557956524[/C][/ROW]
[ROW][C]63[/C][C]5553[/C][C]5318.16948704825[/C][C]234.830512951748[/C][/ROW]
[ROW][C]64[/C][C]5548[/C][C]5508.31476600351[/C][C]39.685233996488[/C][/ROW]
[ROW][C]65[/C][C]5519[/C][C]5515.85010705521[/C][C]3.14989294478528[/C][/ROW]
[ROW][C]66[/C][C]5798[/C][C]5744.67343453053[/C][C]53.3265654694669[/C][/ROW]
[ROW][C]67[/C][C]4918[/C][C]5166.07210668315[/C][C]-248.072106683153[/C][/ROW]
[ROW][C]68[/C][C]5271[/C][C]5106.06401948865[/C][C]164.935980511353[/C][/ROW]
[ROW][C]69[/C][C]5492[/C][C]5348.74752972512[/C][C]143.252470274876[/C][/ROW]
[ROW][C]70[/C][C]5547[/C][C]5554.12911373293[/C][C]-7.12911373292536[/C][/ROW]
[ROW][C]71[/C][C]5244[/C][C]5445.49865435756[/C][C]-201.498654357555[/C][/ROW]
[ROW][C]72[/C][C]5149[/C][C]5277.235183373[/C][C]-128.235183373004[/C][/ROW]
[ROW][C]73[/C][C]5453[/C][C]5363.19035349752[/C][C]89.8096465024755[/C][/ROW]
[ROW][C]74[/C][C]5584[/C][C]5820.69004535802[/C][C]-236.690045358023[/C][/ROW]
[ROW][C]75[/C][C]5773[/C][C]5754.93191094132[/C][C]18.0680890586818[/C][/ROW]
[ROW][C]76[/C][C]5811[/C][C]5729.02946205272[/C][C]81.9705379472834[/C][/ROW]
[ROW][C]77[/C][C]5687[/C][C]5757.76131214343[/C][C]-70.7613121434297[/C][/ROW]
[ROW][C]78[/C][C]5647[/C][C]5935.78548612007[/C][C]-288.785486120075[/C][/ROW]
[ROW][C]79[/C][C]4892[/C][C]5015.08786094045[/C][C]-123.087860940449[/C][/ROW]
[ROW][C]80[/C][C]5235[/C][C]5136.80201792723[/C][C]98.1979820727702[/C][/ROW]
[ROW][C]81[/C][C]5311[/C][C]5314.50147610762[/C][C]-3.50147610762451[/C][/ROW]
[ROW][C]82[/C][C]5378[/C][C]5362.09935227649[/C][C]15.9006477235098[/C][/ROW]
[ROW][C]83[/C][C]4994[/C][C]5218.1752095931[/C][C]-224.175209593097[/C][/ROW]
[ROW][C]84[/C][C]4559[/C][C]5038.38000546945[/C][C]-479.380005469446[/C][/ROW]
[ROW][C]85[/C][C]4895[/C][C]4885.0580900862[/C][C]9.94190991380037[/C][/ROW]
[ROW][C]86[/C][C]5104[/C][C]5191.84754632209[/C][C]-87.8475463220911[/C][/ROW]
[ROW][C]87[/C][C]5477[/C][C]5284.55998583043[/C][C]192.440014169565[/C][/ROW]
[ROW][C]88[/C][C]5302[/C][C]5396.78678289661[/C][C]-94.7867828966055[/C][/ROW]
[ROW][C]89[/C][C]5360[/C][C]5240.12398477802[/C][C]119.876015221978[/C][/ROW]
[ROW][C]90[/C][C]5540[/C][C]5506.33073556795[/C][C]33.6692644320528[/C][/ROW]
[ROW][C]91[/C][C]4877[/C][C]4865.99415351668[/C][C]11.0058464833201[/C][/ROW]
[ROW][C]92[/C][C]5241[/C][C]5135.80281786072[/C][C]105.197182139282[/C][/ROW]
[ROW][C]93[/C][C]5233[/C][C]5290.97761930752[/C][C]-57.977619307524[/C][/ROW]
[ROW][C]94[/C][C]5561[/C][C]5294.50673218048[/C][C]266.493267819515[/C][/ROW]
[ROW][C]95[/C][C]5049[/C][C]5289.19927954769[/C][C]-240.199279547685[/C][/ROW]
[ROW][C]96[/C][C]4482[/C][C]5037.18849157558[/C][C]-555.188491575579[/C][/ROW]
[ROW][C]97[/C][C]4846[/C][C]4929.95161137501[/C][C]-83.9516113750105[/C][/ROW]
[ROW][C]98[/C][C]4636[/C][C]5136.79688391669[/C][C]-500.796883916692[/C][/ROW]
[ROW][C]99[/C][C]4431[/C][C]4960.26372166779[/C][C]-529.263721667791[/C][/ROW]
[ROW][C]100[/C][C]4702[/C][C]4427.31411107698[/C][C]274.685888923024[/C][/ROW]
[ROW][C]101[/C][C]4775[/C][C]4590.33415276681[/C][C]184.665847233193[/C][/ROW]
[ROW][C]102[/C][C]4834[/C][C]4873.2482543425[/C][C]-39.2482543425003[/C][/ROW]
[ROW][C]103[/C][C]4344[/C][C]4155.75654501247[/C][C]188.243454987529[/C][/ROW]
[ROW][C]104[/C][C]4800[/C][C]4571.23220569513[/C][C]228.767794304868[/C][/ROW]
[ROW][C]105[/C][C]4981[/C][C]4774.68796308586[/C][C]206.312036914143[/C][/ROW]
[ROW][C]106[/C][C]5069[/C][C]5047.96541981491[/C][C]21.0345801850854[/C][/ROW]
[ROW][C]107[/C][C]4655[/C][C]4727.8395247093[/C][C]-72.839524709304[/C][/ROW]
[ROW][C]108[/C][C]4254[/C][C]4526.81190300248[/C][C]-272.811903002479[/C][/ROW]
[ROW][C]109[/C][C]4753[/C][C]4738.76828177526[/C][C]14.2317182247416[/C][/ROW]
[ROW][C]110[/C][C]4888[/C][C]4925.18510533818[/C][C]-37.185105338177[/C][/ROW]
[ROW][C]111[/C][C]5048[/C][C]5104.90353447468[/C][C]-56.9035344746799[/C][/ROW]
[ROW][C]112[/C][C]4991[/C][C]5126.61064373537[/C][C]-135.610643735369[/C][/ROW]
[ROW][C]113[/C][C]4962[/C][C]4953.67649210778[/C][C]8.32350789222437[/C][/ROW]
[ROW][C]114[/C][C]5150[/C][C]5050.34885536889[/C][C]99.6511446311115[/C][/ROW]
[ROW][C]115[/C][C]4444[/C][C]4494.01568232276[/C][C]-50.0156823227562[/C][/ROW]
[ROW][C]116[/C][C]4815[/C][C]4732.68338894853[/C][C]82.3166110514703[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=300203&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=300203&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
1341793748.54807692308430.451923076921
1446224537.6021296617984.3978703382081
1547984811.73147073735-13.731470737348
1646734722.44088053793-49.4408805379262
1746354707.19538353325-72.1953835332524
1848754984.47222734614-109.472227346138
1940974078.3638303069518.6361696930508
2042624371.41920615869-109.419206158688
2141354446.64941312531-311.649413125313
2242384284.71655105458-46.7165510545783
2338914234.98229293118-343.982292931177
2435734053.1985539328-480.198553932796
2539633623.51261589351339.487384106494
2641924250.30737658325-58.3073765832523
2743064375.27029753141-69.2702975314069
2843164217.7338841841498.2661158158589
2942494297.07457801677-48.0745780167663
3044084569.95529388877-161.955293888775
3137313636.0333543085194.9666456914879
3240963945.38018632177150.619813678232
3341024166.63440570471-64.6344057047099
3439624247.89304309221-285.893043092213
3538453935.06652099447-90.0665209944736
3637343912.71321980597-178.713219805971
3739333896.271968951636.7280310483952
3841764191.51187958896-15.5118795889612
3941504340.23252090248-190.232520902483
4041374117.301244864919.6987551351012
4140164093.27302953616-77.2730295361634
4241134308.00197953628-195.001979536279
4336113395.06266876034215.937331239657
4434743801.90339674264-327.903396742635
4536543587.9822025913366.0177974086741
4637123707.994619189214.00538081078867
4733943654.41926329243-260.419263292431
4833483467.94829824302-119.948298243018
4934763533.97852257319-57.9785225731916
5039083731.53372450989176.466275490111
5140093980.6920490034628.3079509965442
5241023967.38863577311134.611364226891
5342534005.62107884545247.37892115455
5445324445.3279812136286.6720187863848
5540803845.40374589724234.59625410276
5644024148.46209251389253.537907486114
5745974484.73688520217112.263114797834
5848444638.01061270382205.989387296176
5948774696.36446844587180.635531554126
6047354903.65903294331-168.659032943309
6147684964.6167958448-196.6167958448
6252515123.76244204348127.237557956524
6355535318.16948704825234.830512951748
6455485508.3147660035139.685233996488
6555195515.850107055213.14989294478528
6657985744.6734345305353.3265654694669
6749185166.07210668315-248.072106683153
6852715106.06401948865164.935980511353
6954925348.74752972512143.252470274876
7055475554.12911373293-7.12911373292536
7152445445.49865435756-201.498654357555
7251495277.235183373-128.235183373004
7354535363.1903534975289.8096465024755
7455845820.69004535802-236.690045358023
7557735754.9319109413218.0680890586818
7658115729.0294620527281.9705379472834
7756875757.76131214343-70.7613121434297
7856475935.78548612007-288.785486120075
7948925015.08786094045-123.087860940449
8052355136.8020179272398.1979820727702
8153115314.50147610762-3.50147610762451
8253785362.0993522764915.9006477235098
8349945218.1752095931-224.175209593097
8445595038.38000546945-479.380005469446
8548954885.05809008629.94190991380037
8651045191.84754632209-87.8475463220911
8754775284.55998583043192.440014169565
8853025396.78678289661-94.7867828966055
8953605240.12398477802119.876015221978
9055405506.3307355679533.6692644320528
9148774865.9941535166811.0058464833201
9252415135.80281786072105.197182139282
9352335290.97761930752-57.977619307524
9455615294.50673218048266.493267819515
9550495289.19927954769-240.199279547685
9644825037.18849157558-555.188491575579
9748464929.95161137501-83.9516113750105
9846365136.79688391669-500.796883916692
9944314960.26372166779-529.263721667791
10047024427.31411107698274.685888923024
10147754590.33415276681184.665847233193
10248344873.2482543425-39.2482543425003
10343444155.75654501247188.243454987529
10448004571.23220569513228.767794304868
10549814774.68796308586206.312036914143
10650695047.9654198149121.0345801850854
10746554727.8395247093-72.839524709304
10842544526.81190300248-272.811903002479
10947534738.7682817752614.2317182247416
11048884925.18510533818-37.185105338177
11150485104.90353447468-56.9035344746799
11249915126.61064373537-135.610643735369
11349624953.676492107788.32350789222437
11451505050.3488553688999.6511446311115
11544444494.01568232276-50.0156823227562
11648154732.6833889485382.3166110514703







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
1174814.733724351054439.449063223375190.01838547872
1184881.08643432974402.686761200715359.48610745869
1194518.13243502533952.563141297425083.70172875318
1204324.58953772793681.242707934224967.93636752158
1214811.530602715294096.691299307045526.36990612355
1224974.251405378474192.446880489545756.0559302674
1235177.792692940134332.444344637216023.14104124304
1245226.269838021114320.051760251596132.48791579062
1255192.657900262234227.712373880396157.60342664407
1265304.943229686454283.0189401936326.8675191799
1274638.250228938973560.795455666575715.70500221137
1284946.352829726993814.580810232456078.12484922153

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
117 & 4814.73372435105 & 4439.44906322337 & 5190.01838547872 \tabularnewline
118 & 4881.0864343297 & 4402.68676120071 & 5359.48610745869 \tabularnewline
119 & 4518.1324350253 & 3952.56314129742 & 5083.70172875318 \tabularnewline
120 & 4324.5895377279 & 3681.24270793422 & 4967.93636752158 \tabularnewline
121 & 4811.53060271529 & 4096.69129930704 & 5526.36990612355 \tabularnewline
122 & 4974.25140537847 & 4192.44688048954 & 5756.0559302674 \tabularnewline
123 & 5177.79269294013 & 4332.44434463721 & 6023.14104124304 \tabularnewline
124 & 5226.26983802111 & 4320.05176025159 & 6132.48791579062 \tabularnewline
125 & 5192.65790026223 & 4227.71237388039 & 6157.60342664407 \tabularnewline
126 & 5304.94322968645 & 4283.018940193 & 6326.8675191799 \tabularnewline
127 & 4638.25022893897 & 3560.79545566657 & 5715.70500221137 \tabularnewline
128 & 4946.35282972699 & 3814.58081023245 & 6078.12484922153 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=300203&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]117[/C][C]4814.73372435105[/C][C]4439.44906322337[/C][C]5190.01838547872[/C][/ROW]
[ROW][C]118[/C][C]4881.0864343297[/C][C]4402.68676120071[/C][C]5359.48610745869[/C][/ROW]
[ROW][C]119[/C][C]4518.1324350253[/C][C]3952.56314129742[/C][C]5083.70172875318[/C][/ROW]
[ROW][C]120[/C][C]4324.5895377279[/C][C]3681.24270793422[/C][C]4967.93636752158[/C][/ROW]
[ROW][C]121[/C][C]4811.53060271529[/C][C]4096.69129930704[/C][C]5526.36990612355[/C][/ROW]
[ROW][C]122[/C][C]4974.25140537847[/C][C]4192.44688048954[/C][C]5756.0559302674[/C][/ROW]
[ROW][C]123[/C][C]5177.79269294013[/C][C]4332.44434463721[/C][C]6023.14104124304[/C][/ROW]
[ROW][C]124[/C][C]5226.26983802111[/C][C]4320.05176025159[/C][C]6132.48791579062[/C][/ROW]
[ROW][C]125[/C][C]5192.65790026223[/C][C]4227.71237388039[/C][C]6157.60342664407[/C][/ROW]
[ROW][C]126[/C][C]5304.94322968645[/C][C]4283.018940193[/C][C]6326.8675191799[/C][/ROW]
[ROW][C]127[/C][C]4638.25022893897[/C][C]3560.79545566657[/C][C]5715.70500221137[/C][/ROW]
[ROW][C]128[/C][C]4946.35282972699[/C][C]3814.58081023245[/C][C]6078.12484922153[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=300203&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=300203&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
1174814.733724351054439.449063223375190.01838547872
1184881.08643432974402.686761200715359.48610745869
1194518.13243502533952.563141297425083.70172875318
1204324.58953772793681.242707934224967.93636752158
1214811.530602715294096.691299307045526.36990612355
1224974.251405378474192.446880489545756.0559302674
1235177.792692940134332.444344637216023.14104124304
1245226.269838021114320.051760251596132.48791579062
1255192.657900262234227.712373880396157.60342664407
1265304.943229686454283.0189401936326.8675191799
1274638.250228938973560.795455666575715.70500221137
1284946.352829726993814.580810232456078.12484922153



Parameters (Session):
par1 = 12 ; par2 = Triple ; par3 = additive ; par4 = 12 ;
Parameters (R input):
par1 = 12 ; par2 = Triple ; par3 = additive ; par4 = 12 ;
R code (references can be found in the software module):
par1 <- as.numeric(par1)
par4 <- as.numeric(par4)
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$fitted[,'xhat']
bitmap(file='test1.png')
op <- par(mfrow=c(2,1))
plot(fit,ylab='Observed (black) / Fitted (red)',main='Interpolation Fit of Exponential Smoothing')
plot(myresid,ylab='Residuals',main='Interpolation Prediction Errors')
par(op)
dev.off()
bitmap(file='test2.png')
p <- predict(fit, par4, prediction.interval=TRUE)
np <- length(p[,1])
plot(fit,p,ylab='Observed (black) / Fitted (red)',main='Extrapolation Fit of Exponential Smoothing')
dev.off()
bitmap(file='test3.png')
op <- par(mfrow = c(2,2))
acf(as.numeric(myresid),lag.max = nx/2,main='Residual ACF')
spectrum(myresid,main='Residals Periodogram')
cpgram(myresid,main='Residal Cumulative Periodogram')
qqnorm(myresid,main='Residual Normal QQ Plot')
qqline(myresid)
par(op)
dev.off()
load(file='createtable')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Estimated Parameters of Exponential Smoothing',2,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'Parameter',header=TRUE)
a<-table.element(a,'Value',header=TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'alpha',header=TRUE)
a<-table.element(a,fit$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')