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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 08:58:02 +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/t14818751263f9d9ykq35iqv92.htm/, Retrieved Fri, 03 May 2024 01:28:27 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=300081, Retrieved Fri, 03 May 2024 01:28:27 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact91
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 07:58:02] [b7b12d6257d20c3ae3b596da588d7d29] [Current]
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Dataseries X:
3655
3390
4000
3810
3790
3790
3350
3900
3725
3945
3840
3625
4000
3915
4200
3900
4140
3945
3735
3970
3745
4140
3840
3570
4085
3865
4280
4280
4240
4065
4060
4265
4085
4450
4195
4160
4580
4130
4645
4375
4480
4485
4465
4515
4465
4790
4270
4495
4490
4275
4695
4630
4560
4665
4725
4840
4745
4940
4635
4910
4690
4585
5065
4705
4580
4660
4510
4885
4765
4700
4590
4655
4845
4495
5020
4535
4700
4435
4285
4780
4450
4875
4670
4325
5000
4675
4950
4790
4785
4520
4735
5055
4640
5045
4710
4650
4915
4260
4505
4575
4785
4610
5220
5285
4870
5440
4615
4645
4845
4780
5005
4905
4630
4785
5160




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=300081&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=300081&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=300081&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
alpha0.351729169266056
beta0
gamma0.665799833057604

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.351729169266056 \tabularnewline
beta & 0 \tabularnewline
gamma & 0.665799833057604 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=300081&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]0.351729169266056[/C][/ROW]
[ROW][C]beta[/C][C]0[/C][/ROW]
[ROW][C]gamma[/C][C]0.665799833057604[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=300081&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=300081&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
alpha0.351729169266056
beta0
gamma0.665799833057604







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
1340003876.01612848607123.983871513929
1439153833.8930285792281.1069714207779
1542004156.9491930581143.0508069418893
1639003881.2879178400218.7120821599797
1741404135.595360459334.40463954066945
1839453960.7937571001-15.7937571000971
1937353532.49447061604202.505529383956
2039704171.83283816704-201.83283816704
2137453901.57953422148-156.57953422148
2241404077.4581921201362.5418078798712
2338403987.44004494371-147.440044943707
2435703710.14540926219-140.145409262191
2540854087.85231726688-2.85231726687925
2638653978.89462126631-113.89462126631
2742804219.6388069784660.361193021542
2842803935.74540066029344.254599339709
2942404307.65183443428-67.6518344342812
3040654091.73672800286-26.7367280028579
3140603740.38154079091319.618459209093
3242654261.344541765373.65545823462617
3340854069.766397270915.2336027290994
3444504424.7006610101325.2993389898693
3541954213.78613585889-18.7861358588862
3641603963.47222840476196.527771595241
3745804575.21222349124.7877765088042
3841304399.77237286694-269.772372866942
3946454696.89176092557-51.8917609255686
4043754471.95931116096-96.9593111609602
4144804513.82312611059-33.8231261105875
4244854316.36093098051168.639069019487
4344654163.33154145928301.668458540716
4445154559.47409939052-44.4740993905161
4544654342.61951028774122.380489712263
4647904764.6679386002525.332061399753
4742704515.86846641795-245.868466417946
4844954267.97954628254227.020453717459
4944904832.47687891007-342.476878910066
5042754404.70173935622-129.701739356222
5146954864.12976166371-169.129761663713
5246304570.4438978595959.5561021404137
5345604698.40824193507-138.40824193507
5446654546.37747339556118.622526604442
5547254424.47821239204300.521787607958
5648404674.43945213124165.560547868758
5747454596.27377174809148.726228251909
5849405000.84071734696-60.8407173469614
5946354586.6224141945448.3775858054551
6049104646.18132207734263.818677922655
6146904988.4624333782-298.462433378201
6245854651.22321861682-66.2232186168176
6350655150.53314665477-85.5331466547714
6447054972.33020625996-267.330206259959
6545804899.49291889765-319.492918897654
6646604793.83646187382-133.836461873819
6745104656.20732976189-146.207329761888
6848854689.09775546469195.902244535306
6947654615.15488919158149.845110808422
7047004927.21482879814-227.214828798139
7145904509.2642763502580.7357236497528
7246554668.75835800398-13.7583580039773
7348454668.40832439068176.591675609324
7444954599.103557134-104.103557133997
7550205072.55528183796-52.555281837962
7645354826.68064058583-291.680640585833
7747004719.69591728389-19.695917283886
7844354800.00200825625-365.002008256252
7942854575.4382010134-290.438201013396
8047804700.8120979214479.1879020785645
8144504569.43171916676-119.431719166759
8248754619.00979443679255.990205563215
8346704505.58500550993164.414994490066
8443254653.5719605814-328.571960581396
8550004621.85995186626378.140048133743
8646754504.82589664323170.17410335677
8749505102.29058075797-152.290580757966
8847904714.187975558375.8120244417005
8947854856.84774906327-71.8477490632749
9045204763.22212428799-243.22212428799
9147354607.82555880105127.17444119895
9250555065.34541684974-10.3454168497383
9346404799.86574256015-159.86574256015
9450455009.1907777431835.8092222568175
9547104766.99624766847-56.9962476684659
9646504617.2722385250232.7277614749828
9749155032.55611568591-117.556115685908
9842604645.14887598692-385.148875986917
9945054896.85985247558-391.859852475579
10045754534.096604249240.9033957507982
10147854598.88156626667186.118433733332
10246104524.6342422762485.3657577237582
10352204643.86301589759576.136984102414
10452855209.8792518623975.1207481376068
10548704896.96561516871-26.9656151687141
10654405252.62220587071187.37779412929
10746155006.2258607207-391.225860720703
10846454774.33853690994-129.338536909944
10948455073.29288655618-228.292886556175
11047804521.32583397355258.674166026452
11150055014.17813128926-9.17813128925991
11249054967.77984093022-62.7798409302222
11346305065.5979660062-435.5979660062
11447854721.9095599316763.0904400683303
11551605043.84114210547116.158857894528

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 4000 & 3876.01612848607 & 123.983871513929 \tabularnewline
14 & 3915 & 3833.89302857922 & 81.1069714207779 \tabularnewline
15 & 4200 & 4156.94919305811 & 43.0508069418893 \tabularnewline
16 & 3900 & 3881.28791784002 & 18.7120821599797 \tabularnewline
17 & 4140 & 4135.59536045933 & 4.40463954066945 \tabularnewline
18 & 3945 & 3960.7937571001 & -15.7937571000971 \tabularnewline
19 & 3735 & 3532.49447061604 & 202.505529383956 \tabularnewline
20 & 3970 & 4171.83283816704 & -201.83283816704 \tabularnewline
21 & 3745 & 3901.57953422148 & -156.57953422148 \tabularnewline
22 & 4140 & 4077.45819212013 & 62.5418078798712 \tabularnewline
23 & 3840 & 3987.44004494371 & -147.440044943707 \tabularnewline
24 & 3570 & 3710.14540926219 & -140.145409262191 \tabularnewline
25 & 4085 & 4087.85231726688 & -2.85231726687925 \tabularnewline
26 & 3865 & 3978.89462126631 & -113.89462126631 \tabularnewline
27 & 4280 & 4219.63880697846 & 60.361193021542 \tabularnewline
28 & 4280 & 3935.74540066029 & 344.254599339709 \tabularnewline
29 & 4240 & 4307.65183443428 & -67.6518344342812 \tabularnewline
30 & 4065 & 4091.73672800286 & -26.7367280028579 \tabularnewline
31 & 4060 & 3740.38154079091 & 319.618459209093 \tabularnewline
32 & 4265 & 4261.34454176537 & 3.65545823462617 \tabularnewline
33 & 4085 & 4069.7663972709 & 15.2336027290994 \tabularnewline
34 & 4450 & 4424.70066101013 & 25.2993389898693 \tabularnewline
35 & 4195 & 4213.78613585889 & -18.7861358588862 \tabularnewline
36 & 4160 & 3963.47222840476 & 196.527771595241 \tabularnewline
37 & 4580 & 4575.2122234912 & 4.7877765088042 \tabularnewline
38 & 4130 & 4399.77237286694 & -269.772372866942 \tabularnewline
39 & 4645 & 4696.89176092557 & -51.8917609255686 \tabularnewline
40 & 4375 & 4471.95931116096 & -96.9593111609602 \tabularnewline
41 & 4480 & 4513.82312611059 & -33.8231261105875 \tabularnewline
42 & 4485 & 4316.36093098051 & 168.639069019487 \tabularnewline
43 & 4465 & 4163.33154145928 & 301.668458540716 \tabularnewline
44 & 4515 & 4559.47409939052 & -44.4740993905161 \tabularnewline
45 & 4465 & 4342.61951028774 & 122.380489712263 \tabularnewline
46 & 4790 & 4764.66793860025 & 25.332061399753 \tabularnewline
47 & 4270 & 4515.86846641795 & -245.868466417946 \tabularnewline
48 & 4495 & 4267.97954628254 & 227.020453717459 \tabularnewline
49 & 4490 & 4832.47687891007 & -342.476878910066 \tabularnewline
50 & 4275 & 4404.70173935622 & -129.701739356222 \tabularnewline
51 & 4695 & 4864.12976166371 & -169.129761663713 \tabularnewline
52 & 4630 & 4570.44389785959 & 59.5561021404137 \tabularnewline
53 & 4560 & 4698.40824193507 & -138.40824193507 \tabularnewline
54 & 4665 & 4546.37747339556 & 118.622526604442 \tabularnewline
55 & 4725 & 4424.47821239204 & 300.521787607958 \tabularnewline
56 & 4840 & 4674.43945213124 & 165.560547868758 \tabularnewline
57 & 4745 & 4596.27377174809 & 148.726228251909 \tabularnewline
58 & 4940 & 5000.84071734696 & -60.8407173469614 \tabularnewline
59 & 4635 & 4586.62241419454 & 48.3775858054551 \tabularnewline
60 & 4910 & 4646.18132207734 & 263.818677922655 \tabularnewline
61 & 4690 & 4988.4624333782 & -298.462433378201 \tabularnewline
62 & 4585 & 4651.22321861682 & -66.2232186168176 \tabularnewline
63 & 5065 & 5150.53314665477 & -85.5331466547714 \tabularnewline
64 & 4705 & 4972.33020625996 & -267.330206259959 \tabularnewline
65 & 4580 & 4899.49291889765 & -319.492918897654 \tabularnewline
66 & 4660 & 4793.83646187382 & -133.836461873819 \tabularnewline
67 & 4510 & 4656.20732976189 & -146.207329761888 \tabularnewline
68 & 4885 & 4689.09775546469 & 195.902244535306 \tabularnewline
69 & 4765 & 4615.15488919158 & 149.845110808422 \tabularnewline
70 & 4700 & 4927.21482879814 & -227.214828798139 \tabularnewline
71 & 4590 & 4509.26427635025 & 80.7357236497528 \tabularnewline
72 & 4655 & 4668.75835800398 & -13.7583580039773 \tabularnewline
73 & 4845 & 4668.40832439068 & 176.591675609324 \tabularnewline
74 & 4495 & 4599.103557134 & -104.103557133997 \tabularnewline
75 & 5020 & 5072.55528183796 & -52.555281837962 \tabularnewline
76 & 4535 & 4826.68064058583 & -291.680640585833 \tabularnewline
77 & 4700 & 4719.69591728389 & -19.695917283886 \tabularnewline
78 & 4435 & 4800.00200825625 & -365.002008256252 \tabularnewline
79 & 4285 & 4575.4382010134 & -290.438201013396 \tabularnewline
80 & 4780 & 4700.81209792144 & 79.1879020785645 \tabularnewline
81 & 4450 & 4569.43171916676 & -119.431719166759 \tabularnewline
82 & 4875 & 4619.00979443679 & 255.990205563215 \tabularnewline
83 & 4670 & 4505.58500550993 & 164.414994490066 \tabularnewline
84 & 4325 & 4653.5719605814 & -328.571960581396 \tabularnewline
85 & 5000 & 4621.85995186626 & 378.140048133743 \tabularnewline
86 & 4675 & 4504.82589664323 & 170.17410335677 \tabularnewline
87 & 4950 & 5102.29058075797 & -152.290580757966 \tabularnewline
88 & 4790 & 4714.1879755583 & 75.8120244417005 \tabularnewline
89 & 4785 & 4856.84774906327 & -71.8477490632749 \tabularnewline
90 & 4520 & 4763.22212428799 & -243.22212428799 \tabularnewline
91 & 4735 & 4607.82555880105 & 127.17444119895 \tabularnewline
92 & 5055 & 5065.34541684974 & -10.3454168497383 \tabularnewline
93 & 4640 & 4799.86574256015 & -159.86574256015 \tabularnewline
94 & 5045 & 5009.19077774318 & 35.8092222568175 \tabularnewline
95 & 4710 & 4766.99624766847 & -56.9962476684659 \tabularnewline
96 & 4650 & 4617.27223852502 & 32.7277614749828 \tabularnewline
97 & 4915 & 5032.55611568591 & -117.556115685908 \tabularnewline
98 & 4260 & 4645.14887598692 & -385.148875986917 \tabularnewline
99 & 4505 & 4896.85985247558 & -391.859852475579 \tabularnewline
100 & 4575 & 4534.0966042492 & 40.9033957507982 \tabularnewline
101 & 4785 & 4598.88156626667 & 186.118433733332 \tabularnewline
102 & 4610 & 4524.63424227624 & 85.3657577237582 \tabularnewline
103 & 5220 & 4643.86301589759 & 576.136984102414 \tabularnewline
104 & 5285 & 5209.87925186239 & 75.1207481376068 \tabularnewline
105 & 4870 & 4896.96561516871 & -26.9656151687141 \tabularnewline
106 & 5440 & 5252.62220587071 & 187.37779412929 \tabularnewline
107 & 4615 & 5006.2258607207 & -391.225860720703 \tabularnewline
108 & 4645 & 4774.33853690994 & -129.338536909944 \tabularnewline
109 & 4845 & 5073.29288655618 & -228.292886556175 \tabularnewline
110 & 4780 & 4521.32583397355 & 258.674166026452 \tabularnewline
111 & 5005 & 5014.17813128926 & -9.17813128925991 \tabularnewline
112 & 4905 & 4967.77984093022 & -62.7798409302222 \tabularnewline
113 & 4630 & 5065.5979660062 & -435.5979660062 \tabularnewline
114 & 4785 & 4721.90955993167 & 63.0904400683303 \tabularnewline
115 & 5160 & 5043.84114210547 & 116.158857894528 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=300081&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]4000[/C][C]3876.01612848607[/C][C]123.983871513929[/C][/ROW]
[ROW][C]14[/C][C]3915[/C][C]3833.89302857922[/C][C]81.1069714207779[/C][/ROW]
[ROW][C]15[/C][C]4200[/C][C]4156.94919305811[/C][C]43.0508069418893[/C][/ROW]
[ROW][C]16[/C][C]3900[/C][C]3881.28791784002[/C][C]18.7120821599797[/C][/ROW]
[ROW][C]17[/C][C]4140[/C][C]4135.59536045933[/C][C]4.40463954066945[/C][/ROW]
[ROW][C]18[/C][C]3945[/C][C]3960.7937571001[/C][C]-15.7937571000971[/C][/ROW]
[ROW][C]19[/C][C]3735[/C][C]3532.49447061604[/C][C]202.505529383956[/C][/ROW]
[ROW][C]20[/C][C]3970[/C][C]4171.83283816704[/C][C]-201.83283816704[/C][/ROW]
[ROW][C]21[/C][C]3745[/C][C]3901.57953422148[/C][C]-156.57953422148[/C][/ROW]
[ROW][C]22[/C][C]4140[/C][C]4077.45819212013[/C][C]62.5418078798712[/C][/ROW]
[ROW][C]23[/C][C]3840[/C][C]3987.44004494371[/C][C]-147.440044943707[/C][/ROW]
[ROW][C]24[/C][C]3570[/C][C]3710.14540926219[/C][C]-140.145409262191[/C][/ROW]
[ROW][C]25[/C][C]4085[/C][C]4087.85231726688[/C][C]-2.85231726687925[/C][/ROW]
[ROW][C]26[/C][C]3865[/C][C]3978.89462126631[/C][C]-113.89462126631[/C][/ROW]
[ROW][C]27[/C][C]4280[/C][C]4219.63880697846[/C][C]60.361193021542[/C][/ROW]
[ROW][C]28[/C][C]4280[/C][C]3935.74540066029[/C][C]344.254599339709[/C][/ROW]
[ROW][C]29[/C][C]4240[/C][C]4307.65183443428[/C][C]-67.6518344342812[/C][/ROW]
[ROW][C]30[/C][C]4065[/C][C]4091.73672800286[/C][C]-26.7367280028579[/C][/ROW]
[ROW][C]31[/C][C]4060[/C][C]3740.38154079091[/C][C]319.618459209093[/C][/ROW]
[ROW][C]32[/C][C]4265[/C][C]4261.34454176537[/C][C]3.65545823462617[/C][/ROW]
[ROW][C]33[/C][C]4085[/C][C]4069.7663972709[/C][C]15.2336027290994[/C][/ROW]
[ROW][C]34[/C][C]4450[/C][C]4424.70066101013[/C][C]25.2993389898693[/C][/ROW]
[ROW][C]35[/C][C]4195[/C][C]4213.78613585889[/C][C]-18.7861358588862[/C][/ROW]
[ROW][C]36[/C][C]4160[/C][C]3963.47222840476[/C][C]196.527771595241[/C][/ROW]
[ROW][C]37[/C][C]4580[/C][C]4575.2122234912[/C][C]4.7877765088042[/C][/ROW]
[ROW][C]38[/C][C]4130[/C][C]4399.77237286694[/C][C]-269.772372866942[/C][/ROW]
[ROW][C]39[/C][C]4645[/C][C]4696.89176092557[/C][C]-51.8917609255686[/C][/ROW]
[ROW][C]40[/C][C]4375[/C][C]4471.95931116096[/C][C]-96.9593111609602[/C][/ROW]
[ROW][C]41[/C][C]4480[/C][C]4513.82312611059[/C][C]-33.8231261105875[/C][/ROW]
[ROW][C]42[/C][C]4485[/C][C]4316.36093098051[/C][C]168.639069019487[/C][/ROW]
[ROW][C]43[/C][C]4465[/C][C]4163.33154145928[/C][C]301.668458540716[/C][/ROW]
[ROW][C]44[/C][C]4515[/C][C]4559.47409939052[/C][C]-44.4740993905161[/C][/ROW]
[ROW][C]45[/C][C]4465[/C][C]4342.61951028774[/C][C]122.380489712263[/C][/ROW]
[ROW][C]46[/C][C]4790[/C][C]4764.66793860025[/C][C]25.332061399753[/C][/ROW]
[ROW][C]47[/C][C]4270[/C][C]4515.86846641795[/C][C]-245.868466417946[/C][/ROW]
[ROW][C]48[/C][C]4495[/C][C]4267.97954628254[/C][C]227.020453717459[/C][/ROW]
[ROW][C]49[/C][C]4490[/C][C]4832.47687891007[/C][C]-342.476878910066[/C][/ROW]
[ROW][C]50[/C][C]4275[/C][C]4404.70173935622[/C][C]-129.701739356222[/C][/ROW]
[ROW][C]51[/C][C]4695[/C][C]4864.12976166371[/C][C]-169.129761663713[/C][/ROW]
[ROW][C]52[/C][C]4630[/C][C]4570.44389785959[/C][C]59.5561021404137[/C][/ROW]
[ROW][C]53[/C][C]4560[/C][C]4698.40824193507[/C][C]-138.40824193507[/C][/ROW]
[ROW][C]54[/C][C]4665[/C][C]4546.37747339556[/C][C]118.622526604442[/C][/ROW]
[ROW][C]55[/C][C]4725[/C][C]4424.47821239204[/C][C]300.521787607958[/C][/ROW]
[ROW][C]56[/C][C]4840[/C][C]4674.43945213124[/C][C]165.560547868758[/C][/ROW]
[ROW][C]57[/C][C]4745[/C][C]4596.27377174809[/C][C]148.726228251909[/C][/ROW]
[ROW][C]58[/C][C]4940[/C][C]5000.84071734696[/C][C]-60.8407173469614[/C][/ROW]
[ROW][C]59[/C][C]4635[/C][C]4586.62241419454[/C][C]48.3775858054551[/C][/ROW]
[ROW][C]60[/C][C]4910[/C][C]4646.18132207734[/C][C]263.818677922655[/C][/ROW]
[ROW][C]61[/C][C]4690[/C][C]4988.4624333782[/C][C]-298.462433378201[/C][/ROW]
[ROW][C]62[/C][C]4585[/C][C]4651.22321861682[/C][C]-66.2232186168176[/C][/ROW]
[ROW][C]63[/C][C]5065[/C][C]5150.53314665477[/C][C]-85.5331466547714[/C][/ROW]
[ROW][C]64[/C][C]4705[/C][C]4972.33020625996[/C][C]-267.330206259959[/C][/ROW]
[ROW][C]65[/C][C]4580[/C][C]4899.49291889765[/C][C]-319.492918897654[/C][/ROW]
[ROW][C]66[/C][C]4660[/C][C]4793.83646187382[/C][C]-133.836461873819[/C][/ROW]
[ROW][C]67[/C][C]4510[/C][C]4656.20732976189[/C][C]-146.207329761888[/C][/ROW]
[ROW][C]68[/C][C]4885[/C][C]4689.09775546469[/C][C]195.902244535306[/C][/ROW]
[ROW][C]69[/C][C]4765[/C][C]4615.15488919158[/C][C]149.845110808422[/C][/ROW]
[ROW][C]70[/C][C]4700[/C][C]4927.21482879814[/C][C]-227.214828798139[/C][/ROW]
[ROW][C]71[/C][C]4590[/C][C]4509.26427635025[/C][C]80.7357236497528[/C][/ROW]
[ROW][C]72[/C][C]4655[/C][C]4668.75835800398[/C][C]-13.7583580039773[/C][/ROW]
[ROW][C]73[/C][C]4845[/C][C]4668.40832439068[/C][C]176.591675609324[/C][/ROW]
[ROW][C]74[/C][C]4495[/C][C]4599.103557134[/C][C]-104.103557133997[/C][/ROW]
[ROW][C]75[/C][C]5020[/C][C]5072.55528183796[/C][C]-52.555281837962[/C][/ROW]
[ROW][C]76[/C][C]4535[/C][C]4826.68064058583[/C][C]-291.680640585833[/C][/ROW]
[ROW][C]77[/C][C]4700[/C][C]4719.69591728389[/C][C]-19.695917283886[/C][/ROW]
[ROW][C]78[/C][C]4435[/C][C]4800.00200825625[/C][C]-365.002008256252[/C][/ROW]
[ROW][C]79[/C][C]4285[/C][C]4575.4382010134[/C][C]-290.438201013396[/C][/ROW]
[ROW][C]80[/C][C]4780[/C][C]4700.81209792144[/C][C]79.1879020785645[/C][/ROW]
[ROW][C]81[/C][C]4450[/C][C]4569.43171916676[/C][C]-119.431719166759[/C][/ROW]
[ROW][C]82[/C][C]4875[/C][C]4619.00979443679[/C][C]255.990205563215[/C][/ROW]
[ROW][C]83[/C][C]4670[/C][C]4505.58500550993[/C][C]164.414994490066[/C][/ROW]
[ROW][C]84[/C][C]4325[/C][C]4653.5719605814[/C][C]-328.571960581396[/C][/ROW]
[ROW][C]85[/C][C]5000[/C][C]4621.85995186626[/C][C]378.140048133743[/C][/ROW]
[ROW][C]86[/C][C]4675[/C][C]4504.82589664323[/C][C]170.17410335677[/C][/ROW]
[ROW][C]87[/C][C]4950[/C][C]5102.29058075797[/C][C]-152.290580757966[/C][/ROW]
[ROW][C]88[/C][C]4790[/C][C]4714.1879755583[/C][C]75.8120244417005[/C][/ROW]
[ROW][C]89[/C][C]4785[/C][C]4856.84774906327[/C][C]-71.8477490632749[/C][/ROW]
[ROW][C]90[/C][C]4520[/C][C]4763.22212428799[/C][C]-243.22212428799[/C][/ROW]
[ROW][C]91[/C][C]4735[/C][C]4607.82555880105[/C][C]127.17444119895[/C][/ROW]
[ROW][C]92[/C][C]5055[/C][C]5065.34541684974[/C][C]-10.3454168497383[/C][/ROW]
[ROW][C]93[/C][C]4640[/C][C]4799.86574256015[/C][C]-159.86574256015[/C][/ROW]
[ROW][C]94[/C][C]5045[/C][C]5009.19077774318[/C][C]35.8092222568175[/C][/ROW]
[ROW][C]95[/C][C]4710[/C][C]4766.99624766847[/C][C]-56.9962476684659[/C][/ROW]
[ROW][C]96[/C][C]4650[/C][C]4617.27223852502[/C][C]32.7277614749828[/C][/ROW]
[ROW][C]97[/C][C]4915[/C][C]5032.55611568591[/C][C]-117.556115685908[/C][/ROW]
[ROW][C]98[/C][C]4260[/C][C]4645.14887598692[/C][C]-385.148875986917[/C][/ROW]
[ROW][C]99[/C][C]4505[/C][C]4896.85985247558[/C][C]-391.859852475579[/C][/ROW]
[ROW][C]100[/C][C]4575[/C][C]4534.0966042492[/C][C]40.9033957507982[/C][/ROW]
[ROW][C]101[/C][C]4785[/C][C]4598.88156626667[/C][C]186.118433733332[/C][/ROW]
[ROW][C]102[/C][C]4610[/C][C]4524.63424227624[/C][C]85.3657577237582[/C][/ROW]
[ROW][C]103[/C][C]5220[/C][C]4643.86301589759[/C][C]576.136984102414[/C][/ROW]
[ROW][C]104[/C][C]5285[/C][C]5209.87925186239[/C][C]75.1207481376068[/C][/ROW]
[ROW][C]105[/C][C]4870[/C][C]4896.96561516871[/C][C]-26.9656151687141[/C][/ROW]
[ROW][C]106[/C][C]5440[/C][C]5252.62220587071[/C][C]187.37779412929[/C][/ROW]
[ROW][C]107[/C][C]4615[/C][C]5006.2258607207[/C][C]-391.225860720703[/C][/ROW]
[ROW][C]108[/C][C]4645[/C][C]4774.33853690994[/C][C]-129.338536909944[/C][/ROW]
[ROW][C]109[/C][C]4845[/C][C]5073.29288655618[/C][C]-228.292886556175[/C][/ROW]
[ROW][C]110[/C][C]4780[/C][C]4521.32583397355[/C][C]258.674166026452[/C][/ROW]
[ROW][C]111[/C][C]5005[/C][C]5014.17813128926[/C][C]-9.17813128925991[/C][/ROW]
[ROW][C]112[/C][C]4905[/C][C]4967.77984093022[/C][C]-62.7798409302222[/C][/ROW]
[ROW][C]113[/C][C]4630[/C][C]5065.5979660062[/C][C]-435.5979660062[/C][/ROW]
[ROW][C]114[/C][C]4785[/C][C]4721.90955993167[/C][C]63.0904400683303[/C][/ROW]
[ROW][C]115[/C][C]5160[/C][C]5043.84114210547[/C][C]116.158857894528[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=300081&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=300081&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
1340003876.01612848607123.983871513929
1439153833.8930285792281.1069714207779
1542004156.9491930581143.0508069418893
1639003881.2879178400218.7120821599797
1741404135.595360459334.40463954066945
1839453960.7937571001-15.7937571000971
1937353532.49447061604202.505529383956
2039704171.83283816704-201.83283816704
2137453901.57953422148-156.57953422148
2241404077.4581921201362.5418078798712
2338403987.44004494371-147.440044943707
2435703710.14540926219-140.145409262191
2540854087.85231726688-2.85231726687925
2638653978.89462126631-113.89462126631
2742804219.6388069784660.361193021542
2842803935.74540066029344.254599339709
2942404307.65183443428-67.6518344342812
3040654091.73672800286-26.7367280028579
3140603740.38154079091319.618459209093
3242654261.344541765373.65545823462617
3340854069.766397270915.2336027290994
3444504424.7006610101325.2993389898693
3541954213.78613585889-18.7861358588862
3641603963.47222840476196.527771595241
3745804575.21222349124.7877765088042
3841304399.77237286694-269.772372866942
3946454696.89176092557-51.8917609255686
4043754471.95931116096-96.9593111609602
4144804513.82312611059-33.8231261105875
4244854316.36093098051168.639069019487
4344654163.33154145928301.668458540716
4445154559.47409939052-44.4740993905161
4544654342.61951028774122.380489712263
4647904764.6679386002525.332061399753
4742704515.86846641795-245.868466417946
4844954267.97954628254227.020453717459
4944904832.47687891007-342.476878910066
5042754404.70173935622-129.701739356222
5146954864.12976166371-169.129761663713
5246304570.4438978595959.5561021404137
5345604698.40824193507-138.40824193507
5446654546.37747339556118.622526604442
5547254424.47821239204300.521787607958
5648404674.43945213124165.560547868758
5747454596.27377174809148.726228251909
5849405000.84071734696-60.8407173469614
5946354586.6224141945448.3775858054551
6049104646.18132207734263.818677922655
6146904988.4624333782-298.462433378201
6245854651.22321861682-66.2232186168176
6350655150.53314665477-85.5331466547714
6447054972.33020625996-267.330206259959
6545804899.49291889765-319.492918897654
6646604793.83646187382-133.836461873819
6745104656.20732976189-146.207329761888
6848854689.09775546469195.902244535306
6947654615.15488919158149.845110808422
7047004927.21482879814-227.214828798139
7145904509.2642763502580.7357236497528
7246554668.75835800398-13.7583580039773
7348454668.40832439068176.591675609324
7444954599.103557134-104.103557133997
7550205072.55528183796-52.555281837962
7645354826.68064058583-291.680640585833
7747004719.69591728389-19.695917283886
7844354800.00200825625-365.002008256252
7942854575.4382010134-290.438201013396
8047804700.8120979214479.1879020785645
8144504569.43171916676-119.431719166759
8248754619.00979443679255.990205563215
8346704505.58500550993164.414994490066
8443254653.5719605814-328.571960581396
8550004621.85995186626378.140048133743
8646754504.82589664323170.17410335677
8749505102.29058075797-152.290580757966
8847904714.187975558375.8120244417005
8947854856.84774906327-71.8477490632749
9045204763.22212428799-243.22212428799
9147354607.82555880105127.17444119895
9250555065.34541684974-10.3454168497383
9346404799.86574256015-159.86574256015
9450455009.1907777431835.8092222568175
9547104766.99624766847-56.9962476684659
9646504617.2722385250232.7277614749828
9749155032.55611568591-117.556115685908
9842604645.14887598692-385.148875986917
9945054896.85985247558-391.859852475579
10045754534.096604249240.9033957507982
10147854598.88156626667186.118433733332
10246104524.6342422762485.3657577237582
10352204643.86301589759576.136984102414
10452855209.8792518623975.1207481376068
10548704896.96561516871-26.9656151687141
10654405252.62220587071187.37779412929
10746155006.2258607207-391.225860720703
10846454774.33853690994-129.338536909944
10948455073.29288655618-228.292886556175
11047804521.32583397355258.674166026452
11150055014.17813128926-9.17813128925991
11249054967.77984093022-62.7798409302222
11346305065.5979660062-435.5979660062
11447854721.9095599316763.0904400683303
11551605043.84114210547116.158857894528







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
1165231.390698689384937.654402967865525.1269944109
1174850.797947224884532.772036242785168.82385820698
1185305.193766809644952.187938598115658.19959502117
1194748.538381125674387.095656244935109.98110600641
1204766.785723775134381.930445580125151.64100197013
1215072.634834775294653.791212503825491.47845704675
1224798.791992940984373.319916852115224.26406902985
1235089.327579262214629.3137044495549.34145407542
1245021.547690104714547.886944067135495.20843614228
1254973.359054855464485.690533569375461.02757614156
1264998.470301350484492.648498452875504.29210424809
1275335.258872022424874.787180897565795.73056314729
1285434.922460806814823.746551050326046.0983705633
1295038.91252381664441.780819729775636.04422790342
1305510.267141489274865.915831120896154.61845185765
1314931.504741864174318.319518969265544.68996475908
1324949.867313415494322.419145385315577.31548144568
1335266.841817412134601.158532547115932.52510227714

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
116 & 5231.39069868938 & 4937.65440296786 & 5525.1269944109 \tabularnewline
117 & 4850.79794722488 & 4532.77203624278 & 5168.82385820698 \tabularnewline
118 & 5305.19376680964 & 4952.18793859811 & 5658.19959502117 \tabularnewline
119 & 4748.53838112567 & 4387.09565624493 & 5109.98110600641 \tabularnewline
120 & 4766.78572377513 & 4381.93044558012 & 5151.64100197013 \tabularnewline
121 & 5072.63483477529 & 4653.79121250382 & 5491.47845704675 \tabularnewline
122 & 4798.79199294098 & 4373.31991685211 & 5224.26406902985 \tabularnewline
123 & 5089.32757926221 & 4629.313704449 & 5549.34145407542 \tabularnewline
124 & 5021.54769010471 & 4547.88694406713 & 5495.20843614228 \tabularnewline
125 & 4973.35905485546 & 4485.69053356937 & 5461.02757614156 \tabularnewline
126 & 4998.47030135048 & 4492.64849845287 & 5504.29210424809 \tabularnewline
127 & 5335.25887202242 & 4874.78718089756 & 5795.73056314729 \tabularnewline
128 & 5434.92246080681 & 4823.74655105032 & 6046.0983705633 \tabularnewline
129 & 5038.9125238166 & 4441.78081972977 & 5636.04422790342 \tabularnewline
130 & 5510.26714148927 & 4865.91583112089 & 6154.61845185765 \tabularnewline
131 & 4931.50474186417 & 4318.31951896926 & 5544.68996475908 \tabularnewline
132 & 4949.86731341549 & 4322.41914538531 & 5577.31548144568 \tabularnewline
133 & 5266.84181741213 & 4601.15853254711 & 5932.52510227714 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=300081&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]116[/C][C]5231.39069868938[/C][C]4937.65440296786[/C][C]5525.1269944109[/C][/ROW]
[ROW][C]117[/C][C]4850.79794722488[/C][C]4532.77203624278[/C][C]5168.82385820698[/C][/ROW]
[ROW][C]118[/C][C]5305.19376680964[/C][C]4952.18793859811[/C][C]5658.19959502117[/C][/ROW]
[ROW][C]119[/C][C]4748.53838112567[/C][C]4387.09565624493[/C][C]5109.98110600641[/C][/ROW]
[ROW][C]120[/C][C]4766.78572377513[/C][C]4381.93044558012[/C][C]5151.64100197013[/C][/ROW]
[ROW][C]121[/C][C]5072.63483477529[/C][C]4653.79121250382[/C][C]5491.47845704675[/C][/ROW]
[ROW][C]122[/C][C]4798.79199294098[/C][C]4373.31991685211[/C][C]5224.26406902985[/C][/ROW]
[ROW][C]123[/C][C]5089.32757926221[/C][C]4629.313704449[/C][C]5549.34145407542[/C][/ROW]
[ROW][C]124[/C][C]5021.54769010471[/C][C]4547.88694406713[/C][C]5495.20843614228[/C][/ROW]
[ROW][C]125[/C][C]4973.35905485546[/C][C]4485.69053356937[/C][C]5461.02757614156[/C][/ROW]
[ROW][C]126[/C][C]4998.47030135048[/C][C]4492.64849845287[/C][C]5504.29210424809[/C][/ROW]
[ROW][C]127[/C][C]5335.25887202242[/C][C]4874.78718089756[/C][C]5795.73056314729[/C][/ROW]
[ROW][C]128[/C][C]5434.92246080681[/C][C]4823.74655105032[/C][C]6046.0983705633[/C][/ROW]
[ROW][C]129[/C][C]5038.9125238166[/C][C]4441.78081972977[/C][C]5636.04422790342[/C][/ROW]
[ROW][C]130[/C][C]5510.26714148927[/C][C]4865.91583112089[/C][C]6154.61845185765[/C][/ROW]
[ROW][C]131[/C][C]4931.50474186417[/C][C]4318.31951896926[/C][C]5544.68996475908[/C][/ROW]
[ROW][C]132[/C][C]4949.86731341549[/C][C]4322.41914538531[/C][C]5577.31548144568[/C][/ROW]
[ROW][C]133[/C][C]5266.84181741213[/C][C]4601.15853254711[/C][C]5932.52510227714[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=300081&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=300081&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
1165231.390698689384937.654402967865525.1269944109
1174850.797947224884532.772036242785168.82385820698
1185305.193766809644952.187938598115658.19959502117
1194748.538381125674387.095656244935109.98110600641
1204766.785723775134381.930445580125151.64100197013
1215072.634834775294653.791212503825491.47845704675
1224798.791992940984373.319916852115224.26406902985
1235089.327579262214629.3137044495549.34145407542
1245021.547690104714547.886944067135495.20843614228
1254973.359054855464485.690533569375461.02757614156
1264998.470301350484492.648498452875504.29210424809
1275335.258872022424874.787180897565795.73056314729
1285434.922460806814823.746551050326046.0983705633
1295038.91252381664441.780819729775636.04422790342
1305510.267141489274865.915831120896154.61845185765
1314931.504741864174318.319518969265544.68996475908
1324949.867313415494322.419145385315577.31548144568
1335266.841817412134601.158532547115932.52510227714



Parameters (Session):
par1 = 12 ; par2 = Triple ; par3 = multiplicative ; par4 = 18 ;
Parameters (R input):
par1 = 12 ; par2 = Triple ; par3 = multiplicative ; par4 = 18 ;
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')