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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 16:42:09 +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/t14819029465ko8qk2ty5wurql.htm/, Retrieved Thu, 02 May 2024 16:19:35 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=300381, Retrieved Thu, 02 May 2024 16:19:35 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact90
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [ARIMA Backward Selection] [] [2016-12-16 13:36:55] [683f400e1b95307fc738e729f07c4fce]
-    D  [ARIMA Backward Selection] [] [2016-12-16 14:17:56] [683f400e1b95307fc738e729f07c4fce]
- R  D    [ARIMA Backward Selection] [] [2016-12-16 14:51:40] [683f400e1b95307fc738e729f07c4fce]
- RM D        [Exponential Smoothing] [] [2016-12-16 15:42:09] [404ac5ee4f7301873f6a96ef36861981] [Current]
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Post a new message
Dataseries X:
1880
3600
4600
6560
7840
8560
10120
9240
9320
7000
3960
4680
3920
1560
4800
5240
8000
9760
9800
9280
7680
7760
5680
4560
1560
3680
4200
7400
7040
8480
9720
9760
9440
7240
5080
4080
5120
4400
5160
6680
8240
8960
9280
9880
8480
7320
4880
5280
4080
4720
6360
5760
9000
9160
10480
10160
9120
7880
5080
4360
4480
6000
6120
6200
8960
8680
10240
10920
8440
7760
5320
3920
4040
2960
6280
6320
7160
8160




Summary of computational transaction
Raw Input view raw input (R code)
Raw Outputview raw output of R engine
Computing time1 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 time1 seconds \tabularnewline
R ServerBig Analytics Cloud Computing Center \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=300381&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]1 seconds[/C][/ROW] [ROW]R Server[/C]Big Analytics Cloud Computing Center[/C][/ROW] [/TABLE] Source: https://freestatistics.org/blog/index.php?pk=300381&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=300381&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 time1 seconds
R ServerBig Analytics Cloud Computing Center







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.999933893038648
betaFALSE
gammaFALSE

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.999933893038648 \tabularnewline
beta & FALSE \tabularnewline
gamma & FALSE \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=300381&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]0.999933893038648[/C][/ROW]
[ROW][C]beta[/C][C]FALSE[/C][/ROW]
[ROW][C]gamma[/C][C]FALSE[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=300381&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=300381&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
alpha0.999933893038648
betaFALSE
gammaFALSE







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
2360018801720
346003599.886296026471000.11370397353
465604599.933885522021960.06611447798
578406559.870425985121280.12957401488
685607839.91537452373720.084625476275
7101208559.952397393491560.04760260651
8924010119.8968699934-879.896869993427
993209240.0581673083879.941832691622
1070009319.99471528836-2319.99471528836
1139607000.15336780098-3040.15336780098
1246803960.20097530119719.799024698811
1339204679.95241627369-759.952416273693
1415603920.05023814501-2360.05023814501
1548001560.156015749883239.84398425012
1652404799.78582375895440.214176241053
1780005239.970898778462760.02910122154
1897607999.817542862881760.18245713712
1998009759.8836396863340.1163603136665
2092809799.99734802932-519.997348029319
2176809280.03437544459-1600.03437544459
2277607680.1057734106279.8942265893811
2356807759.99471843545-2079.99471843545
2445605680.13750213046-1120.13750213046
2515604560.07404888656-3000.07404888656
2636801560.19832577922119.8016742208
2742003679.85986635265520.140133647351
2874004199.965615116293200.03438488371
2970407399.78845545059-359.788455450594
3084807040.023784521521439.97621547848
3197208479.904807547981240.09519245202
3297609719.9180210750440.0819789249599
3394409759.99735030217-319.997350302168
3472409440.02115405247-2200.02115405247
3550807240.1454367134-2160.1454367134
3640805080.1428006509-1000.1428006509
3751204080.066116401471039.93388359853
3844005119.93125313095-719.931253130948
3951604400.04759246753759.952407532473
4066805159.949761855571520.05023814443
4182406679.899514097651560.10048590235
4289608239.89686649747720.103133502525
4392808959.95239616999320.047603830015
4498809279.97884262542600.021157374578
4584809879.96033442454-1399.96033442454
4673208480.09254712372-1160.09254712372
4748807320.07669019318-2440.07669019318
4852804880.16130605545399.838693944546
4940805279.97356787891-1199.97356787891
5047204080.07932660628639.920673393725
5163604719.957696788781640.04230321122
5257606359.89158178685-599.891581786846
5390005760.039657009613239.96034299039
5491608999.78581606682160.214183933176
55104809159.989408727141320.01059127286
561016010479.9127381109-319.912738110857
57912010160.021148459-1040.02114845901
5878809120.06875263787-1240.06875263787
5950807880.0819771771-2800.0819771771
6043605080.18510491105-720.185104911047
6144804360.0476092489119.952390751103
6260004479.992070311941520.00792968806
6361205999.89951689454120.100483105462
6462006119.99206052280.007939477995
6589606199.994710918242760.00528908176
6686808959.81754443702-279.817544437024
67102408680.01849788761559.9815021124
681092010239.8968743631680.10312563687
69844010919.955040449-2479.95504044896
7077608440.16394229201-680.163942292013
7153207760.04496357145-2440.04496357145
7239205320.1613039581-1400.1613039581
7340403920.09256040921119.907439590793
7429604039.99207328353-1079.99207328353
7562802960.071394994253319.92860500575
7663206279.7805296080240.2194703919822
7771606319.99734121302840.002658786975
7881607159.94446997671000.0555300233

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
2 & 3600 & 1880 & 1720 \tabularnewline
3 & 4600 & 3599.88629602647 & 1000.11370397353 \tabularnewline
4 & 6560 & 4599.93388552202 & 1960.06611447798 \tabularnewline
5 & 7840 & 6559.87042598512 & 1280.12957401488 \tabularnewline
6 & 8560 & 7839.91537452373 & 720.084625476275 \tabularnewline
7 & 10120 & 8559.95239739349 & 1560.04760260651 \tabularnewline
8 & 9240 & 10119.8968699934 & -879.896869993427 \tabularnewline
9 & 9320 & 9240.05816730838 & 79.941832691622 \tabularnewline
10 & 7000 & 9319.99471528836 & -2319.99471528836 \tabularnewline
11 & 3960 & 7000.15336780098 & -3040.15336780098 \tabularnewline
12 & 4680 & 3960.20097530119 & 719.799024698811 \tabularnewline
13 & 3920 & 4679.95241627369 & -759.952416273693 \tabularnewline
14 & 1560 & 3920.05023814501 & -2360.05023814501 \tabularnewline
15 & 4800 & 1560.15601574988 & 3239.84398425012 \tabularnewline
16 & 5240 & 4799.78582375895 & 440.214176241053 \tabularnewline
17 & 8000 & 5239.97089877846 & 2760.02910122154 \tabularnewline
18 & 9760 & 7999.81754286288 & 1760.18245713712 \tabularnewline
19 & 9800 & 9759.88363968633 & 40.1163603136665 \tabularnewline
20 & 9280 & 9799.99734802932 & -519.997348029319 \tabularnewline
21 & 7680 & 9280.03437544459 & -1600.03437544459 \tabularnewline
22 & 7760 & 7680.10577341062 & 79.8942265893811 \tabularnewline
23 & 5680 & 7759.99471843545 & -2079.99471843545 \tabularnewline
24 & 4560 & 5680.13750213046 & -1120.13750213046 \tabularnewline
25 & 1560 & 4560.07404888656 & -3000.07404888656 \tabularnewline
26 & 3680 & 1560.1983257792 & 2119.8016742208 \tabularnewline
27 & 4200 & 3679.85986635265 & 520.140133647351 \tabularnewline
28 & 7400 & 4199.96561511629 & 3200.03438488371 \tabularnewline
29 & 7040 & 7399.78845545059 & -359.788455450594 \tabularnewline
30 & 8480 & 7040.02378452152 & 1439.97621547848 \tabularnewline
31 & 9720 & 8479.90480754798 & 1240.09519245202 \tabularnewline
32 & 9760 & 9719.91802107504 & 40.0819789249599 \tabularnewline
33 & 9440 & 9759.99735030217 & -319.997350302168 \tabularnewline
34 & 7240 & 9440.02115405247 & -2200.02115405247 \tabularnewline
35 & 5080 & 7240.1454367134 & -2160.1454367134 \tabularnewline
36 & 4080 & 5080.1428006509 & -1000.1428006509 \tabularnewline
37 & 5120 & 4080.06611640147 & 1039.93388359853 \tabularnewline
38 & 4400 & 5119.93125313095 & -719.931253130948 \tabularnewline
39 & 5160 & 4400.04759246753 & 759.952407532473 \tabularnewline
40 & 6680 & 5159.94976185557 & 1520.05023814443 \tabularnewline
41 & 8240 & 6679.89951409765 & 1560.10048590235 \tabularnewline
42 & 8960 & 8239.89686649747 & 720.103133502525 \tabularnewline
43 & 9280 & 8959.95239616999 & 320.047603830015 \tabularnewline
44 & 9880 & 9279.97884262542 & 600.021157374578 \tabularnewline
45 & 8480 & 9879.96033442454 & -1399.96033442454 \tabularnewline
46 & 7320 & 8480.09254712372 & -1160.09254712372 \tabularnewline
47 & 4880 & 7320.07669019318 & -2440.07669019318 \tabularnewline
48 & 5280 & 4880.16130605545 & 399.838693944546 \tabularnewline
49 & 4080 & 5279.97356787891 & -1199.97356787891 \tabularnewline
50 & 4720 & 4080.07932660628 & 639.920673393725 \tabularnewline
51 & 6360 & 4719.95769678878 & 1640.04230321122 \tabularnewline
52 & 5760 & 6359.89158178685 & -599.891581786846 \tabularnewline
53 & 9000 & 5760.03965700961 & 3239.96034299039 \tabularnewline
54 & 9160 & 8999.78581606682 & 160.214183933176 \tabularnewline
55 & 10480 & 9159.98940872714 & 1320.01059127286 \tabularnewline
56 & 10160 & 10479.9127381109 & -319.912738110857 \tabularnewline
57 & 9120 & 10160.021148459 & -1040.02114845901 \tabularnewline
58 & 7880 & 9120.06875263787 & -1240.06875263787 \tabularnewline
59 & 5080 & 7880.0819771771 & -2800.0819771771 \tabularnewline
60 & 4360 & 5080.18510491105 & -720.185104911047 \tabularnewline
61 & 4480 & 4360.0476092489 & 119.952390751103 \tabularnewline
62 & 6000 & 4479.99207031194 & 1520.00792968806 \tabularnewline
63 & 6120 & 5999.89951689454 & 120.100483105462 \tabularnewline
64 & 6200 & 6119.992060522 & 80.007939477995 \tabularnewline
65 & 8960 & 6199.99471091824 & 2760.00528908176 \tabularnewline
66 & 8680 & 8959.81754443702 & -279.817544437024 \tabularnewline
67 & 10240 & 8680.0184978876 & 1559.9815021124 \tabularnewline
68 & 10920 & 10239.8968743631 & 680.10312563687 \tabularnewline
69 & 8440 & 10919.955040449 & -2479.95504044896 \tabularnewline
70 & 7760 & 8440.16394229201 & -680.163942292013 \tabularnewline
71 & 5320 & 7760.04496357145 & -2440.04496357145 \tabularnewline
72 & 3920 & 5320.1613039581 & -1400.1613039581 \tabularnewline
73 & 4040 & 3920.09256040921 & 119.907439590793 \tabularnewline
74 & 2960 & 4039.99207328353 & -1079.99207328353 \tabularnewline
75 & 6280 & 2960.07139499425 & 3319.92860500575 \tabularnewline
76 & 6320 & 6279.78052960802 & 40.2194703919822 \tabularnewline
77 & 7160 & 6319.99734121302 & 840.002658786975 \tabularnewline
78 & 8160 & 7159.9444699767 & 1000.0555300233 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=300381&T=2

[TABLE]
[ROW][C]Interpolation Forecasts of Exponential Smoothing[/C][/ROW]
[ROW][C]t[/C][C]Observed[/C][C]Fitted[/C][C]Residuals[/C][/ROW]
[ROW][C]2[/C][C]3600[/C][C]1880[/C][C]1720[/C][/ROW]
[ROW][C]3[/C][C]4600[/C][C]3599.88629602647[/C][C]1000.11370397353[/C][/ROW]
[ROW][C]4[/C][C]6560[/C][C]4599.93388552202[/C][C]1960.06611447798[/C][/ROW]
[ROW][C]5[/C][C]7840[/C][C]6559.87042598512[/C][C]1280.12957401488[/C][/ROW]
[ROW][C]6[/C][C]8560[/C][C]7839.91537452373[/C][C]720.084625476275[/C][/ROW]
[ROW][C]7[/C][C]10120[/C][C]8559.95239739349[/C][C]1560.04760260651[/C][/ROW]
[ROW][C]8[/C][C]9240[/C][C]10119.8968699934[/C][C]-879.896869993427[/C][/ROW]
[ROW][C]9[/C][C]9320[/C][C]9240.05816730838[/C][C]79.941832691622[/C][/ROW]
[ROW][C]10[/C][C]7000[/C][C]9319.99471528836[/C][C]-2319.99471528836[/C][/ROW]
[ROW][C]11[/C][C]3960[/C][C]7000.15336780098[/C][C]-3040.15336780098[/C][/ROW]
[ROW][C]12[/C][C]4680[/C][C]3960.20097530119[/C][C]719.799024698811[/C][/ROW]
[ROW][C]13[/C][C]3920[/C][C]4679.95241627369[/C][C]-759.952416273693[/C][/ROW]
[ROW][C]14[/C][C]1560[/C][C]3920.05023814501[/C][C]-2360.05023814501[/C][/ROW]
[ROW][C]15[/C][C]4800[/C][C]1560.15601574988[/C][C]3239.84398425012[/C][/ROW]
[ROW][C]16[/C][C]5240[/C][C]4799.78582375895[/C][C]440.214176241053[/C][/ROW]
[ROW][C]17[/C][C]8000[/C][C]5239.97089877846[/C][C]2760.02910122154[/C][/ROW]
[ROW][C]18[/C][C]9760[/C][C]7999.81754286288[/C][C]1760.18245713712[/C][/ROW]
[ROW][C]19[/C][C]9800[/C][C]9759.88363968633[/C][C]40.1163603136665[/C][/ROW]
[ROW][C]20[/C][C]9280[/C][C]9799.99734802932[/C][C]-519.997348029319[/C][/ROW]
[ROW][C]21[/C][C]7680[/C][C]9280.03437544459[/C][C]-1600.03437544459[/C][/ROW]
[ROW][C]22[/C][C]7760[/C][C]7680.10577341062[/C][C]79.8942265893811[/C][/ROW]
[ROW][C]23[/C][C]5680[/C][C]7759.99471843545[/C][C]-2079.99471843545[/C][/ROW]
[ROW][C]24[/C][C]4560[/C][C]5680.13750213046[/C][C]-1120.13750213046[/C][/ROW]
[ROW][C]25[/C][C]1560[/C][C]4560.07404888656[/C][C]-3000.07404888656[/C][/ROW]
[ROW][C]26[/C][C]3680[/C][C]1560.1983257792[/C][C]2119.8016742208[/C][/ROW]
[ROW][C]27[/C][C]4200[/C][C]3679.85986635265[/C][C]520.140133647351[/C][/ROW]
[ROW][C]28[/C][C]7400[/C][C]4199.96561511629[/C][C]3200.03438488371[/C][/ROW]
[ROW][C]29[/C][C]7040[/C][C]7399.78845545059[/C][C]-359.788455450594[/C][/ROW]
[ROW][C]30[/C][C]8480[/C][C]7040.02378452152[/C][C]1439.97621547848[/C][/ROW]
[ROW][C]31[/C][C]9720[/C][C]8479.90480754798[/C][C]1240.09519245202[/C][/ROW]
[ROW][C]32[/C][C]9760[/C][C]9719.91802107504[/C][C]40.0819789249599[/C][/ROW]
[ROW][C]33[/C][C]9440[/C][C]9759.99735030217[/C][C]-319.997350302168[/C][/ROW]
[ROW][C]34[/C][C]7240[/C][C]9440.02115405247[/C][C]-2200.02115405247[/C][/ROW]
[ROW][C]35[/C][C]5080[/C][C]7240.1454367134[/C][C]-2160.1454367134[/C][/ROW]
[ROW][C]36[/C][C]4080[/C][C]5080.1428006509[/C][C]-1000.1428006509[/C][/ROW]
[ROW][C]37[/C][C]5120[/C][C]4080.06611640147[/C][C]1039.93388359853[/C][/ROW]
[ROW][C]38[/C][C]4400[/C][C]5119.93125313095[/C][C]-719.931253130948[/C][/ROW]
[ROW][C]39[/C][C]5160[/C][C]4400.04759246753[/C][C]759.952407532473[/C][/ROW]
[ROW][C]40[/C][C]6680[/C][C]5159.94976185557[/C][C]1520.05023814443[/C][/ROW]
[ROW][C]41[/C][C]8240[/C][C]6679.89951409765[/C][C]1560.10048590235[/C][/ROW]
[ROW][C]42[/C][C]8960[/C][C]8239.89686649747[/C][C]720.103133502525[/C][/ROW]
[ROW][C]43[/C][C]9280[/C][C]8959.95239616999[/C][C]320.047603830015[/C][/ROW]
[ROW][C]44[/C][C]9880[/C][C]9279.97884262542[/C][C]600.021157374578[/C][/ROW]
[ROW][C]45[/C][C]8480[/C][C]9879.96033442454[/C][C]-1399.96033442454[/C][/ROW]
[ROW][C]46[/C][C]7320[/C][C]8480.09254712372[/C][C]-1160.09254712372[/C][/ROW]
[ROW][C]47[/C][C]4880[/C][C]7320.07669019318[/C][C]-2440.07669019318[/C][/ROW]
[ROW][C]48[/C][C]5280[/C][C]4880.16130605545[/C][C]399.838693944546[/C][/ROW]
[ROW][C]49[/C][C]4080[/C][C]5279.97356787891[/C][C]-1199.97356787891[/C][/ROW]
[ROW][C]50[/C][C]4720[/C][C]4080.07932660628[/C][C]639.920673393725[/C][/ROW]
[ROW][C]51[/C][C]6360[/C][C]4719.95769678878[/C][C]1640.04230321122[/C][/ROW]
[ROW][C]52[/C][C]5760[/C][C]6359.89158178685[/C][C]-599.891581786846[/C][/ROW]
[ROW][C]53[/C][C]9000[/C][C]5760.03965700961[/C][C]3239.96034299039[/C][/ROW]
[ROW][C]54[/C][C]9160[/C][C]8999.78581606682[/C][C]160.214183933176[/C][/ROW]
[ROW][C]55[/C][C]10480[/C][C]9159.98940872714[/C][C]1320.01059127286[/C][/ROW]
[ROW][C]56[/C][C]10160[/C][C]10479.9127381109[/C][C]-319.912738110857[/C][/ROW]
[ROW][C]57[/C][C]9120[/C][C]10160.021148459[/C][C]-1040.02114845901[/C][/ROW]
[ROW][C]58[/C][C]7880[/C][C]9120.06875263787[/C][C]-1240.06875263787[/C][/ROW]
[ROW][C]59[/C][C]5080[/C][C]7880.0819771771[/C][C]-2800.0819771771[/C][/ROW]
[ROW][C]60[/C][C]4360[/C][C]5080.18510491105[/C][C]-720.185104911047[/C][/ROW]
[ROW][C]61[/C][C]4480[/C][C]4360.0476092489[/C][C]119.952390751103[/C][/ROW]
[ROW][C]62[/C][C]6000[/C][C]4479.99207031194[/C][C]1520.00792968806[/C][/ROW]
[ROW][C]63[/C][C]6120[/C][C]5999.89951689454[/C][C]120.100483105462[/C][/ROW]
[ROW][C]64[/C][C]6200[/C][C]6119.992060522[/C][C]80.007939477995[/C][/ROW]
[ROW][C]65[/C][C]8960[/C][C]6199.99471091824[/C][C]2760.00528908176[/C][/ROW]
[ROW][C]66[/C][C]8680[/C][C]8959.81754443702[/C][C]-279.817544437024[/C][/ROW]
[ROW][C]67[/C][C]10240[/C][C]8680.0184978876[/C][C]1559.9815021124[/C][/ROW]
[ROW][C]68[/C][C]10920[/C][C]10239.8968743631[/C][C]680.10312563687[/C][/ROW]
[ROW][C]69[/C][C]8440[/C][C]10919.955040449[/C][C]-2479.95504044896[/C][/ROW]
[ROW][C]70[/C][C]7760[/C][C]8440.16394229201[/C][C]-680.163942292013[/C][/ROW]
[ROW][C]71[/C][C]5320[/C][C]7760.04496357145[/C][C]-2440.04496357145[/C][/ROW]
[ROW][C]72[/C][C]3920[/C][C]5320.1613039581[/C][C]-1400.1613039581[/C][/ROW]
[ROW][C]73[/C][C]4040[/C][C]3920.09256040921[/C][C]119.907439590793[/C][/ROW]
[ROW][C]74[/C][C]2960[/C][C]4039.99207328353[/C][C]-1079.99207328353[/C][/ROW]
[ROW][C]75[/C][C]6280[/C][C]2960.07139499425[/C][C]3319.92860500575[/C][/ROW]
[ROW][C]76[/C][C]6320[/C][C]6279.78052960802[/C][C]40.2194703919822[/C][/ROW]
[ROW][C]77[/C][C]7160[/C][C]6319.99734121302[/C][C]840.002658786975[/C][/ROW]
[ROW][C]78[/C][C]8160[/C][C]7159.9444699767[/C][C]1000.0555300233[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=300381&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=300381&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
2360018801720
346003599.886296026471000.11370397353
465604599.933885522021960.06611447798
578406559.870425985121280.12957401488
685607839.91537452373720.084625476275
7101208559.952397393491560.04760260651
8924010119.8968699934-879.896869993427
993209240.0581673083879.941832691622
1070009319.99471528836-2319.99471528836
1139607000.15336780098-3040.15336780098
1246803960.20097530119719.799024698811
1339204679.95241627369-759.952416273693
1415603920.05023814501-2360.05023814501
1548001560.156015749883239.84398425012
1652404799.78582375895440.214176241053
1780005239.970898778462760.02910122154
1897607999.817542862881760.18245713712
1998009759.8836396863340.1163603136665
2092809799.99734802932-519.997348029319
2176809280.03437544459-1600.03437544459
2277607680.1057734106279.8942265893811
2356807759.99471843545-2079.99471843545
2445605680.13750213046-1120.13750213046
2515604560.07404888656-3000.07404888656
2636801560.19832577922119.8016742208
2742003679.85986635265520.140133647351
2874004199.965615116293200.03438488371
2970407399.78845545059-359.788455450594
3084807040.023784521521439.97621547848
3197208479.904807547981240.09519245202
3297609719.9180210750440.0819789249599
3394409759.99735030217-319.997350302168
3472409440.02115405247-2200.02115405247
3550807240.1454367134-2160.1454367134
3640805080.1428006509-1000.1428006509
3751204080.066116401471039.93388359853
3844005119.93125313095-719.931253130948
3951604400.04759246753759.952407532473
4066805159.949761855571520.05023814443
4182406679.899514097651560.10048590235
4289608239.89686649747720.103133502525
4392808959.95239616999320.047603830015
4498809279.97884262542600.021157374578
4584809879.96033442454-1399.96033442454
4673208480.09254712372-1160.09254712372
4748807320.07669019318-2440.07669019318
4852804880.16130605545399.838693944546
4940805279.97356787891-1199.97356787891
5047204080.07932660628639.920673393725
5163604719.957696788781640.04230321122
5257606359.89158178685-599.891581786846
5390005760.039657009613239.96034299039
5491608999.78581606682160.214183933176
55104809159.989408727141320.01059127286
561016010479.9127381109-319.912738110857
57912010160.021148459-1040.02114845901
5878809120.06875263787-1240.06875263787
5950807880.0819771771-2800.0819771771
6043605080.18510491105-720.185104911047
6144804360.0476092489119.952390751103
6260004479.992070311941520.00792968806
6361205999.89951689454120.100483105462
6462006119.99206052280.007939477995
6589606199.994710918242760.00528908176
6686808959.81754443702-279.817544437024
67102408680.01849788761559.9815021124
681092010239.8968743631680.10312563687
69844010919.955040449-2479.95504044896
7077608440.16394229201-680.163942292013
7153207760.04496357145-2440.04496357145
7239205320.1613039581-1400.1613039581
7340403920.09256040921119.907439590793
7429604039.99207328353-1079.99207328353
7562802960.071394994253319.92860500575
7663206279.7805296080240.2194703919822
7771606319.99734121302840.002658786975
7881607159.94446997671000.0555300233







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
798159.933889367735068.5129870778111251.3547916576
808159.933889367733788.1490274401812531.7187512953
818159.933889367732805.6717961523913514.1959825831
828159.933889367731977.3986289178214342.4691498176
838159.933889367731247.6721805946715072.1955981408
848159.93388936773587.94725345545415731.92052528
858159.93388936773-18.733563114852616338.6013418503
868159.93388936773-583.41907057628316903.2868493117
878159.93388936773-1113.78384765817433.6516263934
888159.93388936773-1615.4157386450417935.2835173805
898159.93388936773-2092.5331324642918412.4009111997
908159.93388936773-2548.4133088518418868.2810875873

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
79 & 8159.93388936773 & 5068.51298707781 & 11251.3547916576 \tabularnewline
80 & 8159.93388936773 & 3788.14902744018 & 12531.7187512953 \tabularnewline
81 & 8159.93388936773 & 2805.67179615239 & 13514.1959825831 \tabularnewline
82 & 8159.93388936773 & 1977.39862891782 & 14342.4691498176 \tabularnewline
83 & 8159.93388936773 & 1247.67218059467 & 15072.1955981408 \tabularnewline
84 & 8159.93388936773 & 587.947253455454 & 15731.92052528 \tabularnewline
85 & 8159.93388936773 & -18.7335631148526 & 16338.6013418503 \tabularnewline
86 & 8159.93388936773 & -583.419070576283 & 16903.2868493117 \tabularnewline
87 & 8159.93388936773 & -1113.783847658 & 17433.6516263934 \tabularnewline
88 & 8159.93388936773 & -1615.41573864504 & 17935.2835173805 \tabularnewline
89 & 8159.93388936773 & -2092.53313246429 & 18412.4009111997 \tabularnewline
90 & 8159.93388936773 & -2548.41330885184 & 18868.2810875873 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=300381&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]79[/C][C]8159.93388936773[/C][C]5068.51298707781[/C][C]11251.3547916576[/C][/ROW]
[ROW][C]80[/C][C]8159.93388936773[/C][C]3788.14902744018[/C][C]12531.7187512953[/C][/ROW]
[ROW][C]81[/C][C]8159.93388936773[/C][C]2805.67179615239[/C][C]13514.1959825831[/C][/ROW]
[ROW][C]82[/C][C]8159.93388936773[/C][C]1977.39862891782[/C][C]14342.4691498176[/C][/ROW]
[ROW][C]83[/C][C]8159.93388936773[/C][C]1247.67218059467[/C][C]15072.1955981408[/C][/ROW]
[ROW][C]84[/C][C]8159.93388936773[/C][C]587.947253455454[/C][C]15731.92052528[/C][/ROW]
[ROW][C]85[/C][C]8159.93388936773[/C][C]-18.7335631148526[/C][C]16338.6013418503[/C][/ROW]
[ROW][C]86[/C][C]8159.93388936773[/C][C]-583.419070576283[/C][C]16903.2868493117[/C][/ROW]
[ROW][C]87[/C][C]8159.93388936773[/C][C]-1113.783847658[/C][C]17433.6516263934[/C][/ROW]
[ROW][C]88[/C][C]8159.93388936773[/C][C]-1615.41573864504[/C][C]17935.2835173805[/C][/ROW]
[ROW][C]89[/C][C]8159.93388936773[/C][C]-2092.53313246429[/C][C]18412.4009111997[/C][/ROW]
[ROW][C]90[/C][C]8159.93388936773[/C][C]-2548.41330885184[/C][C]18868.2810875873[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=300381&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=300381&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
798159.933889367735068.5129870778111251.3547916576
808159.933889367733788.1490274401812531.7187512953
818159.933889367732805.6717961523913514.1959825831
828159.933889367731977.3986289178214342.4691498176
838159.933889367731247.6721805946715072.1955981408
848159.93388936773587.94725345545415731.92052528
858159.93388936773-18.733563114852616338.6013418503
868159.93388936773-583.41907057628316903.2868493117
878159.93388936773-1113.78384765817433.6516263934
888159.93388936773-1615.4157386450417935.2835173805
898159.93388936773-2092.5331324642918412.4009111997
908159.93388936773-2548.4133088518418868.2810875873



Parameters (Session):
par1 = FALSE ; par2 = 1 ; par3 = 2 ; par4 = 0 ; par5 = 1 ; par6 = 3 ; par7 = 1 ; par8 = 2 ; par9 = 0 ;
Parameters (R input):
par1 = 12 ; par2 = Single ; 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')