Free Statistics

of Irreproducible Research!

Author's title

Author*The author of this computation has been verified*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationSun, 18 Dec 2016 12:47:26 +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/18/t1482061749r2hp9regvl43lhv.htm/, Retrieved Wed, 08 May 2024 07:52:31 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=301014, Retrieved Wed, 08 May 2024 07:52:31 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact114
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [Chi-Squared Test, McNemar Test, and Fisher Exact Test] [] [2015-11-15 16:35:00] [32b17a345b130fdf5cc88718ed94a974]
- RMPD    [Exponential Smoothing] [Exponential Smoot...] [2016-12-18 11:47:26] [2ea868439aa9f960cb5a0f1a9b97f873] [Current]
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Dataseries X:
7085
7390
6920
6955
6965
6990
7080
7030
7090
7035
6960
7035
6845
6970
6885
6935
6480
6340
6200
5990
5920
5750
5675
5890
5655
5515
5585
5630
5720
5650
5645
5735
5680
5620
5525
5500
5545
5430
5290
5235
5085
4885
5120
5030
4860
4915
5030
5115
4880
4780
4765
4815
4980
5050
5280
5040
4980
5025
5175
5205
5155
4995
5035
5005
4975
4940
5015
4920
4950
4930
4905
5015
5010
5045
5000
5060
4950
4995
4975
4930
5000
4955
4900
4910
4940
4945
4975
4900
4950
4865
4870
4785
4715
4630
4515
4510
4485
4470
4385
4310
4370
4425
4460
4430
4360
4320
4370
4370
4305
4255
4310
4375
4365
4400
4385
4305




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=301014&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=301014&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=301014&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
alpha0.937721786399397
beta0.252166254290168
gammaFALSE

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.937721786399397 \tabularnewline
beta & 0.252166254290168 \tabularnewline
gamma & FALSE \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=301014&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]0.937721786399397[/C][/ROW]
[ROW][C]beta[/C][C]0.252166254290168[/C][/ROW]
[ROW][C]gamma[/C][C]FALSE[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=301014&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=301014&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
alpha0.937721786399397
beta0.252166254290168
gammaFALSE







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
369207695-775
469557090.00772794744-135.007727947436
569657053.22598345177-88.2259834517708
669907039.45042596489-49.4504259648929
770807050.3424172514429.6575827485649
870307142.42859690419-112.428596904186
970907074.6924030293815.3075969706233
1070357130.35688284976-95.356882849761
1169607059.70060971233-99.7006097123322
1270356961.395744580973.6042554190954
1368457043.00722119282-198.00722119282
1469706823.10155670581146.89844329419
1568856961.35731697541-76.3573169754081
1669356872.2056990156462.7943009843566
1764806928.38803766983-448.38803766983
1863406399.19692234493-59.1969223449305
1962006220.96098468689-20.9609846868934
2059906073.6232468257-83.623246825704
2159205847.7520379048572.2479620951499
2257505785.12853993434-35.1285399343433
2356755613.5091992149161.490800785089
2458905547.03214412503342.967855874969
2556555825.60104922894-170.601049228936
2655155582.24457364756-67.2445736475602
2755855419.90694470205165.093055297954
2856305514.47557166451115.524428335485
2957205589.87973036644130.120269633558
3056505709.73919937483-59.7391993748279
3156455637.437269896057.56273010395125
3257355630.03412265725104.965877342749
3356805738.78844793999-58.78844793999
3456205680.08555313074-60.0855531307379
3555255605.95839705184-80.9583970518397
3655005493.114752965776.88524703423172
3755455464.2721055772780.7278944227255
3854305523.76237986424-93.7623798642408
3952905397.45810221865-107.458102218652
4052355232.901312092672.09868790733435
4150855171.57457041595-86.5745704159526
4248855006.62540461111-121.625404611113
4351204780.04854701235339.951452987652
4450305066.68789411875-36.6878941187479
4548604991.46903469734-131.469034697343
4649154796.28443148331118.715568516691
4750304863.77507720963166.224922790366
4851155015.1221223553599.8778776446534
4948805127.87139957817-247.871399578165
5047804855.91648840073-75.9164884007314
5147654727.256094941437.7439050586036
5248154714.10252004806100.897479951939
5349804784.0278269818195.972173018204
5450504989.4466758478260.5533241521807
5552805082.19886728932197.801132710677
5650405350.42372894405-310.423728944047
5749805068.67171469333-88.6717146933324
5850254973.8939229654651.1060770345412
5951755022.2734462737152.726553726303
6052055202.058698862342.9413011376555
6151555242.08256215052-87.0825621505219
6249955177.09738897509-182.097388975091
6350354979.9556680233255.04433197668
6450055018.20278656519-13.2027865651935
6549754989.33114064133-14.3311406413331
6649404956.01264534237-16.01264534237
6750154917.3309876639397.6690123360695
6849205008.34608663231-88.346086632313
6949504904.0403008751345.9596991248736
7049304936.54368920522-6.54368920521574
7149054918.26617397283-13.2661739728264
7250154890.54789506517124.452104934827
7350105021.3992142319-11.3992142318966
7450455022.1643130979722.8356869020272
7550005060.4319920234-60.4319920234002
7650605006.3278972836853.6721027163239
7749505071.91309960389-121.913099603895
7849954944.0204425283550.9795574716481
7949754990.30771413674-15.3077141367439
8049304970.81627750461-40.8162775046139
8150004917.7534152047482.2465847952617
8249554999.5374546786-44.5374546786043
8349004951.90193189505-51.9019318950459
8449104885.0877546368524.9122453631462
8549404896.1946990405343.8053009594705
8649454935.376353184299.62364681571307
8749754944.7807502989130.2192497010938
8849004980.64379083333-80.6437908333301
8949504893.4789677836256.5210322163848
9048654948.30165211079-83.3016521107884
9148704852.3119013065817.6880986934202
9247854855.20499952109-70.2049995210946
9347154759.07802478094-44.0780247809362
9446304677.02811480846-47.0281148084568
9545154581.09148891658-66.0914889165824
9645104451.65060999958.3493900009962
9744854452.69805559232.3019444080028
9844704436.9584195818833.0415804181175
9943854429.72542763718-44.7254276371787
10043104338.99276327853-28.9927632785284
10143704256.15728033237113.842719667627
10244254334.1811949371790.8188050628278
10344604412.0902604598747.9097395401332
10444304461.09138319919-31.091383199192
10543604428.65950785722-68.6595078572209
10643204344.76383339042-24.7638333904197
10743704296.1743888181173.8256111818873
10843704357.4913505308612.5086494691377
10943054364.26787901924-59.2678790192404
11042554289.72340420332-34.7234042033233
11143104229.9840598298480.0159401701576
11243754296.7590109091478.2409890908566
11343654380.37055605802-15.3705560580156
11444004372.565966656727.4340333432974
11543854411.3872739383-26.3872739383005
11643054393.4995867691-88.4995867690968

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
3 & 6920 & 7695 & -775 \tabularnewline
4 & 6955 & 7090.00772794744 & -135.007727947436 \tabularnewline
5 & 6965 & 7053.22598345177 & -88.2259834517708 \tabularnewline
6 & 6990 & 7039.45042596489 & -49.4504259648929 \tabularnewline
7 & 7080 & 7050.34241725144 & 29.6575827485649 \tabularnewline
8 & 7030 & 7142.42859690419 & -112.428596904186 \tabularnewline
9 & 7090 & 7074.69240302938 & 15.3075969706233 \tabularnewline
10 & 7035 & 7130.35688284976 & -95.356882849761 \tabularnewline
11 & 6960 & 7059.70060971233 & -99.7006097123322 \tabularnewline
12 & 7035 & 6961.3957445809 & 73.6042554190954 \tabularnewline
13 & 6845 & 7043.00722119282 & -198.00722119282 \tabularnewline
14 & 6970 & 6823.10155670581 & 146.89844329419 \tabularnewline
15 & 6885 & 6961.35731697541 & -76.3573169754081 \tabularnewline
16 & 6935 & 6872.20569901564 & 62.7943009843566 \tabularnewline
17 & 6480 & 6928.38803766983 & -448.38803766983 \tabularnewline
18 & 6340 & 6399.19692234493 & -59.1969223449305 \tabularnewline
19 & 6200 & 6220.96098468689 & -20.9609846868934 \tabularnewline
20 & 5990 & 6073.6232468257 & -83.623246825704 \tabularnewline
21 & 5920 & 5847.75203790485 & 72.2479620951499 \tabularnewline
22 & 5750 & 5785.12853993434 & -35.1285399343433 \tabularnewline
23 & 5675 & 5613.50919921491 & 61.490800785089 \tabularnewline
24 & 5890 & 5547.03214412503 & 342.967855874969 \tabularnewline
25 & 5655 & 5825.60104922894 & -170.601049228936 \tabularnewline
26 & 5515 & 5582.24457364756 & -67.2445736475602 \tabularnewline
27 & 5585 & 5419.90694470205 & 165.093055297954 \tabularnewline
28 & 5630 & 5514.47557166451 & 115.524428335485 \tabularnewline
29 & 5720 & 5589.87973036644 & 130.120269633558 \tabularnewline
30 & 5650 & 5709.73919937483 & -59.7391993748279 \tabularnewline
31 & 5645 & 5637.43726989605 & 7.56273010395125 \tabularnewline
32 & 5735 & 5630.03412265725 & 104.965877342749 \tabularnewline
33 & 5680 & 5738.78844793999 & -58.78844793999 \tabularnewline
34 & 5620 & 5680.08555313074 & -60.0855531307379 \tabularnewline
35 & 5525 & 5605.95839705184 & -80.9583970518397 \tabularnewline
36 & 5500 & 5493.11475296577 & 6.88524703423172 \tabularnewline
37 & 5545 & 5464.27210557727 & 80.7278944227255 \tabularnewline
38 & 5430 & 5523.76237986424 & -93.7623798642408 \tabularnewline
39 & 5290 & 5397.45810221865 & -107.458102218652 \tabularnewline
40 & 5235 & 5232.90131209267 & 2.09868790733435 \tabularnewline
41 & 5085 & 5171.57457041595 & -86.5745704159526 \tabularnewline
42 & 4885 & 5006.62540461111 & -121.625404611113 \tabularnewline
43 & 5120 & 4780.04854701235 & 339.951452987652 \tabularnewline
44 & 5030 & 5066.68789411875 & -36.6878941187479 \tabularnewline
45 & 4860 & 4991.46903469734 & -131.469034697343 \tabularnewline
46 & 4915 & 4796.28443148331 & 118.715568516691 \tabularnewline
47 & 5030 & 4863.77507720963 & 166.224922790366 \tabularnewline
48 & 5115 & 5015.12212235535 & 99.8778776446534 \tabularnewline
49 & 4880 & 5127.87139957817 & -247.871399578165 \tabularnewline
50 & 4780 & 4855.91648840073 & -75.9164884007314 \tabularnewline
51 & 4765 & 4727.2560949414 & 37.7439050586036 \tabularnewline
52 & 4815 & 4714.10252004806 & 100.897479951939 \tabularnewline
53 & 4980 & 4784.0278269818 & 195.972173018204 \tabularnewline
54 & 5050 & 4989.44667584782 & 60.5533241521807 \tabularnewline
55 & 5280 & 5082.19886728932 & 197.801132710677 \tabularnewline
56 & 5040 & 5350.42372894405 & -310.423728944047 \tabularnewline
57 & 4980 & 5068.67171469333 & -88.6717146933324 \tabularnewline
58 & 5025 & 4973.89392296546 & 51.1060770345412 \tabularnewline
59 & 5175 & 5022.2734462737 & 152.726553726303 \tabularnewline
60 & 5205 & 5202.05869886234 & 2.9413011376555 \tabularnewline
61 & 5155 & 5242.08256215052 & -87.0825621505219 \tabularnewline
62 & 4995 & 5177.09738897509 & -182.097388975091 \tabularnewline
63 & 5035 & 4979.95566802332 & 55.04433197668 \tabularnewline
64 & 5005 & 5018.20278656519 & -13.2027865651935 \tabularnewline
65 & 4975 & 4989.33114064133 & -14.3311406413331 \tabularnewline
66 & 4940 & 4956.01264534237 & -16.01264534237 \tabularnewline
67 & 5015 & 4917.33098766393 & 97.6690123360695 \tabularnewline
68 & 4920 & 5008.34608663231 & -88.346086632313 \tabularnewline
69 & 4950 & 4904.04030087513 & 45.9596991248736 \tabularnewline
70 & 4930 & 4936.54368920522 & -6.54368920521574 \tabularnewline
71 & 4905 & 4918.26617397283 & -13.2661739728264 \tabularnewline
72 & 5015 & 4890.54789506517 & 124.452104934827 \tabularnewline
73 & 5010 & 5021.3992142319 & -11.3992142318966 \tabularnewline
74 & 5045 & 5022.16431309797 & 22.8356869020272 \tabularnewline
75 & 5000 & 5060.4319920234 & -60.4319920234002 \tabularnewline
76 & 5060 & 5006.32789728368 & 53.6721027163239 \tabularnewline
77 & 4950 & 5071.91309960389 & -121.913099603895 \tabularnewline
78 & 4995 & 4944.02044252835 & 50.9795574716481 \tabularnewline
79 & 4975 & 4990.30771413674 & -15.3077141367439 \tabularnewline
80 & 4930 & 4970.81627750461 & -40.8162775046139 \tabularnewline
81 & 5000 & 4917.75341520474 & 82.2465847952617 \tabularnewline
82 & 4955 & 4999.5374546786 & -44.5374546786043 \tabularnewline
83 & 4900 & 4951.90193189505 & -51.9019318950459 \tabularnewline
84 & 4910 & 4885.08775463685 & 24.9122453631462 \tabularnewline
85 & 4940 & 4896.19469904053 & 43.8053009594705 \tabularnewline
86 & 4945 & 4935.37635318429 & 9.62364681571307 \tabularnewline
87 & 4975 & 4944.78075029891 & 30.2192497010938 \tabularnewline
88 & 4900 & 4980.64379083333 & -80.6437908333301 \tabularnewline
89 & 4950 & 4893.47896778362 & 56.5210322163848 \tabularnewline
90 & 4865 & 4948.30165211079 & -83.3016521107884 \tabularnewline
91 & 4870 & 4852.31190130658 & 17.6880986934202 \tabularnewline
92 & 4785 & 4855.20499952109 & -70.2049995210946 \tabularnewline
93 & 4715 & 4759.07802478094 & -44.0780247809362 \tabularnewline
94 & 4630 & 4677.02811480846 & -47.0281148084568 \tabularnewline
95 & 4515 & 4581.09148891658 & -66.0914889165824 \tabularnewline
96 & 4510 & 4451.650609999 & 58.3493900009962 \tabularnewline
97 & 4485 & 4452.698055592 & 32.3019444080028 \tabularnewline
98 & 4470 & 4436.95841958188 & 33.0415804181175 \tabularnewline
99 & 4385 & 4429.72542763718 & -44.7254276371787 \tabularnewline
100 & 4310 & 4338.99276327853 & -28.9927632785284 \tabularnewline
101 & 4370 & 4256.15728033237 & 113.842719667627 \tabularnewline
102 & 4425 & 4334.18119493717 & 90.8188050628278 \tabularnewline
103 & 4460 & 4412.09026045987 & 47.9097395401332 \tabularnewline
104 & 4430 & 4461.09138319919 & -31.091383199192 \tabularnewline
105 & 4360 & 4428.65950785722 & -68.6595078572209 \tabularnewline
106 & 4320 & 4344.76383339042 & -24.7638333904197 \tabularnewline
107 & 4370 & 4296.17438881811 & 73.8256111818873 \tabularnewline
108 & 4370 & 4357.49135053086 & 12.5086494691377 \tabularnewline
109 & 4305 & 4364.26787901924 & -59.2678790192404 \tabularnewline
110 & 4255 & 4289.72340420332 & -34.7234042033233 \tabularnewline
111 & 4310 & 4229.98405982984 & 80.0159401701576 \tabularnewline
112 & 4375 & 4296.75901090914 & 78.2409890908566 \tabularnewline
113 & 4365 & 4380.37055605802 & -15.3705560580156 \tabularnewline
114 & 4400 & 4372.5659666567 & 27.4340333432974 \tabularnewline
115 & 4385 & 4411.3872739383 & -26.3872739383005 \tabularnewline
116 & 4305 & 4393.4995867691 & -88.4995867690968 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=301014&T=2

[TABLE]
[ROW][C]Interpolation Forecasts of Exponential Smoothing[/C][/ROW]
[ROW][C]t[/C][C]Observed[/C][C]Fitted[/C][C]Residuals[/C][/ROW]
[ROW][C]3[/C][C]6920[/C][C]7695[/C][C]-775[/C][/ROW]
[ROW][C]4[/C][C]6955[/C][C]7090.00772794744[/C][C]-135.007727947436[/C][/ROW]
[ROW][C]5[/C][C]6965[/C][C]7053.22598345177[/C][C]-88.2259834517708[/C][/ROW]
[ROW][C]6[/C][C]6990[/C][C]7039.45042596489[/C][C]-49.4504259648929[/C][/ROW]
[ROW][C]7[/C][C]7080[/C][C]7050.34241725144[/C][C]29.6575827485649[/C][/ROW]
[ROW][C]8[/C][C]7030[/C][C]7142.42859690419[/C][C]-112.428596904186[/C][/ROW]
[ROW][C]9[/C][C]7090[/C][C]7074.69240302938[/C][C]15.3075969706233[/C][/ROW]
[ROW][C]10[/C][C]7035[/C][C]7130.35688284976[/C][C]-95.356882849761[/C][/ROW]
[ROW][C]11[/C][C]6960[/C][C]7059.70060971233[/C][C]-99.7006097123322[/C][/ROW]
[ROW][C]12[/C][C]7035[/C][C]6961.3957445809[/C][C]73.6042554190954[/C][/ROW]
[ROW][C]13[/C][C]6845[/C][C]7043.00722119282[/C][C]-198.00722119282[/C][/ROW]
[ROW][C]14[/C][C]6970[/C][C]6823.10155670581[/C][C]146.89844329419[/C][/ROW]
[ROW][C]15[/C][C]6885[/C][C]6961.35731697541[/C][C]-76.3573169754081[/C][/ROW]
[ROW][C]16[/C][C]6935[/C][C]6872.20569901564[/C][C]62.7943009843566[/C][/ROW]
[ROW][C]17[/C][C]6480[/C][C]6928.38803766983[/C][C]-448.38803766983[/C][/ROW]
[ROW][C]18[/C][C]6340[/C][C]6399.19692234493[/C][C]-59.1969223449305[/C][/ROW]
[ROW][C]19[/C][C]6200[/C][C]6220.96098468689[/C][C]-20.9609846868934[/C][/ROW]
[ROW][C]20[/C][C]5990[/C][C]6073.6232468257[/C][C]-83.623246825704[/C][/ROW]
[ROW][C]21[/C][C]5920[/C][C]5847.75203790485[/C][C]72.2479620951499[/C][/ROW]
[ROW][C]22[/C][C]5750[/C][C]5785.12853993434[/C][C]-35.1285399343433[/C][/ROW]
[ROW][C]23[/C][C]5675[/C][C]5613.50919921491[/C][C]61.490800785089[/C][/ROW]
[ROW][C]24[/C][C]5890[/C][C]5547.03214412503[/C][C]342.967855874969[/C][/ROW]
[ROW][C]25[/C][C]5655[/C][C]5825.60104922894[/C][C]-170.601049228936[/C][/ROW]
[ROW][C]26[/C][C]5515[/C][C]5582.24457364756[/C][C]-67.2445736475602[/C][/ROW]
[ROW][C]27[/C][C]5585[/C][C]5419.90694470205[/C][C]165.093055297954[/C][/ROW]
[ROW][C]28[/C][C]5630[/C][C]5514.47557166451[/C][C]115.524428335485[/C][/ROW]
[ROW][C]29[/C][C]5720[/C][C]5589.87973036644[/C][C]130.120269633558[/C][/ROW]
[ROW][C]30[/C][C]5650[/C][C]5709.73919937483[/C][C]-59.7391993748279[/C][/ROW]
[ROW][C]31[/C][C]5645[/C][C]5637.43726989605[/C][C]7.56273010395125[/C][/ROW]
[ROW][C]32[/C][C]5735[/C][C]5630.03412265725[/C][C]104.965877342749[/C][/ROW]
[ROW][C]33[/C][C]5680[/C][C]5738.78844793999[/C][C]-58.78844793999[/C][/ROW]
[ROW][C]34[/C][C]5620[/C][C]5680.08555313074[/C][C]-60.0855531307379[/C][/ROW]
[ROW][C]35[/C][C]5525[/C][C]5605.95839705184[/C][C]-80.9583970518397[/C][/ROW]
[ROW][C]36[/C][C]5500[/C][C]5493.11475296577[/C][C]6.88524703423172[/C][/ROW]
[ROW][C]37[/C][C]5545[/C][C]5464.27210557727[/C][C]80.7278944227255[/C][/ROW]
[ROW][C]38[/C][C]5430[/C][C]5523.76237986424[/C][C]-93.7623798642408[/C][/ROW]
[ROW][C]39[/C][C]5290[/C][C]5397.45810221865[/C][C]-107.458102218652[/C][/ROW]
[ROW][C]40[/C][C]5235[/C][C]5232.90131209267[/C][C]2.09868790733435[/C][/ROW]
[ROW][C]41[/C][C]5085[/C][C]5171.57457041595[/C][C]-86.5745704159526[/C][/ROW]
[ROW][C]42[/C][C]4885[/C][C]5006.62540461111[/C][C]-121.625404611113[/C][/ROW]
[ROW][C]43[/C][C]5120[/C][C]4780.04854701235[/C][C]339.951452987652[/C][/ROW]
[ROW][C]44[/C][C]5030[/C][C]5066.68789411875[/C][C]-36.6878941187479[/C][/ROW]
[ROW][C]45[/C][C]4860[/C][C]4991.46903469734[/C][C]-131.469034697343[/C][/ROW]
[ROW][C]46[/C][C]4915[/C][C]4796.28443148331[/C][C]118.715568516691[/C][/ROW]
[ROW][C]47[/C][C]5030[/C][C]4863.77507720963[/C][C]166.224922790366[/C][/ROW]
[ROW][C]48[/C][C]5115[/C][C]5015.12212235535[/C][C]99.8778776446534[/C][/ROW]
[ROW][C]49[/C][C]4880[/C][C]5127.87139957817[/C][C]-247.871399578165[/C][/ROW]
[ROW][C]50[/C][C]4780[/C][C]4855.91648840073[/C][C]-75.9164884007314[/C][/ROW]
[ROW][C]51[/C][C]4765[/C][C]4727.2560949414[/C][C]37.7439050586036[/C][/ROW]
[ROW][C]52[/C][C]4815[/C][C]4714.10252004806[/C][C]100.897479951939[/C][/ROW]
[ROW][C]53[/C][C]4980[/C][C]4784.0278269818[/C][C]195.972173018204[/C][/ROW]
[ROW][C]54[/C][C]5050[/C][C]4989.44667584782[/C][C]60.5533241521807[/C][/ROW]
[ROW][C]55[/C][C]5280[/C][C]5082.19886728932[/C][C]197.801132710677[/C][/ROW]
[ROW][C]56[/C][C]5040[/C][C]5350.42372894405[/C][C]-310.423728944047[/C][/ROW]
[ROW][C]57[/C][C]4980[/C][C]5068.67171469333[/C][C]-88.6717146933324[/C][/ROW]
[ROW][C]58[/C][C]5025[/C][C]4973.89392296546[/C][C]51.1060770345412[/C][/ROW]
[ROW][C]59[/C][C]5175[/C][C]5022.2734462737[/C][C]152.726553726303[/C][/ROW]
[ROW][C]60[/C][C]5205[/C][C]5202.05869886234[/C][C]2.9413011376555[/C][/ROW]
[ROW][C]61[/C][C]5155[/C][C]5242.08256215052[/C][C]-87.0825621505219[/C][/ROW]
[ROW][C]62[/C][C]4995[/C][C]5177.09738897509[/C][C]-182.097388975091[/C][/ROW]
[ROW][C]63[/C][C]5035[/C][C]4979.95566802332[/C][C]55.04433197668[/C][/ROW]
[ROW][C]64[/C][C]5005[/C][C]5018.20278656519[/C][C]-13.2027865651935[/C][/ROW]
[ROW][C]65[/C][C]4975[/C][C]4989.33114064133[/C][C]-14.3311406413331[/C][/ROW]
[ROW][C]66[/C][C]4940[/C][C]4956.01264534237[/C][C]-16.01264534237[/C][/ROW]
[ROW][C]67[/C][C]5015[/C][C]4917.33098766393[/C][C]97.6690123360695[/C][/ROW]
[ROW][C]68[/C][C]4920[/C][C]5008.34608663231[/C][C]-88.346086632313[/C][/ROW]
[ROW][C]69[/C][C]4950[/C][C]4904.04030087513[/C][C]45.9596991248736[/C][/ROW]
[ROW][C]70[/C][C]4930[/C][C]4936.54368920522[/C][C]-6.54368920521574[/C][/ROW]
[ROW][C]71[/C][C]4905[/C][C]4918.26617397283[/C][C]-13.2661739728264[/C][/ROW]
[ROW][C]72[/C][C]5015[/C][C]4890.54789506517[/C][C]124.452104934827[/C][/ROW]
[ROW][C]73[/C][C]5010[/C][C]5021.3992142319[/C][C]-11.3992142318966[/C][/ROW]
[ROW][C]74[/C][C]5045[/C][C]5022.16431309797[/C][C]22.8356869020272[/C][/ROW]
[ROW][C]75[/C][C]5000[/C][C]5060.4319920234[/C][C]-60.4319920234002[/C][/ROW]
[ROW][C]76[/C][C]5060[/C][C]5006.32789728368[/C][C]53.6721027163239[/C][/ROW]
[ROW][C]77[/C][C]4950[/C][C]5071.91309960389[/C][C]-121.913099603895[/C][/ROW]
[ROW][C]78[/C][C]4995[/C][C]4944.02044252835[/C][C]50.9795574716481[/C][/ROW]
[ROW][C]79[/C][C]4975[/C][C]4990.30771413674[/C][C]-15.3077141367439[/C][/ROW]
[ROW][C]80[/C][C]4930[/C][C]4970.81627750461[/C][C]-40.8162775046139[/C][/ROW]
[ROW][C]81[/C][C]5000[/C][C]4917.75341520474[/C][C]82.2465847952617[/C][/ROW]
[ROW][C]82[/C][C]4955[/C][C]4999.5374546786[/C][C]-44.5374546786043[/C][/ROW]
[ROW][C]83[/C][C]4900[/C][C]4951.90193189505[/C][C]-51.9019318950459[/C][/ROW]
[ROW][C]84[/C][C]4910[/C][C]4885.08775463685[/C][C]24.9122453631462[/C][/ROW]
[ROW][C]85[/C][C]4940[/C][C]4896.19469904053[/C][C]43.8053009594705[/C][/ROW]
[ROW][C]86[/C][C]4945[/C][C]4935.37635318429[/C][C]9.62364681571307[/C][/ROW]
[ROW][C]87[/C][C]4975[/C][C]4944.78075029891[/C][C]30.2192497010938[/C][/ROW]
[ROW][C]88[/C][C]4900[/C][C]4980.64379083333[/C][C]-80.6437908333301[/C][/ROW]
[ROW][C]89[/C][C]4950[/C][C]4893.47896778362[/C][C]56.5210322163848[/C][/ROW]
[ROW][C]90[/C][C]4865[/C][C]4948.30165211079[/C][C]-83.3016521107884[/C][/ROW]
[ROW][C]91[/C][C]4870[/C][C]4852.31190130658[/C][C]17.6880986934202[/C][/ROW]
[ROW][C]92[/C][C]4785[/C][C]4855.20499952109[/C][C]-70.2049995210946[/C][/ROW]
[ROW][C]93[/C][C]4715[/C][C]4759.07802478094[/C][C]-44.0780247809362[/C][/ROW]
[ROW][C]94[/C][C]4630[/C][C]4677.02811480846[/C][C]-47.0281148084568[/C][/ROW]
[ROW][C]95[/C][C]4515[/C][C]4581.09148891658[/C][C]-66.0914889165824[/C][/ROW]
[ROW][C]96[/C][C]4510[/C][C]4451.650609999[/C][C]58.3493900009962[/C][/ROW]
[ROW][C]97[/C][C]4485[/C][C]4452.698055592[/C][C]32.3019444080028[/C][/ROW]
[ROW][C]98[/C][C]4470[/C][C]4436.95841958188[/C][C]33.0415804181175[/C][/ROW]
[ROW][C]99[/C][C]4385[/C][C]4429.72542763718[/C][C]-44.7254276371787[/C][/ROW]
[ROW][C]100[/C][C]4310[/C][C]4338.99276327853[/C][C]-28.9927632785284[/C][/ROW]
[ROW][C]101[/C][C]4370[/C][C]4256.15728033237[/C][C]113.842719667627[/C][/ROW]
[ROW][C]102[/C][C]4425[/C][C]4334.18119493717[/C][C]90.8188050628278[/C][/ROW]
[ROW][C]103[/C][C]4460[/C][C]4412.09026045987[/C][C]47.9097395401332[/C][/ROW]
[ROW][C]104[/C][C]4430[/C][C]4461.09138319919[/C][C]-31.091383199192[/C][/ROW]
[ROW][C]105[/C][C]4360[/C][C]4428.65950785722[/C][C]-68.6595078572209[/C][/ROW]
[ROW][C]106[/C][C]4320[/C][C]4344.76383339042[/C][C]-24.7638333904197[/C][/ROW]
[ROW][C]107[/C][C]4370[/C][C]4296.17438881811[/C][C]73.8256111818873[/C][/ROW]
[ROW][C]108[/C][C]4370[/C][C]4357.49135053086[/C][C]12.5086494691377[/C][/ROW]
[ROW][C]109[/C][C]4305[/C][C]4364.26787901924[/C][C]-59.2678790192404[/C][/ROW]
[ROW][C]110[/C][C]4255[/C][C]4289.72340420332[/C][C]-34.7234042033233[/C][/ROW]
[ROW][C]111[/C][C]4310[/C][C]4229.98405982984[/C][C]80.0159401701576[/C][/ROW]
[ROW][C]112[/C][C]4375[/C][C]4296.75901090914[/C][C]78.2409890908566[/C][/ROW]
[ROW][C]113[/C][C]4365[/C][C]4380.37055605802[/C][C]-15.3705560580156[/C][/ROW]
[ROW][C]114[/C][C]4400[/C][C]4372.5659666567[/C][C]27.4340333432974[/C][/ROW]
[ROW][C]115[/C][C]4385[/C][C]4411.3872739383[/C][C]-26.3872739383005[/C][/ROW]
[ROW][C]116[/C][C]4305[/C][C]4393.4995867691[/C][C]-88.4995867690968[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=301014&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=301014&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
369207695-775
469557090.00772794744-135.007727947436
569657053.22598345177-88.2259834517708
669907039.45042596489-49.4504259648929
770807050.3424172514429.6575827485649
870307142.42859690419-112.428596904186
970907074.6924030293815.3075969706233
1070357130.35688284976-95.356882849761
1169607059.70060971233-99.7006097123322
1270356961.395744580973.6042554190954
1368457043.00722119282-198.00722119282
1469706823.10155670581146.89844329419
1568856961.35731697541-76.3573169754081
1669356872.2056990156462.7943009843566
1764806928.38803766983-448.38803766983
1863406399.19692234493-59.1969223449305
1962006220.96098468689-20.9609846868934
2059906073.6232468257-83.623246825704
2159205847.7520379048572.2479620951499
2257505785.12853993434-35.1285399343433
2356755613.5091992149161.490800785089
2458905547.03214412503342.967855874969
2556555825.60104922894-170.601049228936
2655155582.24457364756-67.2445736475602
2755855419.90694470205165.093055297954
2856305514.47557166451115.524428335485
2957205589.87973036644130.120269633558
3056505709.73919937483-59.7391993748279
3156455637.437269896057.56273010395125
3257355630.03412265725104.965877342749
3356805738.78844793999-58.78844793999
3456205680.08555313074-60.0855531307379
3555255605.95839705184-80.9583970518397
3655005493.114752965776.88524703423172
3755455464.2721055772780.7278944227255
3854305523.76237986424-93.7623798642408
3952905397.45810221865-107.458102218652
4052355232.901312092672.09868790733435
4150855171.57457041595-86.5745704159526
4248855006.62540461111-121.625404611113
4351204780.04854701235339.951452987652
4450305066.68789411875-36.6878941187479
4548604991.46903469734-131.469034697343
4649154796.28443148331118.715568516691
4750304863.77507720963166.224922790366
4851155015.1221223553599.8778776446534
4948805127.87139957817-247.871399578165
5047804855.91648840073-75.9164884007314
5147654727.256094941437.7439050586036
5248154714.10252004806100.897479951939
5349804784.0278269818195.972173018204
5450504989.4466758478260.5533241521807
5552805082.19886728932197.801132710677
5650405350.42372894405-310.423728944047
5749805068.67171469333-88.6717146933324
5850254973.8939229654651.1060770345412
5951755022.2734462737152.726553726303
6052055202.058698862342.9413011376555
6151555242.08256215052-87.0825621505219
6249955177.09738897509-182.097388975091
6350354979.9556680233255.04433197668
6450055018.20278656519-13.2027865651935
6549754989.33114064133-14.3311406413331
6649404956.01264534237-16.01264534237
6750154917.3309876639397.6690123360695
6849205008.34608663231-88.346086632313
6949504904.0403008751345.9596991248736
7049304936.54368920522-6.54368920521574
7149054918.26617397283-13.2661739728264
7250154890.54789506517124.452104934827
7350105021.3992142319-11.3992142318966
7450455022.1643130979722.8356869020272
7550005060.4319920234-60.4319920234002
7650605006.3278972836853.6721027163239
7749505071.91309960389-121.913099603895
7849954944.0204425283550.9795574716481
7949754990.30771413674-15.3077141367439
8049304970.81627750461-40.8162775046139
8150004917.7534152047482.2465847952617
8249554999.5374546786-44.5374546786043
8349004951.90193189505-51.9019318950459
8449104885.0877546368524.9122453631462
8549404896.1946990405343.8053009594705
8649454935.376353184299.62364681571307
8749754944.7807502989130.2192497010938
8849004980.64379083333-80.6437908333301
8949504893.4789677836256.5210322163848
9048654948.30165211079-83.3016521107884
9148704852.3119013065817.6880986934202
9247854855.20499952109-70.2049995210946
9347154759.07802478094-44.0780247809362
9446304677.02811480846-47.0281148084568
9545154581.09148891658-66.0914889165824
9645104451.65060999958.3493900009962
9744854452.69805559232.3019444080028
9844704436.9584195818833.0415804181175
9943854429.72542763718-44.7254276371787
10043104338.99276327853-28.9927632785284
10143704256.15728033237113.842719667627
10244254334.1811949371790.8188050628278
10344604412.0902604598747.9097395401332
10444304461.09138319919-31.091383199192
10543604428.65950785722-68.6595078572209
10643204344.76383339042-24.7638333904197
10743704296.1743888181173.8256111818873
10843704357.4913505308612.5086494691377
10943054364.26787901924-59.2678790192404
11042554289.72340420332-34.7234042033233
11143104229.9840598298480.0159401701576
11243754296.7590109091478.2409890908566
11343654380.37055605802-15.3705560580156
11444004372.565966656727.4340333432974
11543854411.3872739383-26.3872739383005
11643054393.4995867691-88.4995867690968







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
1174296.441059913954040.39666962814552.4854501998
1184282.370523659523887.471784477774677.26926284128
1194268.29998740513733.134905493734803.46506931647
1204254.229451150683572.8631716174935.59573068436
1214240.158914896263405.382678296565074.93515149595
1224226.088378641833230.343900959795221.83285632388
1234212.017842387413047.733327832275376.30235694255
1244197.947306132992857.67241335675538.22219890927
1254183.876769878562660.336989638425707.41655011871
1264169.806233624142455.92182178215883.69064546618
1274155.735697369722244.624225275956066.84716946349
1284141.665161115292026.636406740266256.69391549032

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
117 & 4296.44105991395 & 4040.3966696281 & 4552.4854501998 \tabularnewline
118 & 4282.37052365952 & 3887.47178447777 & 4677.26926284128 \tabularnewline
119 & 4268.2999874051 & 3733.13490549373 & 4803.46506931647 \tabularnewline
120 & 4254.22945115068 & 3572.863171617 & 4935.59573068436 \tabularnewline
121 & 4240.15891489626 & 3405.38267829656 & 5074.93515149595 \tabularnewline
122 & 4226.08837864183 & 3230.34390095979 & 5221.83285632388 \tabularnewline
123 & 4212.01784238741 & 3047.73332783227 & 5376.30235694255 \tabularnewline
124 & 4197.94730613299 & 2857.6724133567 & 5538.22219890927 \tabularnewline
125 & 4183.87676987856 & 2660.33698963842 & 5707.41655011871 \tabularnewline
126 & 4169.80623362414 & 2455.9218217821 & 5883.69064546618 \tabularnewline
127 & 4155.73569736972 & 2244.62422527595 & 6066.84716946349 \tabularnewline
128 & 4141.66516111529 & 2026.63640674026 & 6256.69391549032 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=301014&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]4296.44105991395[/C][C]4040.3966696281[/C][C]4552.4854501998[/C][/ROW]
[ROW][C]118[/C][C]4282.37052365952[/C][C]3887.47178447777[/C][C]4677.26926284128[/C][/ROW]
[ROW][C]119[/C][C]4268.2999874051[/C][C]3733.13490549373[/C][C]4803.46506931647[/C][/ROW]
[ROW][C]120[/C][C]4254.22945115068[/C][C]3572.863171617[/C][C]4935.59573068436[/C][/ROW]
[ROW][C]121[/C][C]4240.15891489626[/C][C]3405.38267829656[/C][C]5074.93515149595[/C][/ROW]
[ROW][C]122[/C][C]4226.08837864183[/C][C]3230.34390095979[/C][C]5221.83285632388[/C][/ROW]
[ROW][C]123[/C][C]4212.01784238741[/C][C]3047.73332783227[/C][C]5376.30235694255[/C][/ROW]
[ROW][C]124[/C][C]4197.94730613299[/C][C]2857.6724133567[/C][C]5538.22219890927[/C][/ROW]
[ROW][C]125[/C][C]4183.87676987856[/C][C]2660.33698963842[/C][C]5707.41655011871[/C][/ROW]
[ROW][C]126[/C][C]4169.80623362414[/C][C]2455.9218217821[/C][C]5883.69064546618[/C][/ROW]
[ROW][C]127[/C][C]4155.73569736972[/C][C]2244.62422527595[/C][C]6066.84716946349[/C][/ROW]
[ROW][C]128[/C][C]4141.66516111529[/C][C]2026.63640674026[/C][C]6256.69391549032[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=301014&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=301014&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
1174296.441059913954040.39666962814552.4854501998
1184282.370523659523887.471784477774677.26926284128
1194268.29998740513733.134905493734803.46506931647
1204254.229451150683572.8631716174935.59573068436
1214240.158914896263405.382678296565074.93515149595
1224226.088378641833230.343900959795221.83285632388
1234212.017842387413047.733327832275376.30235694255
1244197.947306132992857.67241335675538.22219890927
1254183.876769878562660.336989638425707.41655011871
1264169.806233624142455.92182178215883.69064546618
1274155.735697369722244.624225275956066.84716946349
1284141.665161115292026.636406740266256.69391549032



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