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of Irreproducible Research!

Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationMon, 01 Aug 2011 05:46:12 -0400
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2011/Aug/01/t13121922937s4xw1en921fkn2.htm/, Retrieved Tue, 14 May 2024 22:40:49 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=123238, Retrieved Tue, 14 May 2024 22:40:49 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywordsvicky Koopmans
Estimated Impact149
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [tijdreeks1-stap26] [2011-08-01 09:46:12] [30681199eb2b91d06bf445c1ee7d20a2] [Current]
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Dataseries X:
5115
5105
5094
5074
5280
5270
5115
5012
5022
5022
5032
5053
5053
4960
4919
4960
5105
5084
4888
4722
4691
4629
4671
4722
4702
4660
4578
4660
4733
4712
4474
4371
4268
4185
4175
4237
4154
4123
4092
4268
4288
4185
3906
3782
3586
3503
3544
3606
3606
3555
3544
3710
3844
3782
3575
3472
3255
3121
3224
3327
3327
3193
3183
3358
3472
3431
3224
3090
2800
2687
2728
2904
2914
2656
2749
2976
3079
3017
2738
2542
2315
2139
2211
2366
2325
2098
2170
2397
2521
2449
2170
2046
1860
1664
1695
1850
1870
1684
1715
1974
2036
1932
1550
1354
1095
837
920
1033
1013
816
930
1209
1333
1271
1023
827
620
382
424
496




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time1 seconds
R Server'Herman Ole Andreas Wold' @ wold.wessa.net

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input & view raw input (R code)  \tabularnewline
Raw Output & view raw output of R engine  \tabularnewline
Computing time & 1 seconds \tabularnewline
R Server & 'Herman Ole Andreas Wold' @ wold.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=123238&T=0

[TABLE]
[ROW][C]Summary of computational transaction[/C][/ROW]
[ROW][C]Raw Input[/C][C]view raw input (R code) [/C][/ROW]
[ROW][C]Raw Output[/C][C]view raw output of R engine [/C][/ROW]
[ROW][C]Computing time[/C][C]1 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Herman Ole Andreas Wold' @ wold.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=123238&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=123238&T=0

As an alternative you can also use a QR Code:  

The GUIDs for individual cells are displayed in the table below:

Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time1 seconds
R Server'Herman Ole Andreas Wold' @ wold.wessa.net







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.380191006554846
beta0.0252544559107445
gamma1

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.380191006554846 \tabularnewline
beta & 0.0252544559107445 \tabularnewline
gamma & 1 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=123238&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]0.380191006554846[/C][/ROW]
[ROW][C]beta[/C][C]0.0252544559107445[/C][/ROW]
[ROW][C]gamma[/C][C]1[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=123238&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=123238&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
alpha0.380191006554846
beta0.0252544559107445
gamma1







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
1350535133.87302878633-80.8730287863291
1449605010.80601901116-50.8060190111628
1549194955.58012531093-36.5801253109348
1649604992.21609204544-32.2160920454398
1751055136.20733039843-31.2073303984307
1850845110.92864044658-26.9286404465829
1948884892.27951665708-4.27951665708133
2047224778.74861764177-56.7486176417688
2146914756.9965618405-65.9965618405013
2246294720.28002615971-91.2800261597113
2346714682.23918792126-11.2391879212619
2447224687.3797875258934.6202124741094
2547024646.6754971177755.324502882233
2646604595.0050685136264.9949314863807
2745784591.12806743161-13.1280674316085
2846604632.6144943700927.385505629908
2947334787.24325513203-54.2432551320344
3047124753.65826971498-41.658269714977
3144744553.70359160627-79.7035916062732
3243714385.85078833728-14.8507883372768
3342684371.16686887095-103.166868870946
3441854302.49663357858-117.49663357858
3541754296.05028553239-121.050285532389
3642374278.69315571681-41.69315571681
3741544219.1005690026-65.1005690026032
3841234126.807521421-3.80752142100027
3940924048.6875598958543.3124401041482
4042684120.62332370017147.376676299828
4142884253.5701511713334.4298488286695
4241854255.95621840488-70.9562184048791
4339064036.13523235005-130.135232350053
4437823893.14848196471-111.148481964715
4535863786.33819442232-200.338194422317
4635033667.01601936599-164.016019365988
4735443624.85483499811-80.8548349981143
4836063650.86435169954-44.8643516995421
4936063573.3557094767432.6442905232575
5035553550.970787371574.02921262843256
5135443502.2931638765941.7068361234137
5237103610.6786776059399.3213223940734
5338443644.22302656921199.776973430794
5437823645.98482081529136.01517918471
5535753488.6316910746886.3683089253182
5634723444.158280851327.8417191487029
5732553341.601067865-86.6010678650005
5831213287.79414475406-166.794144754064
5932243289.53550997354-65.5355099735389
6033273336.92548811233-9.92548811232882
6133273321.623186882545.3768131174611
6231933274.92801490197-81.9280149019673
6331833217.71076452964-34.7107645296423
6433583317.3464322386340.6535677613656
6534723379.3650485603492.6349514396588
6634313308.09286719734122.907132802657
6732243137.4020695772186.5979304227899
6830903065.4994013497324.500598650272
6928002907.42295534471-107.422955344709
7026872798.34886833018-111.348868330177
7127282864.58504118845-136.585041188448
7229042900.382477715733.61752228426894
7329142894.6176223454619.382377654535
7426562806.74961051955-150.749610519555
7527492745.817541039543.18245896046028
7629762878.3417097454397.6582902545683
7730792977.66814867064101.331851329358
7830172933.6653674149183.3346325850889
7927382752.07121722149-14.071217221488
8025422618.15493621556-76.1549362155606
8123152372.43114426872-57.4311442687235
8221392283.62965620258-144.629656202577
8322112296.53584608138-85.5358460813814
8423662400.72036844065-34.7203684406486
8523252380.71345530821-55.7134553082064
8620982186.00250584201-88.0025058420056
8721702217.36094689124-47.3609468912446
8823972339.3843644835357.6156355164712
8925212399.70303552858121.296964471419
9024492359.4895607871289.5104392128837
9121702166.018386618733.98161338126874
9220462025.0898369725120.9101630274861
9318601860.53589032305-0.535890323048079
9416641754.01026242456-90.0102624245633
9516951795.68591741083-100.68591741083
9618501882.11293339532-32.1129333953231
9718701844.8379864939125.1620135060882
9816841691.69280394138-7.69280394137809
9917151753.78237623362-38.7823762336166
10019741894.9134927373979.0865072626134
10120361978.1558670319657.8441329680445
10219321906.5903091167425.4096908832587
10315501688.03397690572-138.033976905718
10413541525.46386329796-171.463863297965
10510951314.95749094422-219.957490944216
1068371108.2480521792-271.248052179199
1079201025.98210219777-105.982102197769
10810331058.93290009048-25.9329000904847
10910131029.78814186008-16.7881418600762
110816899.093662777456-83.0936627774558
111930863.71894798805366.2810520119471
1121209976.731173632949232.268826367051
11313331057.50327318595275.496726814053
11412711072.98657680454198.01342319546
1151023932.51173264994990.4882673500509
116827867.776007121037-40.7760071210371
117620723.804459626064-103.804459626064
118382566.153465597267-184.153465597267
119424553.353531010591-129.353531010591
120496551.759505801099-55.7595058010993

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 5053 & 5133.87302878633 & -80.8730287863291 \tabularnewline
14 & 4960 & 5010.80601901116 & -50.8060190111628 \tabularnewline
15 & 4919 & 4955.58012531093 & -36.5801253109348 \tabularnewline
16 & 4960 & 4992.21609204544 & -32.2160920454398 \tabularnewline
17 & 5105 & 5136.20733039843 & -31.2073303984307 \tabularnewline
18 & 5084 & 5110.92864044658 & -26.9286404465829 \tabularnewline
19 & 4888 & 4892.27951665708 & -4.27951665708133 \tabularnewline
20 & 4722 & 4778.74861764177 & -56.7486176417688 \tabularnewline
21 & 4691 & 4756.9965618405 & -65.9965618405013 \tabularnewline
22 & 4629 & 4720.28002615971 & -91.2800261597113 \tabularnewline
23 & 4671 & 4682.23918792126 & -11.2391879212619 \tabularnewline
24 & 4722 & 4687.37978752589 & 34.6202124741094 \tabularnewline
25 & 4702 & 4646.67549711777 & 55.324502882233 \tabularnewline
26 & 4660 & 4595.00506851362 & 64.9949314863807 \tabularnewline
27 & 4578 & 4591.12806743161 & -13.1280674316085 \tabularnewline
28 & 4660 & 4632.61449437009 & 27.385505629908 \tabularnewline
29 & 4733 & 4787.24325513203 & -54.2432551320344 \tabularnewline
30 & 4712 & 4753.65826971498 & -41.658269714977 \tabularnewline
31 & 4474 & 4553.70359160627 & -79.7035916062732 \tabularnewline
32 & 4371 & 4385.85078833728 & -14.8507883372768 \tabularnewline
33 & 4268 & 4371.16686887095 & -103.166868870946 \tabularnewline
34 & 4185 & 4302.49663357858 & -117.49663357858 \tabularnewline
35 & 4175 & 4296.05028553239 & -121.050285532389 \tabularnewline
36 & 4237 & 4278.69315571681 & -41.69315571681 \tabularnewline
37 & 4154 & 4219.1005690026 & -65.1005690026032 \tabularnewline
38 & 4123 & 4126.807521421 & -3.80752142100027 \tabularnewline
39 & 4092 & 4048.68755989585 & 43.3124401041482 \tabularnewline
40 & 4268 & 4120.62332370017 & 147.376676299828 \tabularnewline
41 & 4288 & 4253.57015117133 & 34.4298488286695 \tabularnewline
42 & 4185 & 4255.95621840488 & -70.9562184048791 \tabularnewline
43 & 3906 & 4036.13523235005 & -130.135232350053 \tabularnewline
44 & 3782 & 3893.14848196471 & -111.148481964715 \tabularnewline
45 & 3586 & 3786.33819442232 & -200.338194422317 \tabularnewline
46 & 3503 & 3667.01601936599 & -164.016019365988 \tabularnewline
47 & 3544 & 3624.85483499811 & -80.8548349981143 \tabularnewline
48 & 3606 & 3650.86435169954 & -44.8643516995421 \tabularnewline
49 & 3606 & 3573.35570947674 & 32.6442905232575 \tabularnewline
50 & 3555 & 3550.97078737157 & 4.02921262843256 \tabularnewline
51 & 3544 & 3502.29316387659 & 41.7068361234137 \tabularnewline
52 & 3710 & 3610.67867760593 & 99.3213223940734 \tabularnewline
53 & 3844 & 3644.22302656921 & 199.776973430794 \tabularnewline
54 & 3782 & 3645.98482081529 & 136.01517918471 \tabularnewline
55 & 3575 & 3488.63169107468 & 86.3683089253182 \tabularnewline
56 & 3472 & 3444.1582808513 & 27.8417191487029 \tabularnewline
57 & 3255 & 3341.601067865 & -86.6010678650005 \tabularnewline
58 & 3121 & 3287.79414475406 & -166.794144754064 \tabularnewline
59 & 3224 & 3289.53550997354 & -65.5355099735389 \tabularnewline
60 & 3327 & 3336.92548811233 & -9.92548811232882 \tabularnewline
61 & 3327 & 3321.62318688254 & 5.3768131174611 \tabularnewline
62 & 3193 & 3274.92801490197 & -81.9280149019673 \tabularnewline
63 & 3183 & 3217.71076452964 & -34.7107645296423 \tabularnewline
64 & 3358 & 3317.34643223863 & 40.6535677613656 \tabularnewline
65 & 3472 & 3379.36504856034 & 92.6349514396588 \tabularnewline
66 & 3431 & 3308.09286719734 & 122.907132802657 \tabularnewline
67 & 3224 & 3137.40206957721 & 86.5979304227899 \tabularnewline
68 & 3090 & 3065.49940134973 & 24.500598650272 \tabularnewline
69 & 2800 & 2907.42295534471 & -107.422955344709 \tabularnewline
70 & 2687 & 2798.34886833018 & -111.348868330177 \tabularnewline
71 & 2728 & 2864.58504118845 & -136.585041188448 \tabularnewline
72 & 2904 & 2900.38247771573 & 3.61752228426894 \tabularnewline
73 & 2914 & 2894.61762234546 & 19.382377654535 \tabularnewline
74 & 2656 & 2806.74961051955 & -150.749610519555 \tabularnewline
75 & 2749 & 2745.81754103954 & 3.18245896046028 \tabularnewline
76 & 2976 & 2878.34170974543 & 97.6582902545683 \tabularnewline
77 & 3079 & 2977.66814867064 & 101.331851329358 \tabularnewline
78 & 3017 & 2933.66536741491 & 83.3346325850889 \tabularnewline
79 & 2738 & 2752.07121722149 & -14.071217221488 \tabularnewline
80 & 2542 & 2618.15493621556 & -76.1549362155606 \tabularnewline
81 & 2315 & 2372.43114426872 & -57.4311442687235 \tabularnewline
82 & 2139 & 2283.62965620258 & -144.629656202577 \tabularnewline
83 & 2211 & 2296.53584608138 & -85.5358460813814 \tabularnewline
84 & 2366 & 2400.72036844065 & -34.7203684406486 \tabularnewline
85 & 2325 & 2380.71345530821 & -55.7134553082064 \tabularnewline
86 & 2098 & 2186.00250584201 & -88.0025058420056 \tabularnewline
87 & 2170 & 2217.36094689124 & -47.3609468912446 \tabularnewline
88 & 2397 & 2339.38436448353 & 57.6156355164712 \tabularnewline
89 & 2521 & 2399.70303552858 & 121.296964471419 \tabularnewline
90 & 2449 & 2359.48956078712 & 89.5104392128837 \tabularnewline
91 & 2170 & 2166.01838661873 & 3.98161338126874 \tabularnewline
92 & 2046 & 2025.08983697251 & 20.9101630274861 \tabularnewline
93 & 1860 & 1860.53589032305 & -0.535890323048079 \tabularnewline
94 & 1664 & 1754.01026242456 & -90.0102624245633 \tabularnewline
95 & 1695 & 1795.68591741083 & -100.68591741083 \tabularnewline
96 & 1850 & 1882.11293339532 & -32.1129333953231 \tabularnewline
97 & 1870 & 1844.83798649391 & 25.1620135060882 \tabularnewline
98 & 1684 & 1691.69280394138 & -7.69280394137809 \tabularnewline
99 & 1715 & 1753.78237623362 & -38.7823762336166 \tabularnewline
100 & 1974 & 1894.91349273739 & 79.0865072626134 \tabularnewline
101 & 2036 & 1978.15586703196 & 57.8441329680445 \tabularnewline
102 & 1932 & 1906.59030911674 & 25.4096908832587 \tabularnewline
103 & 1550 & 1688.03397690572 & -138.033976905718 \tabularnewline
104 & 1354 & 1525.46386329796 & -171.463863297965 \tabularnewline
105 & 1095 & 1314.95749094422 & -219.957490944216 \tabularnewline
106 & 837 & 1108.2480521792 & -271.248052179199 \tabularnewline
107 & 920 & 1025.98210219777 & -105.982102197769 \tabularnewline
108 & 1033 & 1058.93290009048 & -25.9329000904847 \tabularnewline
109 & 1013 & 1029.78814186008 & -16.7881418600762 \tabularnewline
110 & 816 & 899.093662777456 & -83.0936627774558 \tabularnewline
111 & 930 & 863.718947988053 & 66.2810520119471 \tabularnewline
112 & 1209 & 976.731173632949 & 232.268826367051 \tabularnewline
113 & 1333 & 1057.50327318595 & 275.496726814053 \tabularnewline
114 & 1271 & 1072.98657680454 & 198.01342319546 \tabularnewline
115 & 1023 & 932.511732649949 & 90.4882673500509 \tabularnewline
116 & 827 & 867.776007121037 & -40.7760071210371 \tabularnewline
117 & 620 & 723.804459626064 & -103.804459626064 \tabularnewline
118 & 382 & 566.153465597267 & -184.153465597267 \tabularnewline
119 & 424 & 553.353531010591 & -129.353531010591 \tabularnewline
120 & 496 & 551.759505801099 & -55.7595058010993 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=123238&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]5053[/C][C]5133.87302878633[/C][C]-80.8730287863291[/C][/ROW]
[ROW][C]14[/C][C]4960[/C][C]5010.80601901116[/C][C]-50.8060190111628[/C][/ROW]
[ROW][C]15[/C][C]4919[/C][C]4955.58012531093[/C][C]-36.5801253109348[/C][/ROW]
[ROW][C]16[/C][C]4960[/C][C]4992.21609204544[/C][C]-32.2160920454398[/C][/ROW]
[ROW][C]17[/C][C]5105[/C][C]5136.20733039843[/C][C]-31.2073303984307[/C][/ROW]
[ROW][C]18[/C][C]5084[/C][C]5110.92864044658[/C][C]-26.9286404465829[/C][/ROW]
[ROW][C]19[/C][C]4888[/C][C]4892.27951665708[/C][C]-4.27951665708133[/C][/ROW]
[ROW][C]20[/C][C]4722[/C][C]4778.74861764177[/C][C]-56.7486176417688[/C][/ROW]
[ROW][C]21[/C][C]4691[/C][C]4756.9965618405[/C][C]-65.9965618405013[/C][/ROW]
[ROW][C]22[/C][C]4629[/C][C]4720.28002615971[/C][C]-91.2800261597113[/C][/ROW]
[ROW][C]23[/C][C]4671[/C][C]4682.23918792126[/C][C]-11.2391879212619[/C][/ROW]
[ROW][C]24[/C][C]4722[/C][C]4687.37978752589[/C][C]34.6202124741094[/C][/ROW]
[ROW][C]25[/C][C]4702[/C][C]4646.67549711777[/C][C]55.324502882233[/C][/ROW]
[ROW][C]26[/C][C]4660[/C][C]4595.00506851362[/C][C]64.9949314863807[/C][/ROW]
[ROW][C]27[/C][C]4578[/C][C]4591.12806743161[/C][C]-13.1280674316085[/C][/ROW]
[ROW][C]28[/C][C]4660[/C][C]4632.61449437009[/C][C]27.385505629908[/C][/ROW]
[ROW][C]29[/C][C]4733[/C][C]4787.24325513203[/C][C]-54.2432551320344[/C][/ROW]
[ROW][C]30[/C][C]4712[/C][C]4753.65826971498[/C][C]-41.658269714977[/C][/ROW]
[ROW][C]31[/C][C]4474[/C][C]4553.70359160627[/C][C]-79.7035916062732[/C][/ROW]
[ROW][C]32[/C][C]4371[/C][C]4385.85078833728[/C][C]-14.8507883372768[/C][/ROW]
[ROW][C]33[/C][C]4268[/C][C]4371.16686887095[/C][C]-103.166868870946[/C][/ROW]
[ROW][C]34[/C][C]4185[/C][C]4302.49663357858[/C][C]-117.49663357858[/C][/ROW]
[ROW][C]35[/C][C]4175[/C][C]4296.05028553239[/C][C]-121.050285532389[/C][/ROW]
[ROW][C]36[/C][C]4237[/C][C]4278.69315571681[/C][C]-41.69315571681[/C][/ROW]
[ROW][C]37[/C][C]4154[/C][C]4219.1005690026[/C][C]-65.1005690026032[/C][/ROW]
[ROW][C]38[/C][C]4123[/C][C]4126.807521421[/C][C]-3.80752142100027[/C][/ROW]
[ROW][C]39[/C][C]4092[/C][C]4048.68755989585[/C][C]43.3124401041482[/C][/ROW]
[ROW][C]40[/C][C]4268[/C][C]4120.62332370017[/C][C]147.376676299828[/C][/ROW]
[ROW][C]41[/C][C]4288[/C][C]4253.57015117133[/C][C]34.4298488286695[/C][/ROW]
[ROW][C]42[/C][C]4185[/C][C]4255.95621840488[/C][C]-70.9562184048791[/C][/ROW]
[ROW][C]43[/C][C]3906[/C][C]4036.13523235005[/C][C]-130.135232350053[/C][/ROW]
[ROW][C]44[/C][C]3782[/C][C]3893.14848196471[/C][C]-111.148481964715[/C][/ROW]
[ROW][C]45[/C][C]3586[/C][C]3786.33819442232[/C][C]-200.338194422317[/C][/ROW]
[ROW][C]46[/C][C]3503[/C][C]3667.01601936599[/C][C]-164.016019365988[/C][/ROW]
[ROW][C]47[/C][C]3544[/C][C]3624.85483499811[/C][C]-80.8548349981143[/C][/ROW]
[ROW][C]48[/C][C]3606[/C][C]3650.86435169954[/C][C]-44.8643516995421[/C][/ROW]
[ROW][C]49[/C][C]3606[/C][C]3573.35570947674[/C][C]32.6442905232575[/C][/ROW]
[ROW][C]50[/C][C]3555[/C][C]3550.97078737157[/C][C]4.02921262843256[/C][/ROW]
[ROW][C]51[/C][C]3544[/C][C]3502.29316387659[/C][C]41.7068361234137[/C][/ROW]
[ROW][C]52[/C][C]3710[/C][C]3610.67867760593[/C][C]99.3213223940734[/C][/ROW]
[ROW][C]53[/C][C]3844[/C][C]3644.22302656921[/C][C]199.776973430794[/C][/ROW]
[ROW][C]54[/C][C]3782[/C][C]3645.98482081529[/C][C]136.01517918471[/C][/ROW]
[ROW][C]55[/C][C]3575[/C][C]3488.63169107468[/C][C]86.3683089253182[/C][/ROW]
[ROW][C]56[/C][C]3472[/C][C]3444.1582808513[/C][C]27.8417191487029[/C][/ROW]
[ROW][C]57[/C][C]3255[/C][C]3341.601067865[/C][C]-86.6010678650005[/C][/ROW]
[ROW][C]58[/C][C]3121[/C][C]3287.79414475406[/C][C]-166.794144754064[/C][/ROW]
[ROW][C]59[/C][C]3224[/C][C]3289.53550997354[/C][C]-65.5355099735389[/C][/ROW]
[ROW][C]60[/C][C]3327[/C][C]3336.92548811233[/C][C]-9.92548811232882[/C][/ROW]
[ROW][C]61[/C][C]3327[/C][C]3321.62318688254[/C][C]5.3768131174611[/C][/ROW]
[ROW][C]62[/C][C]3193[/C][C]3274.92801490197[/C][C]-81.9280149019673[/C][/ROW]
[ROW][C]63[/C][C]3183[/C][C]3217.71076452964[/C][C]-34.7107645296423[/C][/ROW]
[ROW][C]64[/C][C]3358[/C][C]3317.34643223863[/C][C]40.6535677613656[/C][/ROW]
[ROW][C]65[/C][C]3472[/C][C]3379.36504856034[/C][C]92.6349514396588[/C][/ROW]
[ROW][C]66[/C][C]3431[/C][C]3308.09286719734[/C][C]122.907132802657[/C][/ROW]
[ROW][C]67[/C][C]3224[/C][C]3137.40206957721[/C][C]86.5979304227899[/C][/ROW]
[ROW][C]68[/C][C]3090[/C][C]3065.49940134973[/C][C]24.500598650272[/C][/ROW]
[ROW][C]69[/C][C]2800[/C][C]2907.42295534471[/C][C]-107.422955344709[/C][/ROW]
[ROW][C]70[/C][C]2687[/C][C]2798.34886833018[/C][C]-111.348868330177[/C][/ROW]
[ROW][C]71[/C][C]2728[/C][C]2864.58504118845[/C][C]-136.585041188448[/C][/ROW]
[ROW][C]72[/C][C]2904[/C][C]2900.38247771573[/C][C]3.61752228426894[/C][/ROW]
[ROW][C]73[/C][C]2914[/C][C]2894.61762234546[/C][C]19.382377654535[/C][/ROW]
[ROW][C]74[/C][C]2656[/C][C]2806.74961051955[/C][C]-150.749610519555[/C][/ROW]
[ROW][C]75[/C][C]2749[/C][C]2745.81754103954[/C][C]3.18245896046028[/C][/ROW]
[ROW][C]76[/C][C]2976[/C][C]2878.34170974543[/C][C]97.6582902545683[/C][/ROW]
[ROW][C]77[/C][C]3079[/C][C]2977.66814867064[/C][C]101.331851329358[/C][/ROW]
[ROW][C]78[/C][C]3017[/C][C]2933.66536741491[/C][C]83.3346325850889[/C][/ROW]
[ROW][C]79[/C][C]2738[/C][C]2752.07121722149[/C][C]-14.071217221488[/C][/ROW]
[ROW][C]80[/C][C]2542[/C][C]2618.15493621556[/C][C]-76.1549362155606[/C][/ROW]
[ROW][C]81[/C][C]2315[/C][C]2372.43114426872[/C][C]-57.4311442687235[/C][/ROW]
[ROW][C]82[/C][C]2139[/C][C]2283.62965620258[/C][C]-144.629656202577[/C][/ROW]
[ROW][C]83[/C][C]2211[/C][C]2296.53584608138[/C][C]-85.5358460813814[/C][/ROW]
[ROW][C]84[/C][C]2366[/C][C]2400.72036844065[/C][C]-34.7203684406486[/C][/ROW]
[ROW][C]85[/C][C]2325[/C][C]2380.71345530821[/C][C]-55.7134553082064[/C][/ROW]
[ROW][C]86[/C][C]2098[/C][C]2186.00250584201[/C][C]-88.0025058420056[/C][/ROW]
[ROW][C]87[/C][C]2170[/C][C]2217.36094689124[/C][C]-47.3609468912446[/C][/ROW]
[ROW][C]88[/C][C]2397[/C][C]2339.38436448353[/C][C]57.6156355164712[/C][/ROW]
[ROW][C]89[/C][C]2521[/C][C]2399.70303552858[/C][C]121.296964471419[/C][/ROW]
[ROW][C]90[/C][C]2449[/C][C]2359.48956078712[/C][C]89.5104392128837[/C][/ROW]
[ROW][C]91[/C][C]2170[/C][C]2166.01838661873[/C][C]3.98161338126874[/C][/ROW]
[ROW][C]92[/C][C]2046[/C][C]2025.08983697251[/C][C]20.9101630274861[/C][/ROW]
[ROW][C]93[/C][C]1860[/C][C]1860.53589032305[/C][C]-0.535890323048079[/C][/ROW]
[ROW][C]94[/C][C]1664[/C][C]1754.01026242456[/C][C]-90.0102624245633[/C][/ROW]
[ROW][C]95[/C][C]1695[/C][C]1795.68591741083[/C][C]-100.68591741083[/C][/ROW]
[ROW][C]96[/C][C]1850[/C][C]1882.11293339532[/C][C]-32.1129333953231[/C][/ROW]
[ROW][C]97[/C][C]1870[/C][C]1844.83798649391[/C][C]25.1620135060882[/C][/ROW]
[ROW][C]98[/C][C]1684[/C][C]1691.69280394138[/C][C]-7.69280394137809[/C][/ROW]
[ROW][C]99[/C][C]1715[/C][C]1753.78237623362[/C][C]-38.7823762336166[/C][/ROW]
[ROW][C]100[/C][C]1974[/C][C]1894.91349273739[/C][C]79.0865072626134[/C][/ROW]
[ROW][C]101[/C][C]2036[/C][C]1978.15586703196[/C][C]57.8441329680445[/C][/ROW]
[ROW][C]102[/C][C]1932[/C][C]1906.59030911674[/C][C]25.4096908832587[/C][/ROW]
[ROW][C]103[/C][C]1550[/C][C]1688.03397690572[/C][C]-138.033976905718[/C][/ROW]
[ROW][C]104[/C][C]1354[/C][C]1525.46386329796[/C][C]-171.463863297965[/C][/ROW]
[ROW][C]105[/C][C]1095[/C][C]1314.95749094422[/C][C]-219.957490944216[/C][/ROW]
[ROW][C]106[/C][C]837[/C][C]1108.2480521792[/C][C]-271.248052179199[/C][/ROW]
[ROW][C]107[/C][C]920[/C][C]1025.98210219777[/C][C]-105.982102197769[/C][/ROW]
[ROW][C]108[/C][C]1033[/C][C]1058.93290009048[/C][C]-25.9329000904847[/C][/ROW]
[ROW][C]109[/C][C]1013[/C][C]1029.78814186008[/C][C]-16.7881418600762[/C][/ROW]
[ROW][C]110[/C][C]816[/C][C]899.093662777456[/C][C]-83.0936627774558[/C][/ROW]
[ROW][C]111[/C][C]930[/C][C]863.718947988053[/C][C]66.2810520119471[/C][/ROW]
[ROW][C]112[/C][C]1209[/C][C]976.731173632949[/C][C]232.268826367051[/C][/ROW]
[ROW][C]113[/C][C]1333[/C][C]1057.50327318595[/C][C]275.496726814053[/C][/ROW]
[ROW][C]114[/C][C]1271[/C][C]1072.98657680454[/C][C]198.01342319546[/C][/ROW]
[ROW][C]115[/C][C]1023[/C][C]932.511732649949[/C][C]90.4882673500509[/C][/ROW]
[ROW][C]116[/C][C]827[/C][C]867.776007121037[/C][C]-40.7760071210371[/C][/ROW]
[ROW][C]117[/C][C]620[/C][C]723.804459626064[/C][C]-103.804459626064[/C][/ROW]
[ROW][C]118[/C][C]382[/C][C]566.153465597267[/C][C]-184.153465597267[/C][/ROW]
[ROW][C]119[/C][C]424[/C][C]553.353531010591[/C][C]-129.353531010591[/C][/ROW]
[ROW][C]120[/C][C]496[/C][C]551.759505801099[/C][C]-55.7595058010993[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=123238&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=123238&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
1350535133.87302878633-80.8730287863291
1449605010.80601901116-50.8060190111628
1549194955.58012531093-36.5801253109348
1649604992.21609204544-32.2160920454398
1751055136.20733039843-31.2073303984307
1850845110.92864044658-26.9286404465829
1948884892.27951665708-4.27951665708133
2047224778.74861764177-56.7486176417688
2146914756.9965618405-65.9965618405013
2246294720.28002615971-91.2800261597113
2346714682.23918792126-11.2391879212619
2447224687.3797875258934.6202124741094
2547024646.6754971177755.324502882233
2646604595.0050685136264.9949314863807
2745784591.12806743161-13.1280674316085
2846604632.6144943700927.385505629908
2947334787.24325513203-54.2432551320344
3047124753.65826971498-41.658269714977
3144744553.70359160627-79.7035916062732
3243714385.85078833728-14.8507883372768
3342684371.16686887095-103.166868870946
3441854302.49663357858-117.49663357858
3541754296.05028553239-121.050285532389
3642374278.69315571681-41.69315571681
3741544219.1005690026-65.1005690026032
3841234126.807521421-3.80752142100027
3940924048.6875598958543.3124401041482
4042684120.62332370017147.376676299828
4142884253.5701511713334.4298488286695
4241854255.95621840488-70.9562184048791
4339064036.13523235005-130.135232350053
4437823893.14848196471-111.148481964715
4535863786.33819442232-200.338194422317
4635033667.01601936599-164.016019365988
4735443624.85483499811-80.8548349981143
4836063650.86435169954-44.8643516995421
4936063573.3557094767432.6442905232575
5035553550.970787371574.02921262843256
5135443502.2931638765941.7068361234137
5237103610.6786776059399.3213223940734
5338443644.22302656921199.776973430794
5437823645.98482081529136.01517918471
5535753488.6316910746886.3683089253182
5634723444.158280851327.8417191487029
5732553341.601067865-86.6010678650005
5831213287.79414475406-166.794144754064
5932243289.53550997354-65.5355099735389
6033273336.92548811233-9.92548811232882
6133273321.623186882545.3768131174611
6231933274.92801490197-81.9280149019673
6331833217.71076452964-34.7107645296423
6433583317.3464322386340.6535677613656
6534723379.3650485603492.6349514396588
6634313308.09286719734122.907132802657
6732243137.4020695772186.5979304227899
6830903065.4994013497324.500598650272
6928002907.42295534471-107.422955344709
7026872798.34886833018-111.348868330177
7127282864.58504118845-136.585041188448
7229042900.382477715733.61752228426894
7329142894.6176223454619.382377654535
7426562806.74961051955-150.749610519555
7527492745.817541039543.18245896046028
7629762878.3417097454397.6582902545683
7730792977.66814867064101.331851329358
7830172933.6653674149183.3346325850889
7927382752.07121722149-14.071217221488
8025422618.15493621556-76.1549362155606
8123152372.43114426872-57.4311442687235
8221392283.62965620258-144.629656202577
8322112296.53584608138-85.5358460813814
8423662400.72036844065-34.7203684406486
8523252380.71345530821-55.7134553082064
8620982186.00250584201-88.0025058420056
8721702217.36094689124-47.3609468912446
8823972339.3843644835357.6156355164712
8925212399.70303552858121.296964471419
9024492359.4895607871289.5104392128837
9121702166.018386618733.98161338126874
9220462025.0898369725120.9101630274861
9318601860.53589032305-0.535890323048079
9416641754.01026242456-90.0102624245633
9516951795.68591741083-100.68591741083
9618501882.11293339532-32.1129333953231
9718701844.8379864939125.1620135060882
9816841691.69280394138-7.69280394137809
9917151753.78237623362-38.7823762336166
10019741894.9134927373979.0865072626134
10120361978.1558670319657.8441329680445
10219321906.5903091167425.4096908832587
10315501688.03397690572-138.033976905718
10413541525.46386329796-171.463863297965
10510951314.95749094422-219.957490944216
1068371108.2480521792-271.248052179199
1079201025.98210219777-105.982102197769
10810331058.93290009048-25.9329000904847
10910131029.78814186008-16.7881418600762
110816899.093662777456-83.0936627774558
111930863.71894798805366.2810520119471
1121209976.731173632949232.268826367051
11313331057.50327318595275.496726814053
11412711072.98657680454198.01342319546
1151023932.51173264994990.4882673500509
116827867.776007121037-40.7760071210371
117620723.804459626064-103.804459626064
118382566.153465597267-184.153465597267
119424553.353531010591-129.353531010591
120496551.759505801099-55.7595058010993







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
121501.257670169211313.422343334454689.092997003967
122398.307884131356199.853271805264596.762496457447
123417.668944967911197.598399943482637.73948999234
124465.806036710142209.850040908685721.762032511598
125428.432174713176152.096961530202704.76738789615
126341.07765709229663.2070206101139618.948293574479
127229.162755636759-30.6318419572022488.957353230721
128156.388674650377-96.5163708485036409.293720149258
12996.3825060021343-147.567827007963340.332839012232
13046.7511656422581-181.336983592705274.839314877221
13128.9632718936922-242.650729542289300.577273329673
132-3.58722647100973-284.159768732547276.985315790528

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
121 & 501.257670169211 & 313.422343334454 & 689.092997003967 \tabularnewline
122 & 398.307884131356 & 199.853271805264 & 596.762496457447 \tabularnewline
123 & 417.668944967911 & 197.598399943482 & 637.73948999234 \tabularnewline
124 & 465.806036710142 & 209.850040908685 & 721.762032511598 \tabularnewline
125 & 428.432174713176 & 152.096961530202 & 704.76738789615 \tabularnewline
126 & 341.077657092296 & 63.2070206101139 & 618.948293574479 \tabularnewline
127 & 229.162755636759 & -30.6318419572022 & 488.957353230721 \tabularnewline
128 & 156.388674650377 & -96.5163708485036 & 409.293720149258 \tabularnewline
129 & 96.3825060021343 & -147.567827007963 & 340.332839012232 \tabularnewline
130 & 46.7511656422581 & -181.336983592705 & 274.839314877221 \tabularnewline
131 & 28.9632718936922 & -242.650729542289 & 300.577273329673 \tabularnewline
132 & -3.58722647100973 & -284.159768732547 & 276.985315790528 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=123238&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]121[/C][C]501.257670169211[/C][C]313.422343334454[/C][C]689.092997003967[/C][/ROW]
[ROW][C]122[/C][C]398.307884131356[/C][C]199.853271805264[/C][C]596.762496457447[/C][/ROW]
[ROW][C]123[/C][C]417.668944967911[/C][C]197.598399943482[/C][C]637.73948999234[/C][/ROW]
[ROW][C]124[/C][C]465.806036710142[/C][C]209.850040908685[/C][C]721.762032511598[/C][/ROW]
[ROW][C]125[/C][C]428.432174713176[/C][C]152.096961530202[/C][C]704.76738789615[/C][/ROW]
[ROW][C]126[/C][C]341.077657092296[/C][C]63.2070206101139[/C][C]618.948293574479[/C][/ROW]
[ROW][C]127[/C][C]229.162755636759[/C][C]-30.6318419572022[/C][C]488.957353230721[/C][/ROW]
[ROW][C]128[/C][C]156.388674650377[/C][C]-96.5163708485036[/C][C]409.293720149258[/C][/ROW]
[ROW][C]129[/C][C]96.3825060021343[/C][C]-147.567827007963[/C][C]340.332839012232[/C][/ROW]
[ROW][C]130[/C][C]46.7511656422581[/C][C]-181.336983592705[/C][C]274.839314877221[/C][/ROW]
[ROW][C]131[/C][C]28.9632718936922[/C][C]-242.650729542289[/C][C]300.577273329673[/C][/ROW]
[ROW][C]132[/C][C]-3.58722647100973[/C][C]-284.159768732547[/C][C]276.985315790528[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=123238&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=123238&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
121501.257670169211313.422343334454689.092997003967
122398.307884131356199.853271805264596.762496457447
123417.668944967911197.598399943482637.73948999234
124465.806036710142209.850040908685721.762032511598
125428.432174713176152.096961530202704.76738789615
126341.07765709229663.2070206101139618.948293574479
127229.162755636759-30.6318419572022488.957353230721
128156.388674650377-96.5163708485036409.293720149258
12996.3825060021343-147.567827007963340.332839012232
13046.7511656422581-181.336983592705274.839314877221
13128.9632718936922-242.650729542289300.577273329673
132-3.58722647100973-284.159768732547276.985315790528



Parameters (Session):
par1 = 12 ; par2 = Triple ; par3 = multiplicative ;
Parameters (R input):
par1 = 12 ; par2 = Triple ; par3 = multiplicative ;
R code (references can be found in the software module):
par1 <- as.numeric(par1)
if (par2 == 'Single') K <- 1
if (par2 == 'Double') K <- 2
if (par2 == 'Triple') K <- par1
nx <- length(x)
nxmK <- nx - K
x <- ts(x, frequency = par1)
if (par2 == 'Single') fit <- HoltWinters(x, gamma=F, beta=F)
if (par2 == 'Double') fit <- HoltWinters(x, gamma=F)
if (par2 == 'Triple') fit <- HoltWinters(x, seasonal=par3)
fit
myresid <- x - fit$fitted[,'xhat']
bitmap(file='test1.png')
op <- par(mfrow=c(2,1))
plot(fit,ylab='Observed (black) / Fitted (red)',main='Interpolation Fit of Exponential Smoothing')
plot(myresid,ylab='Residuals',main='Interpolation Prediction Errors')
par(op)
dev.off()
bitmap(file='test2.png')
p <- predict(fit, par1, prediction.interval=TRUE)
np <- length(p[,1])
plot(fit,p,ylab='Observed (black) / Fitted (red)',main='Extrapolation Fit of Exponential Smoothing')
dev.off()
bitmap(file='test3.png')
op <- par(mfrow = c(2,2))
acf(as.numeric(myresid),lag.max = nx/2,main='Residual ACF')
spectrum(myresid,main='Residals Periodogram')
cpgram(myresid,main='Residal Cumulative Periodogram')
qqnorm(myresid,main='Residual Normal QQ Plot')
qqline(myresid)
par(op)
dev.off()
load(file='createtable')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Estimated Parameters of Exponential Smoothing',2,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'Parameter',header=TRUE)
a<-table.element(a,'Value',header=TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'alpha',header=TRUE)
a<-table.element(a,fit$alpha)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'beta',header=TRUE)
a<-table.element(a,fit$beta)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'gamma',header=TRUE)
a<-table.element(a,fit$gamma)
a<-table.row.end(a)
a<-table.end(a)
table.save(a,file='mytable.tab')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Interpolation Forecasts of Exponential Smoothing',4,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'t',header=TRUE)
a<-table.element(a,'Observed',header=TRUE)
a<-table.element(a,'Fitted',header=TRUE)
a<-table.element(a,'Residuals',header=TRUE)
a<-table.row.end(a)
for (i in 1:nxmK) {
a<-table.row.start(a)
a<-table.element(a,i+K,header=TRUE)
a<-table.element(a,x[i+K])
a<-table.element(a,fit$fitted[i,'xhat'])
a<-table.element(a,myresid[i])
a<-table.row.end(a)
}
a<-table.end(a)
table.save(a,file='mytable1.tab')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Extrapolation Forecasts of Exponential Smoothing',4,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'t',header=TRUE)
a<-table.element(a,'Forecast',header=TRUE)
a<-table.element(a,'95% Lower Bound',header=TRUE)
a<-table.element(a,'95% Upper Bound',header=TRUE)
a<-table.row.end(a)
for (i in 1:np) {
a<-table.row.start(a)
a<-table.element(a,nx+i,header=TRUE)
a<-table.element(a,p[i,'fit'])
a<-table.element(a,p[i,'lwr'])
a<-table.element(a,p[i,'upr'])
a<-table.row.end(a)
}
a<-table.end(a)
table.save(a,file='mytable2.tab')