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 computationWed, 02 Dec 2009 13:49:23 -0700
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2009/Dec/02/t1259787084q1n5qsey8g852su.htm/, Retrieved Sun, 28 Apr 2024 00:41:19 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=62584, Retrieved Sun, 28 Apr 2024 00:41:19 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact160
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [Univariate Data Series] [data set] [2008-12-01 19:54:57] [b98453cac15ba1066b407e146608df68]
- RMP   [Exponential Smoothing] [] [2009-11-27 15:04:36] [b98453cac15ba1066b407e146608df68]
-   PD      [Exponential Smoothing] [WS09 - Exponentia...] [2009-12-02 20:49:23] [0cc924834281808eda7297686c82928f] [Current]
- R PD        [Exponential Smoothing] [] [2010-12-07 09:58:27] [d7b28a0391ab3b2ddc9f9fba95a43f33]
Feedback Forum

Post a new message
Dataseries X:
423.4
404.1
500
472.6
496.1
562
434.8
538.2
577.6
518.1
625.2
561.2
523.3
536.1
607.3
637.3
606.9
652.9
617.2
670.4
729.9
677.2
710
844.3
748.2
653.9
742.6
854.2
808.4
1819
1936.5
1966.1
2083.1
1620.1
1527.6
1795
1685.1
1851.8
2164.4
1981.8
1726.5
2144.6
1758.2
1672.9
1837.3
1596.1
1446
1898.4
1964.1
1755.9
2255.3
1881.2
2117.9
1656.5
1544.1
2098.9
2133.3
1963.5
1801.2
2365.4
1936.5
1667.6
1983.5
2058.6
2448.3
1858.1
1625.4
2130.6
2515.7
2230.2
2086.9
2235
2100.2
2288.6
2490
2573.7
2543.8
2004.7
2390
2338.4
2724.5
2292.5
2386
2477.9
2337
2605.1
2560.8
2839.3
2407.2
2085.2
2735.6
2798.7
3053.2
2405
2471.9
2727.3
2790.7
2385.4
3206.6
2705.6
3518.4
1954.9
2584.3
2535.8
2685.9
2866
2236.6
2934.9
2668.6
2371.2
3165.9
2887.2
3112.2
2671.2
2432.6
2812.3
3095.7
2862.9
2607.3
2862.5




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time1 seconds
R Server'Gwilym Jenkins' @ 72.249.127.135

\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 & 'Gwilym Jenkins' @ 72.249.127.135 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=62584&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]'Gwilym Jenkins' @ 72.249.127.135[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=62584&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=62584&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'Gwilym Jenkins' @ 72.249.127.135







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.346213598844670
beta0
gamma0.383242980338082

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.346213598844670 \tabularnewline
beta & 0 \tabularnewline
gamma & 0.383242980338082 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=62584&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]0.346213598844670[/C][/ROW]
[ROW][C]beta[/C][C]0[/C][/ROW]
[ROW][C]gamma[/C][C]0.383242980338082[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=62584&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=62584&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
alpha0.346213598844670
beta0
gamma0.383242980338082







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
13523.3468.44548727656754.8545127234325
14536.1498.6635263766237.4364736233803
15607.3579.70763085453927.5923691454614
16637.3617.18115103587620.1188489641239
17606.9595.82572587945311.074274120547
18652.9641.3310579087411.5689420912598
19617.2544.6048834351472.5951165648603
20670.4703.977363450823-33.5773634508229
21729.9741.541064358148-11.6410643581482
22677.2658.6592735180318.5407264819694
23710798.861606007522-88.8616060075216
24844.3690.582334067552153.717665932448
25748.2709.71818993511438.4818100648864
26653.9727.902110578053-74.0021105780528
27742.6786.505003080898-43.9050030808976
28854.2801.41248465775252.7875153422481
29808.4776.43091303532131.9690869646787
301819838.502991683396980.497008316604
311936.51013.07365058068923.426349419323
321966.11561.72553117971404.37446882029
332083.11819.37286406244263.727135937559
341620.11707.58414162003-87.4841416200336
351527.61923.92162632109-396.321626321093
3617951723.3175278901271.6824721098778
371685.11593.6786885883891.4213114116171
381851.81559.50749420858292.292505791415
392164.41866.573332006297.826667993998
401981.82090.32148568062-108.521485680624
411726.51916.46122352916-189.961223529157
422144.62338.72818934595-194.128189345952
431758.21890.06218712522-131.862187125217
441672.91948.98889262301-276.08889262301
451837.31934.50892901993-97.2089290199256
461596.11620.97248104066-24.8724810406634
4714461770.08600238853-324.086002388528
481898.41710.77199199425187.628008005747
491964.11624.89663314946339.203366850536
501755.91720.6234382004235.2765617995792
512255.31936.06528564962319.234714350378
521881.22064.92035206239-183.720352062393
532117.91844.95589521561272.944104784394
541656.52460.67229645203-804.17229645203
551544.11822.49542625217-278.395426252171
562098.91788.4901141119310.409885888100
572133.32028.5216907021104.778309297903
581963.51775.65577873815187.844221261852
591801.21927.59225463942-126.392254639415
602365.42095.74516966627269.654830333734
611936.52044.36729662966-107.867296629662
621667.61898.40249141378-230.802491413779
631983.52099.91542005586-116.415420055862
642058.61954.26619078847104.333809211530
652448.31944.10187951795504.198120482055
661858.12356.05138517422-497.951385174217
671625.41926.84740134125-301.447401341247
682130.62047.3555531641383.2444468358653
692515.72160.27464522433355.425354775673
702230.21987.49318770981242.706812290192
712086.92078.602735388478.29726461152904
7222352426.31980271082-191.319802710819
732100.22108.74017584760-8.54017584759731
742288.61954.13452021044334.465479789559
7524902431.6522724360358.3477275639693
762573.72388.39421469764185.305785302360
772543.82502.8381592017240.9618407982825
782004.72489.16653498205-484.466534982046
7923902081.16901205823308.830987941765
802338.42586.96443620870-248.564436208704
812724.52674.2559369587750.2440630412284
822292.52319.63032211609-27.1303221160888
8323862253.35109159517132.648908404832
842477.92621.84724829203-143.947248292027
8523372342.08424960309-5.08424960309412
862605.12260.78152706651344.318472933492
872560.82701.82903771605-141.029037716049
882839.32616.73847733390222.561522666096
892407.22708.00758084818-300.807580848181
902085.22430.14911313109-344.949113131093
912735.62262.61109751585472.988902484153
922798.72700.8303148870697.8696851129407
933053.23011.3585007895141.8414992104899
9424052586.50809709010-181.508097090097
952471.92503.40548652555-31.5054865255488
962727.32761.54246769244-34.2424676924356
972790.72537.14929618599253.55070381401
982385.42627.68142370859-242.281423708586
993206.62749.27354456528457.32645543472
1002705.62965.37509735931-259.775097359306
1013518.42749.47352120628768.926478793724
1021954.92787.89219909764-832.992199097638
1032584.32665.32078027908-81.0207802790833
1042535.82823.53661753304-287.736617533041
1052685.92983.28465081925-297.384650819251
10628662409.97324870202456.026751297976
1072236.62585.36521520188-348.765215201880
1082934.92730.88054591979204.01945408021
1092668.62655.5637611175713.0362388824269
1102371.22538.00990550250-166.809905502497
1113165.92854.37120129727311.528798702729
1122887.22840.9825950026246.2174049973773
1133112.22973.4596939424138.740306057599
1142671.22406.86670493956264.333295060444
1152432.62883.44867870295-450.848678702945
1162812.32864.25108391293-51.9510839129271
1173095.73118.23997266485-22.5399726648461
1182862.92789.2355088962273.6644911037783
1192607.32616.46986007017-9.16986007017249
1202862.53055.59449714028-193.094497140276

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
13 & 523.3 & 468.445487276567 & 54.8545127234325 \tabularnewline
14 & 536.1 & 498.66352637662 & 37.4364736233803 \tabularnewline
15 & 607.3 & 579.707630854539 & 27.5923691454614 \tabularnewline
16 & 637.3 & 617.181151035876 & 20.1188489641239 \tabularnewline
17 & 606.9 & 595.825725879453 & 11.074274120547 \tabularnewline
18 & 652.9 & 641.33105790874 & 11.5689420912598 \tabularnewline
19 & 617.2 & 544.60488343514 & 72.5951165648603 \tabularnewline
20 & 670.4 & 703.977363450823 & -33.5773634508229 \tabularnewline
21 & 729.9 & 741.541064358148 & -11.6410643581482 \tabularnewline
22 & 677.2 & 658.65927351803 & 18.5407264819694 \tabularnewline
23 & 710 & 798.861606007522 & -88.8616060075216 \tabularnewline
24 & 844.3 & 690.582334067552 & 153.717665932448 \tabularnewline
25 & 748.2 & 709.718189935114 & 38.4818100648864 \tabularnewline
26 & 653.9 & 727.902110578053 & -74.0021105780528 \tabularnewline
27 & 742.6 & 786.505003080898 & -43.9050030808976 \tabularnewline
28 & 854.2 & 801.412484657752 & 52.7875153422481 \tabularnewline
29 & 808.4 & 776.430913035321 & 31.9690869646787 \tabularnewline
30 & 1819 & 838.502991683396 & 980.497008316604 \tabularnewline
31 & 1936.5 & 1013.07365058068 & 923.426349419323 \tabularnewline
32 & 1966.1 & 1561.72553117971 & 404.37446882029 \tabularnewline
33 & 2083.1 & 1819.37286406244 & 263.727135937559 \tabularnewline
34 & 1620.1 & 1707.58414162003 & -87.4841416200336 \tabularnewline
35 & 1527.6 & 1923.92162632109 & -396.321626321093 \tabularnewline
36 & 1795 & 1723.31752789012 & 71.6824721098778 \tabularnewline
37 & 1685.1 & 1593.67868858838 & 91.4213114116171 \tabularnewline
38 & 1851.8 & 1559.50749420858 & 292.292505791415 \tabularnewline
39 & 2164.4 & 1866.573332006 & 297.826667993998 \tabularnewline
40 & 1981.8 & 2090.32148568062 & -108.521485680624 \tabularnewline
41 & 1726.5 & 1916.46122352916 & -189.961223529157 \tabularnewline
42 & 2144.6 & 2338.72818934595 & -194.128189345952 \tabularnewline
43 & 1758.2 & 1890.06218712522 & -131.862187125217 \tabularnewline
44 & 1672.9 & 1948.98889262301 & -276.08889262301 \tabularnewline
45 & 1837.3 & 1934.50892901993 & -97.2089290199256 \tabularnewline
46 & 1596.1 & 1620.97248104066 & -24.8724810406634 \tabularnewline
47 & 1446 & 1770.08600238853 & -324.086002388528 \tabularnewline
48 & 1898.4 & 1710.77199199425 & 187.628008005747 \tabularnewline
49 & 1964.1 & 1624.89663314946 & 339.203366850536 \tabularnewline
50 & 1755.9 & 1720.62343820042 & 35.2765617995792 \tabularnewline
51 & 2255.3 & 1936.06528564962 & 319.234714350378 \tabularnewline
52 & 1881.2 & 2064.92035206239 & -183.720352062393 \tabularnewline
53 & 2117.9 & 1844.95589521561 & 272.944104784394 \tabularnewline
54 & 1656.5 & 2460.67229645203 & -804.17229645203 \tabularnewline
55 & 1544.1 & 1822.49542625217 & -278.395426252171 \tabularnewline
56 & 2098.9 & 1788.4901141119 & 310.409885888100 \tabularnewline
57 & 2133.3 & 2028.5216907021 & 104.778309297903 \tabularnewline
58 & 1963.5 & 1775.65577873815 & 187.844221261852 \tabularnewline
59 & 1801.2 & 1927.59225463942 & -126.392254639415 \tabularnewline
60 & 2365.4 & 2095.74516966627 & 269.654830333734 \tabularnewline
61 & 1936.5 & 2044.36729662966 & -107.867296629662 \tabularnewline
62 & 1667.6 & 1898.40249141378 & -230.802491413779 \tabularnewline
63 & 1983.5 & 2099.91542005586 & -116.415420055862 \tabularnewline
64 & 2058.6 & 1954.26619078847 & 104.333809211530 \tabularnewline
65 & 2448.3 & 1944.10187951795 & 504.198120482055 \tabularnewline
66 & 1858.1 & 2356.05138517422 & -497.951385174217 \tabularnewline
67 & 1625.4 & 1926.84740134125 & -301.447401341247 \tabularnewline
68 & 2130.6 & 2047.35555316413 & 83.2444468358653 \tabularnewline
69 & 2515.7 & 2160.27464522433 & 355.425354775673 \tabularnewline
70 & 2230.2 & 1987.49318770981 & 242.706812290192 \tabularnewline
71 & 2086.9 & 2078.60273538847 & 8.29726461152904 \tabularnewline
72 & 2235 & 2426.31980271082 & -191.319802710819 \tabularnewline
73 & 2100.2 & 2108.74017584760 & -8.54017584759731 \tabularnewline
74 & 2288.6 & 1954.13452021044 & 334.465479789559 \tabularnewline
75 & 2490 & 2431.65227243603 & 58.3477275639693 \tabularnewline
76 & 2573.7 & 2388.39421469764 & 185.305785302360 \tabularnewline
77 & 2543.8 & 2502.83815920172 & 40.9618407982825 \tabularnewline
78 & 2004.7 & 2489.16653498205 & -484.466534982046 \tabularnewline
79 & 2390 & 2081.16901205823 & 308.830987941765 \tabularnewline
80 & 2338.4 & 2586.96443620870 & -248.564436208704 \tabularnewline
81 & 2724.5 & 2674.25593695877 & 50.2440630412284 \tabularnewline
82 & 2292.5 & 2319.63032211609 & -27.1303221160888 \tabularnewline
83 & 2386 & 2253.35109159517 & 132.648908404832 \tabularnewline
84 & 2477.9 & 2621.84724829203 & -143.947248292027 \tabularnewline
85 & 2337 & 2342.08424960309 & -5.08424960309412 \tabularnewline
86 & 2605.1 & 2260.78152706651 & 344.318472933492 \tabularnewline
87 & 2560.8 & 2701.82903771605 & -141.029037716049 \tabularnewline
88 & 2839.3 & 2616.73847733390 & 222.561522666096 \tabularnewline
89 & 2407.2 & 2708.00758084818 & -300.807580848181 \tabularnewline
90 & 2085.2 & 2430.14911313109 & -344.949113131093 \tabularnewline
91 & 2735.6 & 2262.61109751585 & 472.988902484153 \tabularnewline
92 & 2798.7 & 2700.83031488706 & 97.8696851129407 \tabularnewline
93 & 3053.2 & 3011.35850078951 & 41.8414992104899 \tabularnewline
94 & 2405 & 2586.50809709010 & -181.508097090097 \tabularnewline
95 & 2471.9 & 2503.40548652555 & -31.5054865255488 \tabularnewline
96 & 2727.3 & 2761.54246769244 & -34.2424676924356 \tabularnewline
97 & 2790.7 & 2537.14929618599 & 253.55070381401 \tabularnewline
98 & 2385.4 & 2627.68142370859 & -242.281423708586 \tabularnewline
99 & 3206.6 & 2749.27354456528 & 457.32645543472 \tabularnewline
100 & 2705.6 & 2965.37509735931 & -259.775097359306 \tabularnewline
101 & 3518.4 & 2749.47352120628 & 768.926478793724 \tabularnewline
102 & 1954.9 & 2787.89219909764 & -832.992199097638 \tabularnewline
103 & 2584.3 & 2665.32078027908 & -81.0207802790833 \tabularnewline
104 & 2535.8 & 2823.53661753304 & -287.736617533041 \tabularnewline
105 & 2685.9 & 2983.28465081925 & -297.384650819251 \tabularnewline
106 & 2866 & 2409.97324870202 & 456.026751297976 \tabularnewline
107 & 2236.6 & 2585.36521520188 & -348.765215201880 \tabularnewline
108 & 2934.9 & 2730.88054591979 & 204.01945408021 \tabularnewline
109 & 2668.6 & 2655.56376111757 & 13.0362388824269 \tabularnewline
110 & 2371.2 & 2538.00990550250 & -166.809905502497 \tabularnewline
111 & 3165.9 & 2854.37120129727 & 311.528798702729 \tabularnewline
112 & 2887.2 & 2840.98259500262 & 46.2174049973773 \tabularnewline
113 & 3112.2 & 2973.4596939424 & 138.740306057599 \tabularnewline
114 & 2671.2 & 2406.86670493956 & 264.333295060444 \tabularnewline
115 & 2432.6 & 2883.44867870295 & -450.848678702945 \tabularnewline
116 & 2812.3 & 2864.25108391293 & -51.9510839129271 \tabularnewline
117 & 3095.7 & 3118.23997266485 & -22.5399726648461 \tabularnewline
118 & 2862.9 & 2789.23550889622 & 73.6644911037783 \tabularnewline
119 & 2607.3 & 2616.46986007017 & -9.16986007017249 \tabularnewline
120 & 2862.5 & 3055.59449714028 & -193.094497140276 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=62584&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]523.3[/C][C]468.445487276567[/C][C]54.8545127234325[/C][/ROW]
[ROW][C]14[/C][C]536.1[/C][C]498.66352637662[/C][C]37.4364736233803[/C][/ROW]
[ROW][C]15[/C][C]607.3[/C][C]579.707630854539[/C][C]27.5923691454614[/C][/ROW]
[ROW][C]16[/C][C]637.3[/C][C]617.181151035876[/C][C]20.1188489641239[/C][/ROW]
[ROW][C]17[/C][C]606.9[/C][C]595.825725879453[/C][C]11.074274120547[/C][/ROW]
[ROW][C]18[/C][C]652.9[/C][C]641.33105790874[/C][C]11.5689420912598[/C][/ROW]
[ROW][C]19[/C][C]617.2[/C][C]544.60488343514[/C][C]72.5951165648603[/C][/ROW]
[ROW][C]20[/C][C]670.4[/C][C]703.977363450823[/C][C]-33.5773634508229[/C][/ROW]
[ROW][C]21[/C][C]729.9[/C][C]741.541064358148[/C][C]-11.6410643581482[/C][/ROW]
[ROW][C]22[/C][C]677.2[/C][C]658.65927351803[/C][C]18.5407264819694[/C][/ROW]
[ROW][C]23[/C][C]710[/C][C]798.861606007522[/C][C]-88.8616060075216[/C][/ROW]
[ROW][C]24[/C][C]844.3[/C][C]690.582334067552[/C][C]153.717665932448[/C][/ROW]
[ROW][C]25[/C][C]748.2[/C][C]709.718189935114[/C][C]38.4818100648864[/C][/ROW]
[ROW][C]26[/C][C]653.9[/C][C]727.902110578053[/C][C]-74.0021105780528[/C][/ROW]
[ROW][C]27[/C][C]742.6[/C][C]786.505003080898[/C][C]-43.9050030808976[/C][/ROW]
[ROW][C]28[/C][C]854.2[/C][C]801.412484657752[/C][C]52.7875153422481[/C][/ROW]
[ROW][C]29[/C][C]808.4[/C][C]776.430913035321[/C][C]31.9690869646787[/C][/ROW]
[ROW][C]30[/C][C]1819[/C][C]838.502991683396[/C][C]980.497008316604[/C][/ROW]
[ROW][C]31[/C][C]1936.5[/C][C]1013.07365058068[/C][C]923.426349419323[/C][/ROW]
[ROW][C]32[/C][C]1966.1[/C][C]1561.72553117971[/C][C]404.37446882029[/C][/ROW]
[ROW][C]33[/C][C]2083.1[/C][C]1819.37286406244[/C][C]263.727135937559[/C][/ROW]
[ROW][C]34[/C][C]1620.1[/C][C]1707.58414162003[/C][C]-87.4841416200336[/C][/ROW]
[ROW][C]35[/C][C]1527.6[/C][C]1923.92162632109[/C][C]-396.321626321093[/C][/ROW]
[ROW][C]36[/C][C]1795[/C][C]1723.31752789012[/C][C]71.6824721098778[/C][/ROW]
[ROW][C]37[/C][C]1685.1[/C][C]1593.67868858838[/C][C]91.4213114116171[/C][/ROW]
[ROW][C]38[/C][C]1851.8[/C][C]1559.50749420858[/C][C]292.292505791415[/C][/ROW]
[ROW][C]39[/C][C]2164.4[/C][C]1866.573332006[/C][C]297.826667993998[/C][/ROW]
[ROW][C]40[/C][C]1981.8[/C][C]2090.32148568062[/C][C]-108.521485680624[/C][/ROW]
[ROW][C]41[/C][C]1726.5[/C][C]1916.46122352916[/C][C]-189.961223529157[/C][/ROW]
[ROW][C]42[/C][C]2144.6[/C][C]2338.72818934595[/C][C]-194.128189345952[/C][/ROW]
[ROW][C]43[/C][C]1758.2[/C][C]1890.06218712522[/C][C]-131.862187125217[/C][/ROW]
[ROW][C]44[/C][C]1672.9[/C][C]1948.98889262301[/C][C]-276.08889262301[/C][/ROW]
[ROW][C]45[/C][C]1837.3[/C][C]1934.50892901993[/C][C]-97.2089290199256[/C][/ROW]
[ROW][C]46[/C][C]1596.1[/C][C]1620.97248104066[/C][C]-24.8724810406634[/C][/ROW]
[ROW][C]47[/C][C]1446[/C][C]1770.08600238853[/C][C]-324.086002388528[/C][/ROW]
[ROW][C]48[/C][C]1898.4[/C][C]1710.77199199425[/C][C]187.628008005747[/C][/ROW]
[ROW][C]49[/C][C]1964.1[/C][C]1624.89663314946[/C][C]339.203366850536[/C][/ROW]
[ROW][C]50[/C][C]1755.9[/C][C]1720.62343820042[/C][C]35.2765617995792[/C][/ROW]
[ROW][C]51[/C][C]2255.3[/C][C]1936.06528564962[/C][C]319.234714350378[/C][/ROW]
[ROW][C]52[/C][C]1881.2[/C][C]2064.92035206239[/C][C]-183.720352062393[/C][/ROW]
[ROW][C]53[/C][C]2117.9[/C][C]1844.95589521561[/C][C]272.944104784394[/C][/ROW]
[ROW][C]54[/C][C]1656.5[/C][C]2460.67229645203[/C][C]-804.17229645203[/C][/ROW]
[ROW][C]55[/C][C]1544.1[/C][C]1822.49542625217[/C][C]-278.395426252171[/C][/ROW]
[ROW][C]56[/C][C]2098.9[/C][C]1788.4901141119[/C][C]310.409885888100[/C][/ROW]
[ROW][C]57[/C][C]2133.3[/C][C]2028.5216907021[/C][C]104.778309297903[/C][/ROW]
[ROW][C]58[/C][C]1963.5[/C][C]1775.65577873815[/C][C]187.844221261852[/C][/ROW]
[ROW][C]59[/C][C]1801.2[/C][C]1927.59225463942[/C][C]-126.392254639415[/C][/ROW]
[ROW][C]60[/C][C]2365.4[/C][C]2095.74516966627[/C][C]269.654830333734[/C][/ROW]
[ROW][C]61[/C][C]1936.5[/C][C]2044.36729662966[/C][C]-107.867296629662[/C][/ROW]
[ROW][C]62[/C][C]1667.6[/C][C]1898.40249141378[/C][C]-230.802491413779[/C][/ROW]
[ROW][C]63[/C][C]1983.5[/C][C]2099.91542005586[/C][C]-116.415420055862[/C][/ROW]
[ROW][C]64[/C][C]2058.6[/C][C]1954.26619078847[/C][C]104.333809211530[/C][/ROW]
[ROW][C]65[/C][C]2448.3[/C][C]1944.10187951795[/C][C]504.198120482055[/C][/ROW]
[ROW][C]66[/C][C]1858.1[/C][C]2356.05138517422[/C][C]-497.951385174217[/C][/ROW]
[ROW][C]67[/C][C]1625.4[/C][C]1926.84740134125[/C][C]-301.447401341247[/C][/ROW]
[ROW][C]68[/C][C]2130.6[/C][C]2047.35555316413[/C][C]83.2444468358653[/C][/ROW]
[ROW][C]69[/C][C]2515.7[/C][C]2160.27464522433[/C][C]355.425354775673[/C][/ROW]
[ROW][C]70[/C][C]2230.2[/C][C]1987.49318770981[/C][C]242.706812290192[/C][/ROW]
[ROW][C]71[/C][C]2086.9[/C][C]2078.60273538847[/C][C]8.29726461152904[/C][/ROW]
[ROW][C]72[/C][C]2235[/C][C]2426.31980271082[/C][C]-191.319802710819[/C][/ROW]
[ROW][C]73[/C][C]2100.2[/C][C]2108.74017584760[/C][C]-8.54017584759731[/C][/ROW]
[ROW][C]74[/C][C]2288.6[/C][C]1954.13452021044[/C][C]334.465479789559[/C][/ROW]
[ROW][C]75[/C][C]2490[/C][C]2431.65227243603[/C][C]58.3477275639693[/C][/ROW]
[ROW][C]76[/C][C]2573.7[/C][C]2388.39421469764[/C][C]185.305785302360[/C][/ROW]
[ROW][C]77[/C][C]2543.8[/C][C]2502.83815920172[/C][C]40.9618407982825[/C][/ROW]
[ROW][C]78[/C][C]2004.7[/C][C]2489.16653498205[/C][C]-484.466534982046[/C][/ROW]
[ROW][C]79[/C][C]2390[/C][C]2081.16901205823[/C][C]308.830987941765[/C][/ROW]
[ROW][C]80[/C][C]2338.4[/C][C]2586.96443620870[/C][C]-248.564436208704[/C][/ROW]
[ROW][C]81[/C][C]2724.5[/C][C]2674.25593695877[/C][C]50.2440630412284[/C][/ROW]
[ROW][C]82[/C][C]2292.5[/C][C]2319.63032211609[/C][C]-27.1303221160888[/C][/ROW]
[ROW][C]83[/C][C]2386[/C][C]2253.35109159517[/C][C]132.648908404832[/C][/ROW]
[ROW][C]84[/C][C]2477.9[/C][C]2621.84724829203[/C][C]-143.947248292027[/C][/ROW]
[ROW][C]85[/C][C]2337[/C][C]2342.08424960309[/C][C]-5.08424960309412[/C][/ROW]
[ROW][C]86[/C][C]2605.1[/C][C]2260.78152706651[/C][C]344.318472933492[/C][/ROW]
[ROW][C]87[/C][C]2560.8[/C][C]2701.82903771605[/C][C]-141.029037716049[/C][/ROW]
[ROW][C]88[/C][C]2839.3[/C][C]2616.73847733390[/C][C]222.561522666096[/C][/ROW]
[ROW][C]89[/C][C]2407.2[/C][C]2708.00758084818[/C][C]-300.807580848181[/C][/ROW]
[ROW][C]90[/C][C]2085.2[/C][C]2430.14911313109[/C][C]-344.949113131093[/C][/ROW]
[ROW][C]91[/C][C]2735.6[/C][C]2262.61109751585[/C][C]472.988902484153[/C][/ROW]
[ROW][C]92[/C][C]2798.7[/C][C]2700.83031488706[/C][C]97.8696851129407[/C][/ROW]
[ROW][C]93[/C][C]3053.2[/C][C]3011.35850078951[/C][C]41.8414992104899[/C][/ROW]
[ROW][C]94[/C][C]2405[/C][C]2586.50809709010[/C][C]-181.508097090097[/C][/ROW]
[ROW][C]95[/C][C]2471.9[/C][C]2503.40548652555[/C][C]-31.5054865255488[/C][/ROW]
[ROW][C]96[/C][C]2727.3[/C][C]2761.54246769244[/C][C]-34.2424676924356[/C][/ROW]
[ROW][C]97[/C][C]2790.7[/C][C]2537.14929618599[/C][C]253.55070381401[/C][/ROW]
[ROW][C]98[/C][C]2385.4[/C][C]2627.68142370859[/C][C]-242.281423708586[/C][/ROW]
[ROW][C]99[/C][C]3206.6[/C][C]2749.27354456528[/C][C]457.32645543472[/C][/ROW]
[ROW][C]100[/C][C]2705.6[/C][C]2965.37509735931[/C][C]-259.775097359306[/C][/ROW]
[ROW][C]101[/C][C]3518.4[/C][C]2749.47352120628[/C][C]768.926478793724[/C][/ROW]
[ROW][C]102[/C][C]1954.9[/C][C]2787.89219909764[/C][C]-832.992199097638[/C][/ROW]
[ROW][C]103[/C][C]2584.3[/C][C]2665.32078027908[/C][C]-81.0207802790833[/C][/ROW]
[ROW][C]104[/C][C]2535.8[/C][C]2823.53661753304[/C][C]-287.736617533041[/C][/ROW]
[ROW][C]105[/C][C]2685.9[/C][C]2983.28465081925[/C][C]-297.384650819251[/C][/ROW]
[ROW][C]106[/C][C]2866[/C][C]2409.97324870202[/C][C]456.026751297976[/C][/ROW]
[ROW][C]107[/C][C]2236.6[/C][C]2585.36521520188[/C][C]-348.765215201880[/C][/ROW]
[ROW][C]108[/C][C]2934.9[/C][C]2730.88054591979[/C][C]204.01945408021[/C][/ROW]
[ROW][C]109[/C][C]2668.6[/C][C]2655.56376111757[/C][C]13.0362388824269[/C][/ROW]
[ROW][C]110[/C][C]2371.2[/C][C]2538.00990550250[/C][C]-166.809905502497[/C][/ROW]
[ROW][C]111[/C][C]3165.9[/C][C]2854.37120129727[/C][C]311.528798702729[/C][/ROW]
[ROW][C]112[/C][C]2887.2[/C][C]2840.98259500262[/C][C]46.2174049973773[/C][/ROW]
[ROW][C]113[/C][C]3112.2[/C][C]2973.4596939424[/C][C]138.740306057599[/C][/ROW]
[ROW][C]114[/C][C]2671.2[/C][C]2406.86670493956[/C][C]264.333295060444[/C][/ROW]
[ROW][C]115[/C][C]2432.6[/C][C]2883.44867870295[/C][C]-450.848678702945[/C][/ROW]
[ROW][C]116[/C][C]2812.3[/C][C]2864.25108391293[/C][C]-51.9510839129271[/C][/ROW]
[ROW][C]117[/C][C]3095.7[/C][C]3118.23997266485[/C][C]-22.5399726648461[/C][/ROW]
[ROW][C]118[/C][C]2862.9[/C][C]2789.23550889622[/C][C]73.6644911037783[/C][/ROW]
[ROW][C]119[/C][C]2607.3[/C][C]2616.46986007017[/C][C]-9.16986007017249[/C][/ROW]
[ROW][C]120[/C][C]2862.5[/C][C]3055.59449714028[/C][C]-193.094497140276[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=62584&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=62584&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
13523.3468.44548727656754.8545127234325
14536.1498.6635263766237.4364736233803
15607.3579.70763085453927.5923691454614
16637.3617.18115103587620.1188489641239
17606.9595.82572587945311.074274120547
18652.9641.3310579087411.5689420912598
19617.2544.6048834351472.5951165648603
20670.4703.977363450823-33.5773634508229
21729.9741.541064358148-11.6410643581482
22677.2658.6592735180318.5407264819694
23710798.861606007522-88.8616060075216
24844.3690.582334067552153.717665932448
25748.2709.71818993511438.4818100648864
26653.9727.902110578053-74.0021105780528
27742.6786.505003080898-43.9050030808976
28854.2801.41248465775252.7875153422481
29808.4776.43091303532131.9690869646787
301819838.502991683396980.497008316604
311936.51013.07365058068923.426349419323
321966.11561.72553117971404.37446882029
332083.11819.37286406244263.727135937559
341620.11707.58414162003-87.4841416200336
351527.61923.92162632109-396.321626321093
3617951723.3175278901271.6824721098778
371685.11593.6786885883891.4213114116171
381851.81559.50749420858292.292505791415
392164.41866.573332006297.826667993998
401981.82090.32148568062-108.521485680624
411726.51916.46122352916-189.961223529157
422144.62338.72818934595-194.128189345952
431758.21890.06218712522-131.862187125217
441672.91948.98889262301-276.08889262301
451837.31934.50892901993-97.2089290199256
461596.11620.97248104066-24.8724810406634
4714461770.08600238853-324.086002388528
481898.41710.77199199425187.628008005747
491964.11624.89663314946339.203366850536
501755.91720.6234382004235.2765617995792
512255.31936.06528564962319.234714350378
521881.22064.92035206239-183.720352062393
532117.91844.95589521561272.944104784394
541656.52460.67229645203-804.17229645203
551544.11822.49542625217-278.395426252171
562098.91788.4901141119310.409885888100
572133.32028.5216907021104.778309297903
581963.51775.65577873815187.844221261852
591801.21927.59225463942-126.392254639415
602365.42095.74516966627269.654830333734
611936.52044.36729662966-107.867296629662
621667.61898.40249141378-230.802491413779
631983.52099.91542005586-116.415420055862
642058.61954.26619078847104.333809211530
652448.31944.10187951795504.198120482055
661858.12356.05138517422-497.951385174217
671625.41926.84740134125-301.447401341247
682130.62047.3555531641383.2444468358653
692515.72160.27464522433355.425354775673
702230.21987.49318770981242.706812290192
712086.92078.602735388478.29726461152904
7222352426.31980271082-191.319802710819
732100.22108.74017584760-8.54017584759731
742288.61954.13452021044334.465479789559
7524902431.6522724360358.3477275639693
762573.72388.39421469764185.305785302360
772543.82502.8381592017240.9618407982825
782004.72489.16653498205-484.466534982046
7923902081.16901205823308.830987941765
802338.42586.96443620870-248.564436208704
812724.52674.2559369587750.2440630412284
822292.52319.63032211609-27.1303221160888
8323862253.35109159517132.648908404832
842477.92621.84724829203-143.947248292027
8523372342.08424960309-5.08424960309412
862605.12260.78152706651344.318472933492
872560.82701.82903771605-141.029037716049
882839.32616.73847733390222.561522666096
892407.22708.00758084818-300.807580848181
902085.22430.14911313109-344.949113131093
912735.62262.61109751585472.988902484153
922798.72700.8303148870697.8696851129407
933053.23011.3585007895141.8414992104899
9424052586.50809709010-181.508097090097
952471.92503.40548652555-31.5054865255488
962727.32761.54246769244-34.2424676924356
972790.72537.14929618599253.55070381401
982385.42627.68142370859-242.281423708586
993206.62749.27354456528457.32645543472
1002705.62965.37509735931-259.775097359306
1013518.42749.47352120628768.926478793724
1021954.92787.89219909764-832.992199097638
1032584.32665.32078027908-81.0207802790833
1042535.82823.53661753304-287.736617533041
1052685.92983.28465081925-297.384650819251
10628662409.97324870202456.026751297976
1072236.62585.36521520188-348.765215201880
1082934.92730.88054591979204.01945408021
1092668.62655.5637611175713.0362388824269
1102371.22538.00990550250-166.809905502497
1113165.92854.37120129727311.528798702729
1122887.22840.9825950026246.2174049973773
1133112.22973.4596939424138.740306057599
1142671.22406.86670493956264.333295060444
1152432.62883.44867870295-450.848678702945
1162812.32864.25108391293-51.9510839129271
1173095.73118.23997266485-22.5399726648461
1182862.92789.2355088962273.6644911037783
1192607.32616.46986007017-9.16986007017249
1202862.53055.59449714028-193.094497140276







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
1212785.130590868082448.173988604403122.08719313175
1222608.844713896622225.712311945842991.9771158474
1233133.376535004862668.858303156333597.89476685338
1242939.469849807112453.540990353113425.39870926110
1253081.700958319862544.273792810563619.12812382917
1262491.156405097811989.244872868232993.06793732739
1272685.164323597762122.105619808543248.22302738699
1282928.008794446822296.648279106023559.36930978763
1293216.246279071432508.811578149713923.68097999316
1302907.891271318932230.933729200663584.84881343719
1312682.806041299792021.832937457903343.77914514167
1323088.466874938222398.256356453663778.67739342277

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
121 & 2785.13059086808 & 2448.17398860440 & 3122.08719313175 \tabularnewline
122 & 2608.84471389662 & 2225.71231194584 & 2991.9771158474 \tabularnewline
123 & 3133.37653500486 & 2668.85830315633 & 3597.89476685338 \tabularnewline
124 & 2939.46984980711 & 2453.54099035311 & 3425.39870926110 \tabularnewline
125 & 3081.70095831986 & 2544.27379281056 & 3619.12812382917 \tabularnewline
126 & 2491.15640509781 & 1989.24487286823 & 2993.06793732739 \tabularnewline
127 & 2685.16432359776 & 2122.10561980854 & 3248.22302738699 \tabularnewline
128 & 2928.00879444682 & 2296.64827910602 & 3559.36930978763 \tabularnewline
129 & 3216.24627907143 & 2508.81157814971 & 3923.68097999316 \tabularnewline
130 & 2907.89127131893 & 2230.93372920066 & 3584.84881343719 \tabularnewline
131 & 2682.80604129979 & 2021.83293745790 & 3343.77914514167 \tabularnewline
132 & 3088.46687493822 & 2398.25635645366 & 3778.67739342277 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=62584&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]2785.13059086808[/C][C]2448.17398860440[/C][C]3122.08719313175[/C][/ROW]
[ROW][C]122[/C][C]2608.84471389662[/C][C]2225.71231194584[/C][C]2991.9771158474[/C][/ROW]
[ROW][C]123[/C][C]3133.37653500486[/C][C]2668.85830315633[/C][C]3597.89476685338[/C][/ROW]
[ROW][C]124[/C][C]2939.46984980711[/C][C]2453.54099035311[/C][C]3425.39870926110[/C][/ROW]
[ROW][C]125[/C][C]3081.70095831986[/C][C]2544.27379281056[/C][C]3619.12812382917[/C][/ROW]
[ROW][C]126[/C][C]2491.15640509781[/C][C]1989.24487286823[/C][C]2993.06793732739[/C][/ROW]
[ROW][C]127[/C][C]2685.16432359776[/C][C]2122.10561980854[/C][C]3248.22302738699[/C][/ROW]
[ROW][C]128[/C][C]2928.00879444682[/C][C]2296.64827910602[/C][C]3559.36930978763[/C][/ROW]
[ROW][C]129[/C][C]3216.24627907143[/C][C]2508.81157814971[/C][C]3923.68097999316[/C][/ROW]
[ROW][C]130[/C][C]2907.89127131893[/C][C]2230.93372920066[/C][C]3584.84881343719[/C][/ROW]
[ROW][C]131[/C][C]2682.80604129979[/C][C]2021.83293745790[/C][C]3343.77914514167[/C][/ROW]
[ROW][C]132[/C][C]3088.46687493822[/C][C]2398.25635645366[/C][C]3778.67739342277[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=62584&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=62584&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
1212785.130590868082448.173988604403122.08719313175
1222608.844713896622225.712311945842991.9771158474
1233133.376535004862668.858303156333597.89476685338
1242939.469849807112453.540990353113425.39870926110
1253081.700958319862544.273792810563619.12812382917
1262491.156405097811989.244872868232993.06793732739
1272685.164323597762122.105619808543248.22302738699
1282928.008794446822296.648279106023559.36930978763
1293216.246279071432508.811578149713923.68097999316
1302907.891271318932230.933729200663584.84881343719
1312682.806041299792021.832937457903343.77914514167
1323088.466874938222398.256356453663778.67739342277



Parameters (Session):
par1 = FALSE ; par2 = 1 ; par3 = 1 ; par4 = 1 ; par5 = 12 ; par6 = 3 ; par7 = 1 ; par8 = 2 ; par9 = 1 ;
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=0, beta=0)
if (par2 == 'Double') fit <- HoltWinters(x, gamma=0)
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')