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Description of Statistical Computation

Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationSun, 29 May 2011 11:49:58 +0000
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/May/29/t1306669571zl6vq66uv347m46.htm/, Retrieved Wed, 08 May 2024 02:18:39 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=122548, Retrieved Wed, 08 May 2024 02:18:39 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywordsKDGP2W102
Estimated Impact170

Tree of Dependent Computations

Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [Exponential Smoothing] [] [2011-05-29 11:49:58] [d41d8cd98f00b204e9800998ecf8427e] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
505,7
55,7
735,7
575,9
545,8
905,8
765,8
945,7
15,7
645,7
155,9
416
825,8
725,9
925,9
556
116,1
876,3
336,2
186,1
286,1
26
915,8
405,7
965,7
395,6
425,8
545,6
65,6
445,6
895,5
175,4
715,4
865,5
57,4
145,4
315,3
635,4
5,2
515,2
515,1
955
955
634,9
205
275
425
84,9
534,7
4,8
704,7
684,7
884,6
994,6
294,7
524,7
914,5
564,4
984,5
934,4
514,6
474,5
784,4
504,5
824,4
414,6
964,7
64,6
244,7
344,7
34,7
685
425
484,8
785,1
704,9
245,4
285,6
218,8
706,1
856,2
456,6
606,8
527,3
657,8
948,2
486,6
238,9
289,4
969,5
589,5
189,7
639,8
9710,1
969,9
939,9
859,7
679,9
879,9
329,8
349,6
39,5
849,5
449,6
749,6
249,7
649,8
619,4
939
778,9

Tables (Output of Computation)





Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'Herman Ole Andreas Wold' @ www.yougetit.org

\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 & 2 seconds \tabularnewline
R Server & 'Herman Ole Andreas Wold' @ www.yougetit.org \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=122548&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]2 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Herman Ole Andreas Wold' @ www.yougetit.org[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=122548&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=122548&T=0

As an alternative you can also use a QR Code:  
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 time2 seconds
R Server'Herman Ole Andreas Wold' @ www.yougetit.org






Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.29089981285969
beta0.129402100573134
gammaFALSE

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.29089981285969 \tabularnewline
beta & 0.129402100573134 \tabularnewline
gamma & FALSE \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=122548&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]0.29089981285969[/C][/ROW]
[ROW][C]beta[/C][C]0.129402100573134[/C][/ROW]
[ROW][C]gamma[/C][C]FALSE[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=122548&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=122548&T=1

As an alternative you can also use a QR Code:  
QR Code


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

Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.29089981285969
beta0.129402100573134
gammaFALSE






Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
3735.7-394.31130
4575.9-473.0465685389261048.94656853893
5545.8-535.8860203089521081.68602030895
6905.8-548.4836141568791454.28361415688
7765.8-397.9489714755751163.74897147557
8945.7-288.1237449358261233.82374493583
915.7-111.468894886917127.168894886917
10645.7-251.952708950638897.652708950638
11155.9-134.512542722383290.412542722383
12416-182.786414262083598.786414262083
13825.8-118.814239240618944.614239240618
14725.981.3173434025964644.582656597404
15925.9218.433849937693707.466150062307
16556400.474334378469155.525665621531
17116.1427.809895101609-311.709895101609
18876.3307.493008467076568.806991532924
19336.2464.729947599733-128.529947599733
20186.1414.273442800663-228.173442800663
21286.1326.241520299882-40.141520299882
2226291.396999737334-265.396999737334
23915.8181.035350668403734.764649331597
24405.7389.27931825450516.4206817454948
25965.7389.175284593019576.524715406981
26395.6573.707556372317-178.107556372316
27425.8532.012930425985-106.212930425985
28545.6507.2342593979838.3657406020197
2965.6525.957700086072-460.357700086072
30445.6382.2733187415963.3266812584102
31895.5393.312435156616502.187564843384
32175.4550.919970504003-375.519970504003
33715.4439.066832234116276.333167765884
34865.5527.239672276702338.260327723298
3557.4646.16026092256-588.76026092256
36145.4473.248003734599-327.848003734599
37315.3363.89387557431-48.5938755743102
38635.4333.945499501746301.454500498254
395.2417.173796403027-411.973796403027
40515.2277.357986331911237.842013668089
41515.1335.526571864868179.573428135132
42955383.504527737267571.495472262733
43955567.00536373342387.994636266579
44634.9711.731141145494-76.8311411454937
45205718.347028651095-513.347028651095
46275578.656579926155-303.656579926155
47425488.534484632216-63.534484632216
4884.9465.872230341771-380.972230341771
49534.7336.526439718177198.173560281823
504.8383.113907817676-378.313907817676
51704.7247.760391178728456.939608821272
52684.7372.58256531853312.11743468147
53884.6467.025047316543417.574952683457
54994.6607.863895069212386.736104930788
55294.7754.289653094595-459.589653094595
56524.7637.219051653267-112.519051653267
57914.5616.875663288503297.624336711497
58564.4727.046396692355-162.646396692355
59984.5697.201953955125287.298046044875
60934.4809.061039211828125.338960788172
61514.6878.524397248303-363.924397248303
62474.5791.96191286089-317.461912860891
63784.4706.96512283091577.4348771690849
64504.5739.758619827906-235.258619827906
65824.4672.733785820247151.666214179753
66414.6723.974492020653-309.374492020653
67964.7629.45274457231335.247255427689
6864.6735.07107096115-670.471070961149
69244.7522.887550484607-278.187550484607
70344.7414.34740570933-69.6474057093298
7134.7363.849809467486-329.149809467486
72685225.47281084047459.52718915953
73425333.81980702675491.1801929732464
74484.8338.447031230024146.352968769976
75785.1364.63317724615420.46682275385
76704.9486.38664439218218.513355607821
77245.4557.617394219456-312.217394219456
78285.6462.705854248112-177.105854248112
79218.8400.431432002451-181.631432002451
80706.1330.003359532417376.096640467583
81856.2435.975702424141420.224297575859
82456.6570.603295427711-114.003295427711
83606.8545.53275021231861.2672497876823
84527.3573.754659753437-46.4546597534367
85657.8568.89159103510388.9084089648967
86948.2606.752397078215341.447602921785
87486.6730.929935493442-244.329935493442
88238.9675.507574399983-436.607574399983
89289.4547.716444757507-258.316444757507
90969.5462.066353332924507.433646667076
91589.5618.274168730914-28.7741687309144
92189.7617.416083594395-427.716083594395
93639.8484.405333513077155.394666486923
949710.1526.87092021629183.2290797838
95969.93541.21657067186-2571.31657067186
96939.93039.37490104804-2099.47490104804
97859.72595.76125277685-1736.06125277685
98679.92192.51393172237-1512.61393172237
99879.91797.32799746341-917.427997463409
100329.81540.74675501591-1210.94675501591
101349.61153.19723550532-803.597235505315
10239.5853.895766611914-814.395766611914
103849.5520.796669051269328.703330948731
104449.6532.598279934586-82.9982799345859
105749.6421.511661118665328.088338881335
106249.7442.360307493709-192.660307493709
107649.8304.47094911205345.32905088795
108619.4336.081832042037283.318167957963
109939360.318719799598578.681280200402
110778.9492.260008170372286.639991829628

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
3 & 735.7 & -394.3 & 1130 \tabularnewline
4 & 575.9 & -473.046568538926 & 1048.94656853893 \tabularnewline
5 & 545.8 & -535.886020308952 & 1081.68602030895 \tabularnewline
6 & 905.8 & -548.483614156879 & 1454.28361415688 \tabularnewline
7 & 765.8 & -397.948971475575 & 1163.74897147557 \tabularnewline
8 & 945.7 & -288.123744935826 & 1233.82374493583 \tabularnewline
9 & 15.7 & -111.468894886917 & 127.168894886917 \tabularnewline
10 & 645.7 & -251.952708950638 & 897.652708950638 \tabularnewline
11 & 155.9 & -134.512542722383 & 290.412542722383 \tabularnewline
12 & 416 & -182.786414262083 & 598.786414262083 \tabularnewline
13 & 825.8 & -118.814239240618 & 944.614239240618 \tabularnewline
14 & 725.9 & 81.3173434025964 & 644.582656597404 \tabularnewline
15 & 925.9 & 218.433849937693 & 707.466150062307 \tabularnewline
16 & 556 & 400.474334378469 & 155.525665621531 \tabularnewline
17 & 116.1 & 427.809895101609 & -311.709895101609 \tabularnewline
18 & 876.3 & 307.493008467076 & 568.806991532924 \tabularnewline
19 & 336.2 & 464.729947599733 & -128.529947599733 \tabularnewline
20 & 186.1 & 414.273442800663 & -228.173442800663 \tabularnewline
21 & 286.1 & 326.241520299882 & -40.141520299882 \tabularnewline
22 & 26 & 291.396999737334 & -265.396999737334 \tabularnewline
23 & 915.8 & 181.035350668403 & 734.764649331597 \tabularnewline
24 & 405.7 & 389.279318254505 & 16.4206817454948 \tabularnewline
25 & 965.7 & 389.175284593019 & 576.524715406981 \tabularnewline
26 & 395.6 & 573.707556372317 & -178.107556372316 \tabularnewline
27 & 425.8 & 532.012930425985 & -106.212930425985 \tabularnewline
28 & 545.6 & 507.23425939798 & 38.3657406020197 \tabularnewline
29 & 65.6 & 525.957700086072 & -460.357700086072 \tabularnewline
30 & 445.6 & 382.27331874159 & 63.3266812584102 \tabularnewline
31 & 895.5 & 393.312435156616 & 502.187564843384 \tabularnewline
32 & 175.4 & 550.919970504003 & -375.519970504003 \tabularnewline
33 & 715.4 & 439.066832234116 & 276.333167765884 \tabularnewline
34 & 865.5 & 527.239672276702 & 338.260327723298 \tabularnewline
35 & 57.4 & 646.16026092256 & -588.76026092256 \tabularnewline
36 & 145.4 & 473.248003734599 & -327.848003734599 \tabularnewline
37 & 315.3 & 363.89387557431 & -48.5938755743102 \tabularnewline
38 & 635.4 & 333.945499501746 & 301.454500498254 \tabularnewline
39 & 5.2 & 417.173796403027 & -411.973796403027 \tabularnewline
40 & 515.2 & 277.357986331911 & 237.842013668089 \tabularnewline
41 & 515.1 & 335.526571864868 & 179.573428135132 \tabularnewline
42 & 955 & 383.504527737267 & 571.495472262733 \tabularnewline
43 & 955 & 567.00536373342 & 387.994636266579 \tabularnewline
44 & 634.9 & 711.731141145494 & -76.8311411454937 \tabularnewline
45 & 205 & 718.347028651095 & -513.347028651095 \tabularnewline
46 & 275 & 578.656579926155 & -303.656579926155 \tabularnewline
47 & 425 & 488.534484632216 & -63.534484632216 \tabularnewline
48 & 84.9 & 465.872230341771 & -380.972230341771 \tabularnewline
49 & 534.7 & 336.526439718177 & 198.173560281823 \tabularnewline
50 & 4.8 & 383.113907817676 & -378.313907817676 \tabularnewline
51 & 704.7 & 247.760391178728 & 456.939608821272 \tabularnewline
52 & 684.7 & 372.58256531853 & 312.11743468147 \tabularnewline
53 & 884.6 & 467.025047316543 & 417.574952683457 \tabularnewline
54 & 994.6 & 607.863895069212 & 386.736104930788 \tabularnewline
55 & 294.7 & 754.289653094595 & -459.589653094595 \tabularnewline
56 & 524.7 & 637.219051653267 & -112.519051653267 \tabularnewline
57 & 914.5 & 616.875663288503 & 297.624336711497 \tabularnewline
58 & 564.4 & 727.046396692355 & -162.646396692355 \tabularnewline
59 & 984.5 & 697.201953955125 & 287.298046044875 \tabularnewline
60 & 934.4 & 809.061039211828 & 125.338960788172 \tabularnewline
61 & 514.6 & 878.524397248303 & -363.924397248303 \tabularnewline
62 & 474.5 & 791.96191286089 & -317.461912860891 \tabularnewline
63 & 784.4 & 706.965122830915 & 77.4348771690849 \tabularnewline
64 & 504.5 & 739.758619827906 & -235.258619827906 \tabularnewline
65 & 824.4 & 672.733785820247 & 151.666214179753 \tabularnewline
66 & 414.6 & 723.974492020653 & -309.374492020653 \tabularnewline
67 & 964.7 & 629.45274457231 & 335.247255427689 \tabularnewline
68 & 64.6 & 735.07107096115 & -670.471070961149 \tabularnewline
69 & 244.7 & 522.887550484607 & -278.187550484607 \tabularnewline
70 & 344.7 & 414.34740570933 & -69.6474057093298 \tabularnewline
71 & 34.7 & 363.849809467486 & -329.149809467486 \tabularnewline
72 & 685 & 225.47281084047 & 459.52718915953 \tabularnewline
73 & 425 & 333.819807026754 & 91.1801929732464 \tabularnewline
74 & 484.8 & 338.447031230024 & 146.352968769976 \tabularnewline
75 & 785.1 & 364.63317724615 & 420.46682275385 \tabularnewline
76 & 704.9 & 486.38664439218 & 218.513355607821 \tabularnewline
77 & 245.4 & 557.617394219456 & -312.217394219456 \tabularnewline
78 & 285.6 & 462.705854248112 & -177.105854248112 \tabularnewline
79 & 218.8 & 400.431432002451 & -181.631432002451 \tabularnewline
80 & 706.1 & 330.003359532417 & 376.096640467583 \tabularnewline
81 & 856.2 & 435.975702424141 & 420.224297575859 \tabularnewline
82 & 456.6 & 570.603295427711 & -114.003295427711 \tabularnewline
83 & 606.8 & 545.532750212318 & 61.2672497876823 \tabularnewline
84 & 527.3 & 573.754659753437 & -46.4546597534367 \tabularnewline
85 & 657.8 & 568.891591035103 & 88.9084089648967 \tabularnewline
86 & 948.2 & 606.752397078215 & 341.447602921785 \tabularnewline
87 & 486.6 & 730.929935493442 & -244.329935493442 \tabularnewline
88 & 238.9 & 675.507574399983 & -436.607574399983 \tabularnewline
89 & 289.4 & 547.716444757507 & -258.316444757507 \tabularnewline
90 & 969.5 & 462.066353332924 & 507.433646667076 \tabularnewline
91 & 589.5 & 618.274168730914 & -28.7741687309144 \tabularnewline
92 & 189.7 & 617.416083594395 & -427.716083594395 \tabularnewline
93 & 639.8 & 484.405333513077 & 155.394666486923 \tabularnewline
94 & 9710.1 & 526.8709202162 & 9183.2290797838 \tabularnewline
95 & 969.9 & 3541.21657067186 & -2571.31657067186 \tabularnewline
96 & 939.9 & 3039.37490104804 & -2099.47490104804 \tabularnewline
97 & 859.7 & 2595.76125277685 & -1736.06125277685 \tabularnewline
98 & 679.9 & 2192.51393172237 & -1512.61393172237 \tabularnewline
99 & 879.9 & 1797.32799746341 & -917.427997463409 \tabularnewline
100 & 329.8 & 1540.74675501591 & -1210.94675501591 \tabularnewline
101 & 349.6 & 1153.19723550532 & -803.597235505315 \tabularnewline
102 & 39.5 & 853.895766611914 & -814.395766611914 \tabularnewline
103 & 849.5 & 520.796669051269 & 328.703330948731 \tabularnewline
104 & 449.6 & 532.598279934586 & -82.9982799345859 \tabularnewline
105 & 749.6 & 421.511661118665 & 328.088338881335 \tabularnewline
106 & 249.7 & 442.360307493709 & -192.660307493709 \tabularnewline
107 & 649.8 & 304.47094911205 & 345.32905088795 \tabularnewline
108 & 619.4 & 336.081832042037 & 283.318167957963 \tabularnewline
109 & 939 & 360.318719799598 & 578.681280200402 \tabularnewline
110 & 778.9 & 492.260008170372 & 286.639991829628 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=122548&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]735.7[/C][C]-394.3[/C][C]1130[/C][/ROW]
[ROW][C]4[/C][C]575.9[/C][C]-473.046568538926[/C][C]1048.94656853893[/C][/ROW]
[ROW][C]5[/C][C]545.8[/C][C]-535.886020308952[/C][C]1081.68602030895[/C][/ROW]
[ROW][C]6[/C][C]905.8[/C][C]-548.483614156879[/C][C]1454.28361415688[/C][/ROW]
[ROW][C]7[/C][C]765.8[/C][C]-397.948971475575[/C][C]1163.74897147557[/C][/ROW]
[ROW][C]8[/C][C]945.7[/C][C]-288.123744935826[/C][C]1233.82374493583[/C][/ROW]
[ROW][C]9[/C][C]15.7[/C][C]-111.468894886917[/C][C]127.168894886917[/C][/ROW]
[ROW][C]10[/C][C]645.7[/C][C]-251.952708950638[/C][C]897.652708950638[/C][/ROW]
[ROW][C]11[/C][C]155.9[/C][C]-134.512542722383[/C][C]290.412542722383[/C][/ROW]
[ROW][C]12[/C][C]416[/C][C]-182.786414262083[/C][C]598.786414262083[/C][/ROW]
[ROW][C]13[/C][C]825.8[/C][C]-118.814239240618[/C][C]944.614239240618[/C][/ROW]
[ROW][C]14[/C][C]725.9[/C][C]81.3173434025964[/C][C]644.582656597404[/C][/ROW]
[ROW][C]15[/C][C]925.9[/C][C]218.433849937693[/C][C]707.466150062307[/C][/ROW]
[ROW][C]16[/C][C]556[/C][C]400.474334378469[/C][C]155.525665621531[/C][/ROW]
[ROW][C]17[/C][C]116.1[/C][C]427.809895101609[/C][C]-311.709895101609[/C][/ROW]
[ROW][C]18[/C][C]876.3[/C][C]307.493008467076[/C][C]568.806991532924[/C][/ROW]
[ROW][C]19[/C][C]336.2[/C][C]464.729947599733[/C][C]-128.529947599733[/C][/ROW]
[ROW][C]20[/C][C]186.1[/C][C]414.273442800663[/C][C]-228.173442800663[/C][/ROW]
[ROW][C]21[/C][C]286.1[/C][C]326.241520299882[/C][C]-40.141520299882[/C][/ROW]
[ROW][C]22[/C][C]26[/C][C]291.396999737334[/C][C]-265.396999737334[/C][/ROW]
[ROW][C]23[/C][C]915.8[/C][C]181.035350668403[/C][C]734.764649331597[/C][/ROW]
[ROW][C]24[/C][C]405.7[/C][C]389.279318254505[/C][C]16.4206817454948[/C][/ROW]
[ROW][C]25[/C][C]965.7[/C][C]389.175284593019[/C][C]576.524715406981[/C][/ROW]
[ROW][C]26[/C][C]395.6[/C][C]573.707556372317[/C][C]-178.107556372316[/C][/ROW]
[ROW][C]27[/C][C]425.8[/C][C]532.012930425985[/C][C]-106.212930425985[/C][/ROW]
[ROW][C]28[/C][C]545.6[/C][C]507.23425939798[/C][C]38.3657406020197[/C][/ROW]
[ROW][C]29[/C][C]65.6[/C][C]525.957700086072[/C][C]-460.357700086072[/C][/ROW]
[ROW][C]30[/C][C]445.6[/C][C]382.27331874159[/C][C]63.3266812584102[/C][/ROW]
[ROW][C]31[/C][C]895.5[/C][C]393.312435156616[/C][C]502.187564843384[/C][/ROW]
[ROW][C]32[/C][C]175.4[/C][C]550.919970504003[/C][C]-375.519970504003[/C][/ROW]
[ROW][C]33[/C][C]715.4[/C][C]439.066832234116[/C][C]276.333167765884[/C][/ROW]
[ROW][C]34[/C][C]865.5[/C][C]527.239672276702[/C][C]338.260327723298[/C][/ROW]
[ROW][C]35[/C][C]57.4[/C][C]646.16026092256[/C][C]-588.76026092256[/C][/ROW]
[ROW][C]36[/C][C]145.4[/C][C]473.248003734599[/C][C]-327.848003734599[/C][/ROW]
[ROW][C]37[/C][C]315.3[/C][C]363.89387557431[/C][C]-48.5938755743102[/C][/ROW]
[ROW][C]38[/C][C]635.4[/C][C]333.945499501746[/C][C]301.454500498254[/C][/ROW]
[ROW][C]39[/C][C]5.2[/C][C]417.173796403027[/C][C]-411.973796403027[/C][/ROW]
[ROW][C]40[/C][C]515.2[/C][C]277.357986331911[/C][C]237.842013668089[/C][/ROW]
[ROW][C]41[/C][C]515.1[/C][C]335.526571864868[/C][C]179.573428135132[/C][/ROW]
[ROW][C]42[/C][C]955[/C][C]383.504527737267[/C][C]571.495472262733[/C][/ROW]
[ROW][C]43[/C][C]955[/C][C]567.00536373342[/C][C]387.994636266579[/C][/ROW]
[ROW][C]44[/C][C]634.9[/C][C]711.731141145494[/C][C]-76.8311411454937[/C][/ROW]
[ROW][C]45[/C][C]205[/C][C]718.347028651095[/C][C]-513.347028651095[/C][/ROW]
[ROW][C]46[/C][C]275[/C][C]578.656579926155[/C][C]-303.656579926155[/C][/ROW]
[ROW][C]47[/C][C]425[/C][C]488.534484632216[/C][C]-63.534484632216[/C][/ROW]
[ROW][C]48[/C][C]84.9[/C][C]465.872230341771[/C][C]-380.972230341771[/C][/ROW]
[ROW][C]49[/C][C]534.7[/C][C]336.526439718177[/C][C]198.173560281823[/C][/ROW]
[ROW][C]50[/C][C]4.8[/C][C]383.113907817676[/C][C]-378.313907817676[/C][/ROW]
[ROW][C]51[/C][C]704.7[/C][C]247.760391178728[/C][C]456.939608821272[/C][/ROW]
[ROW][C]52[/C][C]684.7[/C][C]372.58256531853[/C][C]312.11743468147[/C][/ROW]
[ROW][C]53[/C][C]884.6[/C][C]467.025047316543[/C][C]417.574952683457[/C][/ROW]
[ROW][C]54[/C][C]994.6[/C][C]607.863895069212[/C][C]386.736104930788[/C][/ROW]
[ROW][C]55[/C][C]294.7[/C][C]754.289653094595[/C][C]-459.589653094595[/C][/ROW]
[ROW][C]56[/C][C]524.7[/C][C]637.219051653267[/C][C]-112.519051653267[/C][/ROW]
[ROW][C]57[/C][C]914.5[/C][C]616.875663288503[/C][C]297.624336711497[/C][/ROW]
[ROW][C]58[/C][C]564.4[/C][C]727.046396692355[/C][C]-162.646396692355[/C][/ROW]
[ROW][C]59[/C][C]984.5[/C][C]697.201953955125[/C][C]287.298046044875[/C][/ROW]
[ROW][C]60[/C][C]934.4[/C][C]809.061039211828[/C][C]125.338960788172[/C][/ROW]
[ROW][C]61[/C][C]514.6[/C][C]878.524397248303[/C][C]-363.924397248303[/C][/ROW]
[ROW][C]62[/C][C]474.5[/C][C]791.96191286089[/C][C]-317.461912860891[/C][/ROW]
[ROW][C]63[/C][C]784.4[/C][C]706.965122830915[/C][C]77.4348771690849[/C][/ROW]
[ROW][C]64[/C][C]504.5[/C][C]739.758619827906[/C][C]-235.258619827906[/C][/ROW]
[ROW][C]65[/C][C]824.4[/C][C]672.733785820247[/C][C]151.666214179753[/C][/ROW]
[ROW][C]66[/C][C]414.6[/C][C]723.974492020653[/C][C]-309.374492020653[/C][/ROW]
[ROW][C]67[/C][C]964.7[/C][C]629.45274457231[/C][C]335.247255427689[/C][/ROW]
[ROW][C]68[/C][C]64.6[/C][C]735.07107096115[/C][C]-670.471070961149[/C][/ROW]
[ROW][C]69[/C][C]244.7[/C][C]522.887550484607[/C][C]-278.187550484607[/C][/ROW]
[ROW][C]70[/C][C]344.7[/C][C]414.34740570933[/C][C]-69.6474057093298[/C][/ROW]
[ROW][C]71[/C][C]34.7[/C][C]363.849809467486[/C][C]-329.149809467486[/C][/ROW]
[ROW][C]72[/C][C]685[/C][C]225.47281084047[/C][C]459.52718915953[/C][/ROW]
[ROW][C]73[/C][C]425[/C][C]333.819807026754[/C][C]91.1801929732464[/C][/ROW]
[ROW][C]74[/C][C]484.8[/C][C]338.447031230024[/C][C]146.352968769976[/C][/ROW]
[ROW][C]75[/C][C]785.1[/C][C]364.63317724615[/C][C]420.46682275385[/C][/ROW]
[ROW][C]76[/C][C]704.9[/C][C]486.38664439218[/C][C]218.513355607821[/C][/ROW]
[ROW][C]77[/C][C]245.4[/C][C]557.617394219456[/C][C]-312.217394219456[/C][/ROW]
[ROW][C]78[/C][C]285.6[/C][C]462.705854248112[/C][C]-177.105854248112[/C][/ROW]
[ROW][C]79[/C][C]218.8[/C][C]400.431432002451[/C][C]-181.631432002451[/C][/ROW]
[ROW][C]80[/C][C]706.1[/C][C]330.003359532417[/C][C]376.096640467583[/C][/ROW]
[ROW][C]81[/C][C]856.2[/C][C]435.975702424141[/C][C]420.224297575859[/C][/ROW]
[ROW][C]82[/C][C]456.6[/C][C]570.603295427711[/C][C]-114.003295427711[/C][/ROW]
[ROW][C]83[/C][C]606.8[/C][C]545.532750212318[/C][C]61.2672497876823[/C][/ROW]
[ROW][C]84[/C][C]527.3[/C][C]573.754659753437[/C][C]-46.4546597534367[/C][/ROW]
[ROW][C]85[/C][C]657.8[/C][C]568.891591035103[/C][C]88.9084089648967[/C][/ROW]
[ROW][C]86[/C][C]948.2[/C][C]606.752397078215[/C][C]341.447602921785[/C][/ROW]
[ROW][C]87[/C][C]486.6[/C][C]730.929935493442[/C][C]-244.329935493442[/C][/ROW]
[ROW][C]88[/C][C]238.9[/C][C]675.507574399983[/C][C]-436.607574399983[/C][/ROW]
[ROW][C]89[/C][C]289.4[/C][C]547.716444757507[/C][C]-258.316444757507[/C][/ROW]
[ROW][C]90[/C][C]969.5[/C][C]462.066353332924[/C][C]507.433646667076[/C][/ROW]
[ROW][C]91[/C][C]589.5[/C][C]618.274168730914[/C][C]-28.7741687309144[/C][/ROW]
[ROW][C]92[/C][C]189.7[/C][C]617.416083594395[/C][C]-427.716083594395[/C][/ROW]
[ROW][C]93[/C][C]639.8[/C][C]484.405333513077[/C][C]155.394666486923[/C][/ROW]
[ROW][C]94[/C][C]9710.1[/C][C]526.8709202162[/C][C]9183.2290797838[/C][/ROW]
[ROW][C]95[/C][C]969.9[/C][C]3541.21657067186[/C][C]-2571.31657067186[/C][/ROW]
[ROW][C]96[/C][C]939.9[/C][C]3039.37490104804[/C][C]-2099.47490104804[/C][/ROW]
[ROW][C]97[/C][C]859.7[/C][C]2595.76125277685[/C][C]-1736.06125277685[/C][/ROW]
[ROW][C]98[/C][C]679.9[/C][C]2192.51393172237[/C][C]-1512.61393172237[/C][/ROW]
[ROW][C]99[/C][C]879.9[/C][C]1797.32799746341[/C][C]-917.427997463409[/C][/ROW]
[ROW][C]100[/C][C]329.8[/C][C]1540.74675501591[/C][C]-1210.94675501591[/C][/ROW]
[ROW][C]101[/C][C]349.6[/C][C]1153.19723550532[/C][C]-803.597235505315[/C][/ROW]
[ROW][C]102[/C][C]39.5[/C][C]853.895766611914[/C][C]-814.395766611914[/C][/ROW]
[ROW][C]103[/C][C]849.5[/C][C]520.796669051269[/C][C]328.703330948731[/C][/ROW]
[ROW][C]104[/C][C]449.6[/C][C]532.598279934586[/C][C]-82.9982799345859[/C][/ROW]
[ROW][C]105[/C][C]749.6[/C][C]421.511661118665[/C][C]328.088338881335[/C][/ROW]
[ROW][C]106[/C][C]249.7[/C][C]442.360307493709[/C][C]-192.660307493709[/C][/ROW]
[ROW][C]107[/C][C]649.8[/C][C]304.47094911205[/C][C]345.32905088795[/C][/ROW]
[ROW][C]108[/C][C]619.4[/C][C]336.081832042037[/C][C]283.318167957963[/C][/ROW]
[ROW][C]109[/C][C]939[/C][C]360.318719799598[/C][C]578.681280200402[/C][/ROW]
[ROW][C]110[/C][C]778.9[/C][C]492.260008170372[/C][C]286.639991829628[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=122548&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=122548&T=2

As an alternative you can also use a QR Code:  
QR Code


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

Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
3735.7-394.31130
4575.9-473.0465685389261048.94656853893
5545.8-535.8860203089521081.68602030895
6905.8-548.4836141568791454.28361415688
7765.8-397.9489714755751163.74897147557
8945.7-288.1237449358261233.82374493583
915.7-111.468894886917127.168894886917
10645.7-251.952708950638897.652708950638
11155.9-134.512542722383290.412542722383
12416-182.786414262083598.786414262083
13825.8-118.814239240618944.614239240618
14725.981.3173434025964644.582656597404
15925.9218.433849937693707.466150062307
16556400.474334378469155.525665621531
17116.1427.809895101609-311.709895101609
18876.3307.493008467076568.806991532924
19336.2464.729947599733-128.529947599733
20186.1414.273442800663-228.173442800663
21286.1326.241520299882-40.141520299882
2226291.396999737334-265.396999737334
23915.8181.035350668403734.764649331597
24405.7389.27931825450516.4206817454948
25965.7389.175284593019576.524715406981
26395.6573.707556372317-178.107556372316
27425.8532.012930425985-106.212930425985
28545.6507.2342593979838.3657406020197
2965.6525.957700086072-460.357700086072
30445.6382.2733187415963.3266812584102
31895.5393.312435156616502.187564843384
32175.4550.919970504003-375.519970504003
33715.4439.066832234116276.333167765884
34865.5527.239672276702338.260327723298
3557.4646.16026092256-588.76026092256
36145.4473.248003734599-327.848003734599
37315.3363.89387557431-48.5938755743102
38635.4333.945499501746301.454500498254
395.2417.173796403027-411.973796403027
40515.2277.357986331911237.842013668089
41515.1335.526571864868179.573428135132
42955383.504527737267571.495472262733
43955567.00536373342387.994636266579
44634.9711.731141145494-76.8311411454937
45205718.347028651095-513.347028651095
46275578.656579926155-303.656579926155
47425488.534484632216-63.534484632216
4884.9465.872230341771-380.972230341771
49534.7336.526439718177198.173560281823
504.8383.113907817676-378.313907817676
51704.7247.760391178728456.939608821272
52684.7372.58256531853312.11743468147
53884.6467.025047316543417.574952683457
54994.6607.863895069212386.736104930788
55294.7754.289653094595-459.589653094595
56524.7637.219051653267-112.519051653267
57914.5616.875663288503297.624336711497
58564.4727.046396692355-162.646396692355
59984.5697.201953955125287.298046044875
60934.4809.061039211828125.338960788172
61514.6878.524397248303-363.924397248303
62474.5791.96191286089-317.461912860891
63784.4706.96512283091577.4348771690849
64504.5739.758619827906-235.258619827906
65824.4672.733785820247151.666214179753
66414.6723.974492020653-309.374492020653
67964.7629.45274457231335.247255427689
6864.6735.07107096115-670.471070961149
69244.7522.887550484607-278.187550484607
70344.7414.34740570933-69.6474057093298
7134.7363.849809467486-329.149809467486
72685225.47281084047459.52718915953
73425333.81980702675491.1801929732464
74484.8338.447031230024146.352968769976
75785.1364.63317724615420.46682275385
76704.9486.38664439218218.513355607821
77245.4557.617394219456-312.217394219456
78285.6462.705854248112-177.105854248112
79218.8400.431432002451-181.631432002451
80706.1330.003359532417376.096640467583
81856.2435.975702424141420.224297575859
82456.6570.603295427711-114.003295427711
83606.8545.53275021231861.2672497876823
84527.3573.754659753437-46.4546597534367
85657.8568.89159103510388.9084089648967
86948.2606.752397078215341.447602921785
87486.6730.929935493442-244.329935493442
88238.9675.507574399983-436.607574399983
89289.4547.716444757507-258.316444757507
90969.5462.066353332924507.433646667076
91589.5618.274168730914-28.7741687309144
92189.7617.416083594395-427.716083594395
93639.8484.405333513077155.394666486923
949710.1526.87092021629183.2290797838
95969.93541.21657067186-2571.31657067186
96939.93039.37490104804-2099.47490104804
97859.72595.76125277685-1736.06125277685
98679.92192.51393172237-1512.61393172237
99879.91797.32799746341-917.427997463409
100329.81540.74675501591-1210.94675501591
101349.61153.19723550532-803.597235505315
10239.5853.895766611914-814.395766611914
103849.5520.796669051269328.703330948731
104449.6532.598279934586-82.9982799345859
105749.6421.511661118665328.088338881335
106249.7442.360307493709-192.660307493709
107649.8304.47094911205345.32905088795
108619.4336.081832042037283.318167957963
109939360.318719799598578.681280200402
110778.9492.260008170372286.639991829628






Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
111550.036543045553-1559.585579167652659.65866525876
112524.429557939392-1696.132283056482744.99139893526
113498.822572833231-1852.277722521722849.92286818818
114473.21558772707-2027.474586882312973.90576233645
115447.608602620909-2220.88233138273116.09953662452
116422.001617514748-2431.498490895243275.50172592474
117396.394632408587-2658.261008471443451.05027328861
118370.787647302426-2900.119143683153641.694438288
119345.180662196265-3156.077118234233846.43844262676
120319.573677090104-3425.217136420294064.3644906005
121293.966691983942-3706.708317881134294.64170184902
122268.359706877781-3999.806838760934536.52625251649

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
111 & 550.036543045553 & -1559.58557916765 & 2659.65866525876 \tabularnewline
112 & 524.429557939392 & -1696.13228305648 & 2744.99139893526 \tabularnewline
113 & 498.822572833231 & -1852.27772252172 & 2849.92286818818 \tabularnewline
114 & 473.21558772707 & -2027.47458688231 & 2973.90576233645 \tabularnewline
115 & 447.608602620909 & -2220.8823313827 & 3116.09953662452 \tabularnewline
116 & 422.001617514748 & -2431.49849089524 & 3275.50172592474 \tabularnewline
117 & 396.394632408587 & -2658.26100847144 & 3451.05027328861 \tabularnewline
118 & 370.787647302426 & -2900.11914368315 & 3641.694438288 \tabularnewline
119 & 345.180662196265 & -3156.07711823423 & 3846.43844262676 \tabularnewline
120 & 319.573677090104 & -3425.21713642029 & 4064.3644906005 \tabularnewline
121 & 293.966691983942 & -3706.70831788113 & 4294.64170184902 \tabularnewline
122 & 268.359706877781 & -3999.80683876093 & 4536.52625251649 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=122548&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]111[/C][C]550.036543045553[/C][C]-1559.58557916765[/C][C]2659.65866525876[/C][/ROW]
[ROW][C]112[/C][C]524.429557939392[/C][C]-1696.13228305648[/C][C]2744.99139893526[/C][/ROW]
[ROW][C]113[/C][C]498.822572833231[/C][C]-1852.27772252172[/C][C]2849.92286818818[/C][/ROW]
[ROW][C]114[/C][C]473.21558772707[/C][C]-2027.47458688231[/C][C]2973.90576233645[/C][/ROW]
[ROW][C]115[/C][C]447.608602620909[/C][C]-2220.8823313827[/C][C]3116.09953662452[/C][/ROW]
[ROW][C]116[/C][C]422.001617514748[/C][C]-2431.49849089524[/C][C]3275.50172592474[/C][/ROW]
[ROW][C]117[/C][C]396.394632408587[/C][C]-2658.26100847144[/C][C]3451.05027328861[/C][/ROW]
[ROW][C]118[/C][C]370.787647302426[/C][C]-2900.11914368315[/C][C]3641.694438288[/C][/ROW]
[ROW][C]119[/C][C]345.180662196265[/C][C]-3156.07711823423[/C][C]3846.43844262676[/C][/ROW]
[ROW][C]120[/C][C]319.573677090104[/C][C]-3425.21713642029[/C][C]4064.3644906005[/C][/ROW]
[ROW][C]121[/C][C]293.966691983942[/C][C]-3706.70831788113[/C][C]4294.64170184902[/C][/ROW]
[ROW][C]122[/C][C]268.359706877781[/C][C]-3999.80683876093[/C][C]4536.52625251649[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=122548&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=122548&T=3

As an alternative you can also use a QR Code:  
QR Code


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

Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
111550.036543045553-1559.585579167652659.65866525876
112524.429557939392-1696.132283056482744.99139893526
113498.822572833231-1852.277722521722849.92286818818
114473.21558772707-2027.474586882312973.90576233645
115447.608602620909-2220.88233138273116.09953662452
116422.001617514748-2431.498490895243275.50172592474
117396.394632408587-2658.261008471443451.05027328861
118370.787647302426-2900.119143683153641.694438288
119345.180662196265-3156.077118234233846.43844262676
120319.573677090104-3425.217136420294064.3644906005
121293.966691983942-3706.708317881134294.64170184902
122268.359706877781-3999.806838760934536.52625251649


Figures (Output of Computation)

Input Parameters & R Code

Parameters (Session):
par1 = 12 ; par2 = Double ; par3 = additive ;
Parameters (R input):
par1 = 12 ; par2 = Double ; par3 = additive ;
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')