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The Seatbelt Law - Q2

*The author of this computation has been verified*
R Software Module: rwasp_multipleregression.wasp (opens new window with default values)
Title produced by software: Multiple Regression
Date of computation: Sun, 23 Nov 2008 13:29:31 -0700
 
Cite this page as follows:
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL http://www.freestatistics.org/blog/date/2008/Nov/23/t1227472266pesanu0v6iig981.htm/, Retrieved Sun, 23 Nov 2008 20:31:16 +0000
 
BibTeX entries for LaTeX users:
@Manual{KEY,
    author = {{YOUR NAME}},
    publisher = {Office for Research Development and Education},
    title = {Statistical Computations at FreeStatistics.org, URL http://www.freestatistics.org/blog/date/2008/Nov/23/t1227472266pesanu0v6iig981.htm/},
    year = {2008},
}
@Manual{R,
    title = {R: A Language and Environment for Statistical Computing},
    author = {{R Development Core Team}},
    organization = {R Foundation for Statistical Computing},
    address = {Vienna, Austria},
    year = {2008},
    note = {{ISBN} 3-900051-07-0},
    url = {http://www.R-project.org},
}
 
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
 
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Original text written by user:
 
IsPrivate?
No (this computation is public)
 
User-defined keywords:
 
Dataseries X:
» Textbox « » Textfile « » CSV «
-183.9235445 -177.0726091 -228.6351091 -237.4476091 -127.7601091 -193.0101091 -220.6351091 -164.5101091 -268.3226091 -333.6976091 -34.26010911 -154.8851091 -97.74528053 101.1056549 2.543154874 -43.26934513 -163.5818451 -162.8318451 46.54315487 26.66815487 -107.1443451 42.48065487 76.91815487 196.2931549 201.4329835 12.28391886 -0.278581137 42.90891886 87.59641886 84.34641886 57.72141886 173.8464189 -185.9660811 47.65891886 89.09641886 -68.52858114 272.6112475 146.4621829 162.8996829 10.08718285 279.7746829 212.5246829 248.8996829 -41.97531715 -5.787817149 52.83718285 274.2746829 414.6496829 310.7895114 362.6404468 26.07794684 403.2654468 327.9529468 193.7029468 317.0779468 202.2029468 321.3904468 178.0154468 16.45294684 -68.17205316 -157.0322246 -76.18128917 -81.74378917 -134.5562892 77.13121083 199.8812108 105.2562108 198.3812108 262.5687108 196.1937108 11.63121083 -145.9937892 -166.8539606 -202.0030252 43.43447482 -113.3780252 -113.6905252 -155.9405252 -210.5655252 -124.4405252 -64.25302518 -298.6280252 -154.1905252 23.18447482 -249.6756966 118.1752388 -180.3872612 -79.19976119 -81.51226119 -246.7622612 -105.3872612 -319.2622612 -72.07476119 -90.44976119 -80.01226119 119.3627388 -53.49743261 -114.6464972 -155.2089972 -50.02149721 -196.3339972 -14.58399721 -82.20899721 17.91600279 -162.8964972 -132.2714972 -16.83399721 81.54100279 275.6808314 -32.46823322 17.96926678 27.15676678 -123.1557332 108.5942668 67.96926678 34.09426678 -13.71823322 -113.0932332 54.34426678 149.7192668 153.8590954 -28.28996923 238.1475308 50.33503077 8.022530771 -61.22746923 -140.8524692 -28.72746923 9.460030771 -121.9149692 41.52253077 115.8975308 27.03735936 -91.11170524 3.325794759 -29.48670524 -73.79920524 50.95079476 -86.67420524 -9.54920524 -66.36170524 73.26329476 -216.2992052 -128.9242052 -142.7843767 27.06655875 60.50405875 35.69155875 16.37905875 -64.87094125 115.5040587 -30.37094125 87.81655875 205.4415587 -64.12094125 -322.7459413 -139.6061127 35.24482274 -4.317677263 17.86982274 2.557322737 129.3073227 -16.31767726 164.8073227 21.99482274 138.6198227 87.05732274 51.43232274 -80.42784867 -105.1918797 5.245620328 68.43312033 -0.879379672 -105.1293797 -82.75437967 -132.6293797 102.5581203 23.18312033 -180.3793797 -267.0043797 30.13544892 23.98638432 90.42388432 31.61138432 81.29888432 25.04888432 -13.57611568 33.54888432 140.7363843 132.3613843 94.79888432 4.173884316
 
Output produced by software:

Enter (or paste) a matrix (table) containing all data (time) series. Every column represents a different variable and must be delimited by a space or Tab. Every row represents a period in time (or category) and must be delimited by hard returns. The easiest way to enter data is to copy and paste a block of spreadsheet cells. Please, do not use commas or spaces to seperate groups of digits!


Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time5 seconds
R Server'Gwilym Jenkins' @ 72.249.127.135


Multiple Linear Regression - Estimated Regression Equation
Errors[t] = + 1.20198233833674e-08 -6.85143675911739e-09M1[t] -4.27405754507521e-09M2[t] + 1.49088077674049e-09M3[t] -9.11914198313833e-09M4[t] -5.41725605677436e-10M5[t] -7.71440372504663e-09M6[t] -7.63695966622339e-09M7[t] -1.13095059100368e-08M8[t] -5.48219372198194e-09M9[t] -1.17798002830589e-08M10[t] -1.07734579173514e-09M11[t] -7.74003795362138e-11t + e[t]


Multiple Linear Regression - Ordinary Least Squares
VariableParameterS.D.T-STAT
H0: parameter = 0		2-tail p-value1-tail p-value
(Intercept)1.20198233833674e-0843.045604010.5
M1-6.85143675911739e-0953.781331010.5
M2-4.27405754507521e-0953.773653010.5
M31.49088077674049e-0953.766706010.5
M4-9.11914198313833e-0953.76049010.5
M5-5.41725605677436e-1053.755004010.5
M6-7.71440372504663e-0953.750249010.5
M7-7.63695966622339e-0953.746226010.5
M8-1.13095059100368e-0853.742934010.5
M9-5.48219372198194e-0953.740373010.5
M10-1.17798002830589e-0853.738544010.5
M11-1.07734579173514e-0953.737446010.5
t-7.74003795362138e-110.198293010.5


Multiple Linear Regression - Regression Statistics
Multiple R4.14091037033251e-11
R-squared1.71471386951273e-21
Adjusted R-squared-0.0670391061452513
F-TEST (value)2.55778152202316e-20
F-TEST (DF numerator)12
F-TEST (DF denominator)179
p-value1
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation151.991415338604
Sum Squared Residuals4135148.87025712


Multiple Linear Regression - Actuals, Interpolation, and Residuals
Time or IndexActualsInterpolation
Forecast		Residuals
Prediction Error
1-183.92354455.09101028001169e-09-183.923544505091
2-177.07260917.59069962441572e-09-177.072609107591
3-228.63510911.32775426209264e-08-228.635109113278
4-237.44760912.59072407970962e-09-237.447609102591
5-127.76010911.10911742012831e-08-127.760109111091
6-193.01010913.8411940295191e-09-193.010109103841
7-220.63510913.84076770387765e-09-220.635109103841
8-164.51010919.10915787244448e-11-164.510109100091
9-268.32260915.84100234846119e-09-268.322609105841
10-333.6976091-5.33702859684126e-10-333.697609099466
11-34.260109111.00907229239056e-08-34.2601091200907
12-154.88510911.10911457795737e-08-154.885109111091
13-97.745280534.16223144839023e-09-97.7452805341622
14101.10565496.66238975099986e-09101.105654893338
152.5431548741.23497256865335e-082.54315486165027
16-43.269345131.66220814890039e-09-43.2693451316622
17-163.58184511.01622674719692e-08-163.581845110162
18-162.83184512.91228730020521e-09-162.831845102912
1946.543154872.91220914050427e-0946.5431548670878
2026.66815487-8.37740543602195e-1026.6681548708377
21-107.14434514.91212404085672e-09-107.144345104912
2242.48065487-1.46278722468196e-0942.4806548714628
2376.918154879.16222120395105e-0976.9181548608378
24196.29315491.01622390502598e-08196.293154889838
25201.43298353.23345261676877e-09201.432983496767
2612.283918865.7335700631711e-0912.2839188542664
27-0.2785811371.14209173229796e-08-0.278581148420917
2842.908918867.33393790142145e-1042.9089188592666
2987.596418869.23343179692893e-0987.5964188507666
3084.346418861.98348004687432e-0984.3464188580165
3157.721418861.98343030888282e-0957.7214188580166
32173.8464189-1.76646608451847e-09173.846418901766
33-185.96608113.98330257667112e-09-185.966081103983
3447.65891886-2.39155895087606e-0947.6589188623916
3589.096418868.23338552891073e-0989.0964188517666
36-68.528581149.23336074265535e-09-68.5285811492334
37272.61124752.30460273087374e-09272.611247497695
38146.46218294.80477524433809e-09146.462182895195
39162.89968291.04921582533279e-08162.899682889508
4010.08718285-1.95420568616100e-1010.0871828501954
41279.77468298.30453927846975e-09279.774682891695
42212.52468291.05472963696229e-09212.524682898945
43248.89968291.05458752841514e-09248.899682898945
44-41.97531715-2.69536570840501e-09-41.9753171473046
45-5.7878171493.05449798787549e-09-5.7878171520545
4652.83718285-3.32039462591638e-0952.8371828533204
47274.27468297.30443616703269e-09274.274682892696
48414.64968298.30442559163203e-09414.649682891696
49310.78951141.37589495352586e-09310.789511398624
50362.64044683.87598220186192e-09362.640446796124
5126.077946849.56330481471923e-0926.0779468304367
52403.2654468-1.12441966848564e-09403.265446801124
53327.95294687.375774657703e-09327.952946792624
54193.70294681.25879751067259e-10193.702946799874
55317.07794681.25737642520107e-10317.077946799874
56202.2029468-3.62410901288968e-09202.202946803624
57321.39044682.12560280488105e-09321.390446797874
58178.0154468-4.24910240326426e-09178.015446804249
5916.452946846.37576036410792e-0916.4529468336242
60-68.172053167.37576044684829e-09-68.1720531673758
61-157.03222464.47045067630825e-10-157.032224600447
62-76.181289172.9471465268216e-09-76.1812891729471
63-81.743789178.63450111410202e-09-81.7437891786345
64-134.5562892-2.05304218070523e-09-134.556289197947
6577.131210836.44699582608155e-0977.131210823553
66199.8812108-8.02884869699483e-10199.881210800803
67105.2562108-8.02998556537204e-10105.256210800803
68198.3812108-4.55290205536585e-09198.381210804553
69262.56871081.19678134069545e-09262.568710798803
70196.1937108-5.17789544574043e-09196.193710805178
7111.631210835.44696199256123e-0911.6312108245530
72-145.99378926.44698161522683e-09-145.993789206447
73-166.8539606-4.81776396554778e-10-166.853960599518
74-202.00302522.01839611690957e-09-202.003025202018
7543.434474827.70570096619849e-0943.4344748122943
76-113.3780252-2.98180680147198e-09-113.378025197018
77-113.69052525.51820278360537e-09-113.690525205518
78-155.9405252-1.73173475559452e-09-155.940525198268
79-210.5655252-1.73176317730395e-09-210.565525198268
80-124.4405252-5.48173773040617e-09-124.440525194518
81-64.253025182.68059352492855e-10-64.253025180268
82-298.6280252-6.10685901847319e-09-298.628025193893
83-154.19052524.51822756986076e-09-154.190525204518
8423.184474825.51815304561387e-0923.1844748144818
85-249.6756966-1.41051259561209e-09-249.675696598589
86118.17523881.08957465272397e-09118.175238798910
87-180.38726126.77692924000439e-09-180.387261206777
88-79.19976119-3.91062826565758e-09-79.1997611860894
89-81.512261194.58939553027449e-09-81.5122611945894
90-246.7622612-2.66052779807069e-09-246.762261197339
91-105.3872612-2.66064148490841e-09-105.387261197339
92-319.2622612-6.41074393570307e-09-319.262261193589
93-72.07476119-6.60747900838032e-10-72.0747611893393
94-90.44976119-7.03558100667578e-09-90.4497611829644
95-80.012261193.58936347311101e-09-80.0122611935894
96119.36273884.58945237369335e-09119.362738795411
97-53.49743261-2.33934116522505e-09-53.4974326076607
98-114.64649721.60753188538365e-10-114.646497200161
99-155.20899725.84810777581879e-09-155.208997205848
100-50.02149721-4.83942130813375e-09-50.0214972051606
101-196.33399723.66063090950774e-09-196.333997203661
102-14.58399721-3.58938834210676e-09-14.5839972064106
103-82.20899721-3.58940610567515e-09-82.2089972064106
10417.91600279-7.33938776420473e-0917.9160027973394
105-162.8964972-1.58951252160477e-09-162.896497198410
106-132.2714972-7.96435983829724e-09-132.271497192036
107-16.833997212.66055621978012e-09-16.8339972126606
10881.541002793.66057406608888e-0981.5410027863394
109275.6808314-3.26821236740216e-09275.680831403268
110-32.46823322-7.68068275647238e-10-32.4682332192319
11117.969266784.91928986434687e-0917.9692667750807
11227.15676678-5.76825343046039e-0927.1567667857683
113-123.15573322.73178102361271e-09-123.155733202732
114108.5942668-4.51814230473246e-09108.594266804518
11567.96926678-4.51819914815133e-0967.9692667845182
11634.09426678-8.26818791210826e-0934.0942667882682
117-13.71823322-2.51833576214722e-09-13.7182332174817
118-113.0932332-8.89318130248284e-09-113.093233191107
11954.344266781.73177028273130e-0954.3442667782682
120149.71926682.73180944532214e-09149.719266797268
121153.8590954-4.19692014475004e-09153.859095404197
122-28.28996923-1.69686487083709e-09-28.2899692283031
123238.14753083.99049326915701e-09238.147530796010
12450.33503077-6.6970073930861e-0950.335030776697
1258.0225307711.80297909935234e-098.02253076919702
126-61.22746923-5.4469921906275e-09-61.227469224553
127-140.8524692-5.4469921906275e-09-140.852469194553
128-28.72746923-9.19699161272547e-09-28.727469220803
1299.460030771-3.44715012090546e-099.46003077444715
130-121.9149692-9.8219601341043e-09-121.914969190178
13141.522530778.02955923973059e-1041.522530769197
132115.89753081.80303061370068e-09115.897530798197
13327.03735936-5.12575937250404e-0927.0373593651258
134-91.11170524-2.62565436059958e-09-91.1117052373744
1353.3257947593.06167979857719e-093.32579475593832
136-29.48670524-7.62584306812641e-09-29.4867052323742
137-73.799205248.74180727805651e-10-73.7992052408742
13850.95079476-6.37579233853103e-0950.9507947663758
139-86.67420524-6.37584207652253e-09-86.6742052336242
140-9.54920524-1.01257846552016e-08-9.54920522987421
141-66.36170524-4.37594849245215e-09-66.361705235624
14273.26329476-1.07507815982899e-0873.2632947707508
143-216.2992052-1.25822907648399e-10-216.299205199874
144-128.92420528.74166516950936e-10-128.924205200874
145-142.7843767-6.05459149483067e-09-142.784376693945
14627.06655875-3.55446161393047e-0927.0665587535545
14760.504058752.13287165706788e-0960.5040587478671
14835.69155875-8.55463611060259e-0935.6915587585546
14916.37905875-5.46265255252365e-1116.3790587500546
150-64.87094125-7.30459248643456e-09-64.8709412426954
151115.5040587-7.30457827557984e-09115.504058707305
152-30.37094125-1.10546025666736e-08-30.3709412389454
15387.81655875-5.30476995663776e-0987.8165587553048
154205.4415587-1.16795320082019e-08205.441558711680
155-64.12094125-1.05465858268872e-09-64.1209412489453
156-322.7459413-5.47402123629581e-11-322.745941299945
157-139.6061127-6.98341295901628e-09-139.606112693017
15835.24482274-4.48326886726136e-0935.2448227444833
159-4.3176772631.20405907466647e-09-4.31767726420406
16017.86982274-9.48346112750187e-0917.8698227494835
1612.557322737-9.83428449785606e-102.55732273798343
162129.3073227-8.23334289634658e-09129.307322708233
163-16.31767726-8.23345303047063e-09-16.3176772517665
164164.8073227-1.19833316603035e-08164.807322711983
16521.99482274-6.23356655182761e-0921.9948227462336
166138.6198227-1.26083534723875e-08138.619822712608
16787.05732274-1.98346583601960e-0987.0573227419835
16851.43232274-9.83483516847627e-1051.4323227409835
169-80.42784867-7.91213494721887e-09-80.4278486620879
170-105.1918797-5.41210454230168e-09-105.191879694588
1715.2456203282.75261591298204e-105.24562032772474
17268.43312033-1.04122648281191e-0868.4331203404123
173-0.879379672-1.91222970791216e-09-0.87937967008777
174-105.1293797-9.16219278224162e-09-105.129379690838
175-82.75437967-9.1622638365152e-09-82.7543796608377
176-132.6293797-1.29121815461986e-08-132.629379687088
177102.5581203-7.16234183073539e-09102.558120307162
17823.18312033-1.35372246745646e-0823.1831203435372
179-180.3793797-2.91220203507692e-09-180.379379697088
180-267.0043797-1.91221261047758e-09-267.004379698088
18130.13544892-8.8409706222592e-0930.135448928841
18223.98638432-6.34088337392313e-0923.9863843263409
18390.42388432-6.5355720835214e-1090.4238843206536
18431.61138432-1.13410578705953e-0831.6113843313411
18581.29888432-2.8410482855179e-0981.298884322841
18625.04888432-1.00910426681367e-0825.0488843300910
187-13.57611568-1.00910586553482e-08-13.5761156699089
18833.54888432-1.38409887995294e-0833.548884333841
189140.7363843-8.09112066235684e-09140.736384308091
190132.3613843-1.44659679790493e-08132.361384314466
19194.79888432-3.84103771011723e-0994.798884323841
1924.173884316-2.84109891168782e-094.1738843188411


Goldfeld-Quandt test for Heteroskedasticity
p-valuesAlternative Hypothesis
breakpoint indexgreater2-sidedless
160.07562956871655140.1512591374331030.924370431283449
170.1766804252400530.3533608504801060.823319574759947
180.1278610319095030.2557220638190050.872138968090497
190.1002714917989260.2005429835978520.899728508201074
200.05436109081530930.1087221816306190.94563890918469
210.02771862899237480.05543725798474970.972281371007625
220.04821332007902040.09642664015804080.95178667992098
230.02879407494231630.05758814988463260.971205925057684
240.03250188084066750.06500376168133490.967498119159333
250.02021281769801630.04042563539603250.979787182301984
260.04401830745844580.08803661491689160.955981692541554
270.03938271217601780.07876542435203560.960617287823982
280.02509785994672910.05019571989345830.97490214005327
290.01482321402687690.02964642805375380.985176785973123
300.008764879854717920.01752975970943580.991235120145282
310.005982331992922170.01196466398584430.994017668007078
320.003438268613663330.006876537227326650.996561731386337
330.008208743913590.016417487827180.99179125608641
340.004822430376892900.009644860753785810.995177569623107
350.004506564527746170.009013129055492350.995493435472254
360.01548280617976570.03096561235953150.984517193820234
370.01184517054596120.02369034109192250.988154829454039
380.008653989775100560.01730797955020110.9913460102249
390.005539260298087930.01107852059617590.994460739701912
400.005570934604076180.01114186920815240.994429065395924
410.005502402280063360.01100480456012670.994497597719937
420.004076424065677060.008152848131354110.995923575934323
430.003036673290749470.006073346581498950.99696332670925
440.01117247689497470.02234495378994950.988827523105025
450.007806292569370020.01561258513874000.99219370743063
460.005880826380426170.01176165276085230.994119173619574
470.004748195000908760.009496390001817520.99525180499909
480.0111886194302010.0223772388604020.9888113805698
490.01085980143274580.02171960286549170.989140198567254
500.01289621334732700.02579242669465390.987103786652673
510.02367357754163170.04734715508326350.976326422458368
520.04759827613045670.09519655226091340.952401723869543
530.05510759283448350.1102151856689670.944892407165516
540.05246091332069280.1049218266413860.947539086679307
550.06411797952106540.1282359590421310.935882020478935
560.06554699050219270.1310939810043850.934453009497807
570.1108023914647440.2216047829294880.889197608535256
580.1079825114255370.2159650228510740.892017488574463
590.2795613362590020.5591226725180040.720438663740998
600.5699883940081150.860023211983770.430011605991885
610.8991846257442970.2016307485114070.100815374255703
620.9610549718609530.07789005627809320.0389450281390466
630.974381243445870.05123751310825850.0256187565541293
640.9888136075485260.02237278490294770.0111863924514739
650.9904829710181430.01903405796371490.00951702898185745
660.9920930578066730.01581388438665460.00790694219332732
670.9936258505889850.01274829882203000.00637414941101498
680.9953289697913660.009342060417268620.00467103020863431
690.9975932168677590.004813566264482540.00240678313224127
700.998374999278680.003250001442639580.00162500072131979
710.9988917613663380.002216477267323420.00110823863366171
720.9995533817613560.0008932364772878640.000446618238643932
730.999854584120790.0002908317584182960.000145415879209148
740.9999607165157487.85669685030423e-053.92834842515211e-05
750.9999489410676750.0001021178646507655.10589323253824e-05
760.9999567585040558.64829918910023e-054.32414959455012e-05
770.9999712152897455.75694205099349e-052.87847102549674e-05
780.9999818985526983.62028946034518e-051.81014473017259e-05
790.9999931364928281.37270143442394e-056.8635071721197e-06
800.999993897972241.22040555182271e-056.10202775911353e-06
810.999991492598871.70148022585063e-058.50740112925317e-06
820.9999983328833993.334233202915e-061.6671166014575e-06
830.9999985679712872.86405742573756e-061.43202871286878e-06
840.999997949085194.10182962186048e-062.05091481093024e-06
850.9999992188601621.56227967700308e-067.81139838501539e-07
860.9999993063715531.38725689467906e-066.93628447339532e-07
870.9999994580491081.08390178500228e-065.4195089250114e-07
880.9999991736738261.65265234817944e-068.26326174089722e-07
890.9999988297345652.34053087099351e-061.17026543549675e-06
900.9999995056699899.88660022417766e-074.94330011208883e-07
910.999999313048291.37390341762802e-066.86951708814009e-07
920.9999999032204281.93559143321176e-079.67795716605878e-08
930.9999998416455983.16708803734875e-071.58354401867438e-07
940.999999767596154.64807701413864e-072.32403850706932e-07
950.9999996288355577.42328886288844e-073.71164443144422e-07
960.9999996712819336.57436133494446e-073.28718066747223e-07
970.9999994465682671.10686346549132e-065.53431732745662e-07
980.9999992193670531.56126589451161e-067.80632947255804e-07
990.9999993949182561.21016348873632e-066.05081744368161e-07
1000.999999018283171.9634336600162e-069.817168300081e-07
1010.9999992811173021.43776539707283e-067.18882698536415e-07
1020.9999987421648442.51567031219336e-061.25783515609668e-06
1030.9999980302787863.93944242880997e-061.96972121440499e-06
1040.9999966524417026.69511659539513e-063.34755829769757e-06
1050.999997578502624.84299475944801e-062.42149737972401e-06
1060.9999979677631074.06447378606593e-062.03223689303296e-06
1070.999996478814977.04237006082137e-063.52118503041069e-06
1080.9999958102918138.37941637358365e-064.18970818679182e-06
1090.9999993726489331.25470213372493e-066.27351066862464e-07
1100.9999988796010372.24079792688001e-061.12039896344001e-06
1110.9999981439875923.71202481511761e-061.85601240755880e-06
1120.9999967995768126.40084637563836e-063.20042318781918e-06
1130.9999962909302467.41813950713576e-063.70906975356788e-06
1140.9999955487964968.90240700882616e-064.45120350441308e-06
1150.999994212153761.15756924820454e-055.78784624102271e-06
1160.9999905237662671.89524674671238e-059.47623373356188e-06
1170.9999847634555283.04730889438192e-051.52365444719096e-05
1180.9999873821130512.52357738980873e-051.26178869490437e-05
1190.9999825080522163.49838955684918e-051.74919477842459e-05
1200.9999931734731421.36530537160194e-056.82652685800971e-06
1210.999997090875235.8182495412991e-062.90912477064955e-06
1220.9999948563219071.02873561867487e-055.14367809337434e-06
1230.9999984908106763.01837864794554e-061.50918932397277e-06
1240.999997527817774.94436446054187e-062.47218223027094e-06
1250.9999956758766678.64824666651431e-064.32412333325716e-06
1260.9999925447557081.49104885846042e-057.45524429230208e-06
1270.999990337334721.93253305589343e-059.66266527946715e-06
1280.9999828946392533.42107214940574e-051.71053607470287e-05
1290.999970392409395.92151812181914e-052.96075906090957e-05
1300.9999833707215883.32585568247414e-051.66292784123707e-05
1310.999979882262674.02354746603295e-052.01177373301648e-05
1320.9999966100150916.77996981731139e-063.38998490865569e-06
1330.9999968549915526.29001689587447e-063.14500844793723e-06
1340.999994599550761.08008984803434e-055.40044924017172e-06
1350.9999898829022862.02341954271341e-051.01170977135670e-05
1360.9999816849609143.66300781721317e-051.83150390860658e-05
1370.9999703507800595.92984398817997e-052.96492199408999e-05
1380.9999589144464458.21711071100684e-054.10855535550342e-05
1390.9999323814789670.0001352370420664726.76185210332358e-05
1400.9998814997555660.0002370004888678970.000118500244433948
1410.9998568398748060.0002863202503887820.000143160125194391
1420.9997645266687440.0004709466625113590.000235473331255679
1430.9998477365403010.0003045269193975490.000152263459698775
1440.9997586936136060.0004826127727870780.000241306386393539
1450.9996442931203580.0007114137592830830.000355706879641541
1460.9994335250088050.001132949982390800.000566474991195399
1470.999100121155520.001799757688958960.00089987884447948
1480.998507002446570.002985995106858920.00149299755342946
1490.9975410887265410.004917822546917610.00245891127345880
1500.9963275045182540.007344990963492870.00367249548174643
1510.9969674268580270.006065146283946290.00303257314197314
1520.995105197892370.009789604215258930.00489480210762947
1530.992506974778490.01498605044301860.0074930252215093
1540.9929455233995490.01410895320090220.00705447660045108
1550.988926486734090.02214702653182100.0110735132659105
1560.9948858396444670.01022832071106640.00511416035553322
1570.993392642283990.01321471543202140.0066073577160107
1580.9904483443826650.01910331123466930.00955165561733466
1590.9849345077803470.03013098443930630.0150654922196531
1600.976267121294660.04746575741068040.0237328787053402
1610.963679902954220.0726401940915580.036320097045779
1620.9671646268024150.06567074639516980.0328353731975849
1630.9512046480912430.09759070381751410.0487953519087571
1640.9761303884229270.04773922315414570.0238696115770728
1650.9622925455081260.07541490898374870.0377074544918743
1660.9540456452320670.09190870953586630.0459543547679331
1670.9713261613390960.05734767732180740.0286738386609037
1680.9991857786336670.001628442732666860.00081422136633343
1690.9978843972447260.004231205510548570.00211560275527429
1700.9947644934638460.01047101307230830.00523550653615414
1710.9880738526936450.02385229461270970.0119261473063549
1720.9920016496018060.01599670079638790.00799835039819396
1730.9828661580120910.03426768397581730.0171338419879086
1740.9577128890827750.08457422183444990.0422871109172250
1750.9276919109099010.1446161781801980.0723080890900988
1760.8311754360415010.3376491279169980.168824563958499


Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity
Description# significant tests% significant testsOK/NOK
1% type I error level930.577639751552795NOK
5% type I error level1280.795031055900621NOK
10% type I error level1450.900621118012422NOK
 
Charts produced by software:
http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Nov/23/t1227472266pesanu0v6iig981/107b9g1227472165.png (open in new window)
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http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Nov/23/t1227472266pesanu0v6iig981/5jf331227472164.ps (open in new window)


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http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Nov/23/t1227472266pesanu0v6iig981/6ph741227472164.ps (open in new window)


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http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Nov/23/t1227472266pesanu0v6iig981/7ci0k1227472165.ps (open in new window)


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http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Nov/23/t1227472266pesanu0v6iig981/89x9f1227472165.ps (open in new window)


http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Nov/23/t1227472266pesanu0v6iig981/9q2vd1227472165.png (open in new window)
http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Nov/23/t1227472266pesanu0v6iig981/9q2vd1227472165.ps (open in new window)


 
Parameters (Session):
par1 = 1 ; par2 = Include Monthly Dummies ; par3 = Linear Trend ;
 
Parameters (R input):
par1 = 1 ; par2 = Include Monthly Dummies ; par3 = Linear Trend ;
 
R code (references can be found in the software module):
library(lattice)
library(lmtest)
n25 <- 25 #minimum number of obs. for Goldfeld-Quandt test
par1 <- as.numeric(par1)
x <- t(y)
k <- length(x[1,])
n <- length(x[,1])
x1 <- cbind(x[,par1], x[,1:k!=par1])
mycolnames <- c(colnames(x)[par1], colnames(x)[1:k!=par1])
colnames(x1) <- mycolnames #colnames(x)[par1]
x <- x1
if (par3 == 'First Differences'){
x2 <- array(0, dim=c(n-1,k), dimnames=list(1:(n-1), paste('(1-B)',colnames(x),sep='')))
for (i in 1:n-1) {
for (j in 1:k) {
x2[i,j] <- x[i+1,j] - x[i,j]
}
}
x <- x2
}
if (par2 == 'Include Monthly Dummies'){
x2 <- array(0, dim=c(n,11), dimnames=list(1:n, paste('M', seq(1:11), sep ='')))
for (i in 1:11){
x2[seq(i,n,12),i] <- 1
}
x <- cbind(x, x2)
}
if (par2 == 'Include Quarterly Dummies'){
x2 <- array(0, dim=c(n,3), dimnames=list(1:n, paste('Q', seq(1:3), sep ='')))
for (i in 1:3){
x2[seq(i,n,4),i] <- 1
}
x <- cbind(x, x2)
}
k <- length(x[1,])
if (par3 == 'Linear Trend'){
x <- cbind(x, c(1:n))
colnames(x)[k+1] <- 't'
}
x
k <- length(x[1,])
df <- as.data.frame(x)
(mylm <- lm(df))
(mysum <- summary(mylm))
if (n > n25) {
kp3 <- k + 3
nmkm3 <- n - k - 3
gqarr <- array(NA, dim=c(nmkm3-kp3+1,3))
numgqtests <- 0
numsignificant1 <- 0
numsignificant5 <- 0
numsignificant10 <- 0
for (mypoint in kp3:nmkm3) {
j <- 0
numgqtests <- numgqtests + 1
for (myalt in c('greater', 'two.sided', 'less')) {
j <- j + 1
gqarr[mypoint-kp3+1,j] <- gqtest(mylm, point=mypoint, alternative=myalt)$p.value
}
if (gqarr[mypoint-kp3+1,2] < 0.01) numsignificant1 <- numsignificant1 + 1
if (gqarr[mypoint-kp3+1,2] < 0.05) numsignificant5 <- numsignificant5 + 1
if (gqarr[mypoint-kp3+1,2] < 0.10) numsignificant10 <- numsignificant10 + 1
}
gqarr
}
bitmap(file='test0.png')
plot(x[,1], type='l', main='Actuals and Interpolation', ylab='value of Actuals and Interpolation (dots)', xlab='time or index')
points(x[,1]-mysum$resid)
grid()
dev.off()
bitmap(file='test1.png')
plot(mysum$resid, type='b', pch=19, main='Residuals', ylab='value of Residuals', xlab='time or index')
grid()
dev.off()
bitmap(file='test2.png')
hist(mysum$resid, main='Residual Histogram', xlab='values of Residuals')
grid()
dev.off()
bitmap(file='test3.png')
densityplot(~mysum$resid,col='black',main='Residual Density Plot', xlab='values of Residuals')
dev.off()
bitmap(file='test4.png')
qqnorm(mysum$resid, main='Residual Normal Q-Q Plot')
qqline(mysum$resid)
grid()
dev.off()
(myerror <- as.ts(mysum$resid))
bitmap(file='test5.png')
dum <- cbind(lag(myerror,k=1),myerror)
dum
dum1 <- dum[2:length(myerror),]
dum1
z <- as.data.frame(dum1)
z
plot(z,main=paste('Residual Lag plot, lowess, and regression line'), ylab='values of Residuals', xlab='lagged values of Residuals')
lines(lowess(z))
abline(lm(z))
grid()
dev.off()
bitmap(file='test6.png')
acf(mysum$resid, lag.max=length(mysum$resid)/2, main='Residual Autocorrelation Function')
grid()
dev.off()
bitmap(file='test7.png')
pacf(mysum$resid, lag.max=length(mysum$resid)/2, main='Residual Partial Autocorrelation Function')
grid()
dev.off()
bitmap(file='test8.png')
opar <- par(mfrow = c(2,2), oma = c(0, 0, 1.1, 0))
plot(mylm, las = 1, sub='Residual Diagnostics')
par(opar)
dev.off()
if (n > n25) {
bitmap(file='test9.png')
plot(kp3:nmkm3,gqarr[,2], main='Goldfeld-Quandt test',ylab='2-sided p-value',xlab='breakpoint')
grid()
dev.off()
}
load(file='createtable')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a, 'Multiple Linear Regression - Estimated Regression Equation', 1, TRUE)
a<-table.row.end(a)
myeq <- colnames(x)[1]
myeq <- paste(myeq, '[t] = ', sep='')
for (i in 1:k){
if (mysum$coefficients[i,1] > 0) myeq <- paste(myeq, '+', '')
myeq <- paste(myeq, mysum$coefficients[i,1], sep=' ')
if (rownames(mysum$coefficients)[i] != '(Intercept)') {
myeq <- paste(myeq, rownames(mysum$coefficients)[i], sep='')
if (rownames(mysum$coefficients)[i] != 't') myeq <- paste(myeq, '[t]', sep='')
}
}
myeq <- paste(myeq, ' + e[t]')
a<-table.row.start(a)
a<-table.element(a, myeq)
a<-table.row.end(a)
a<-table.end(a)
table.save(a,file='mytable1.tab')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,hyperlink('http://www.xycoon.com/ols1.htm','Multiple Linear Regression - Ordinary Least Squares',''), 6, TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'Variable',header=TRUE)
a<-table.element(a,'Parameter',header=TRUE)
a<-table.element(a,'S.D.',header=TRUE)
a<-table.element(a,'T-STAT<br />H0: parameter = 0',header=TRUE)
a<-table.element(a,'2-tail p-value',header=TRUE)
a<-table.element(a,'1-tail p-value',header=TRUE)
a<-table.row.end(a)
for (i in 1:k){
a<-table.row.start(a)
a<-table.element(a,rownames(mysum$coefficients)[i],header=TRUE)
a<-table.element(a,mysum$coefficients[i,1])
a<-table.element(a, round(mysum$coefficients[i,2],6))
a<-table.element(a, round(mysum$coefficients[i,3],4))
a<-table.element(a, round(mysum$coefficients[i,4],6))
a<-table.element(a, round(mysum$coefficients[i,4]/2,6))
a<-table.row.end(a)
}
a<-table.end(a)
table.save(a,file='mytable2.tab')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a, 'Multiple Linear Regression - Regression Statistics', 2, TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a, 'Multiple R',1,TRUE)
a<-table.element(a, sqrt(mysum$r.squared))
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a, 'R-squared',1,TRUE)
a<-table.element(a, mysum$r.squared)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a, 'Adjusted R-squared',1,TRUE)
a<-table.element(a, mysum$adj.r.squared)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a, 'F-TEST (value)',1,TRUE)
a<-table.element(a, mysum$fstatistic[1])
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a, 'F-TEST (DF numerator)',1,TRUE)
a<-table.element(a, mysum$fstatistic[2])
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a, 'F-TEST (DF denominator)',1,TRUE)
a<-table.element(a, mysum$fstatistic[3])
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a, 'p-value',1,TRUE)
a<-table.element(a, 1-pf(mysum$fstatistic[1],mysum$fstatistic[2],mysum$fstatistic[3]))
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a, 'Multiple Linear Regression - Residual Statistics', 2, TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a, 'Residual Standard Deviation',1,TRUE)
a<-table.element(a, mysum$sigma)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a, 'Sum Squared Residuals',1,TRUE)
a<-table.element(a, sum(myerror*myerror))
a<-table.row.end(a)
a<-table.end(a)
table.save(a,file='mytable3.tab')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a, 'Multiple Linear Regression - Actuals, Interpolation, and Residuals', 4, TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a, 'Time or Index', 1, TRUE)
a<-table.element(a, 'Actuals', 1, TRUE)
a<-table.element(a, 'Interpolation<br />Forecast', 1, TRUE)
a<-table.element(a, 'Residuals<br />Prediction Error', 1, TRUE)
a<-table.row.end(a)
for (i in 1:n) {
a<-table.row.start(a)
a<-table.element(a,i, 1, TRUE)
a<-table.element(a,x[i])
a<-table.element(a,x[i]-mysum$resid[i])
a<-table.element(a,mysum$resid[i])
a<-table.row.end(a)
}
a<-table.end(a)
table.save(a,file='mytable4.tab')
if (n > n25) {
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Goldfeld-Quandt test for Heteroskedasticity',4,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'p-values',header=TRUE)
a<-table.element(a,'Alternative Hypothesis',3,header=TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'breakpoint index',header=TRUE)
a<-table.element(a,'greater',header=TRUE)
a<-table.element(a,'2-sided',header=TRUE)
a<-table.element(a,'less',header=TRUE)
a<-table.row.end(a)
for (mypoint in kp3:nmkm3) {
a<-table.row.start(a)
a<-table.element(a,mypoint,header=TRUE)
a<-table.element(a,gqarr[mypoint-kp3+1,1])
a<-table.element(a,gqarr[mypoint-kp3+1,2])
a<-table.element(a,gqarr[mypoint-kp3+1,3])
a<-table.row.end(a)
}
a<-table.end(a)
table.save(a,file='mytable5.tab')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity',4,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'Description',header=TRUE)
a<-table.element(a,'# significant tests',header=TRUE)
a<-table.element(a,'% significant tests',header=TRUE)
a<-table.element(a,'OK/NOK',header=TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'1% type I error level',header=TRUE)
a<-table.element(a,numsignificant1)
a<-table.element(a,numsignificant1/numgqtests)
if (numsignificant1/numgqtests < 0.01) dum <- 'OK' else dum <- 'NOK'
a<-table.element(a,dum)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'5% type I error level',header=TRUE)
a<-table.element(a,numsignificant5)
a<-table.element(a,numsignificant5/numgqtests)
if (numsignificant5/numgqtests < 0.05) dum <- 'OK' else dum <- 'NOK'
a<-table.element(a,dum)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'10% type I error level',header=TRUE)
a<-table.element(a,numsignificant10)
a<-table.element(a,numsignificant10/numgqtests)
if (numsignificant10/numgqtests < 0.1) dum <- 'OK' else dum <- 'NOK'
a<-table.element(a,dum)
a<-table.row.end(a)
a<-table.end(a)
table.save(a,file='mytable6.tab')
}
 




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Software written by Ed van Stee & Patrick Wessa


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