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Q2: the Seatbelt Law & Tutorial

*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 04:29:41 -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/t1227439859b1p1u1d3y34prsa.htm/, Retrieved Sun, 23 Nov 2008 11:30:59 +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/t1227439859b1p1u1d3y34prsa.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 0 -177.0726091 0 -228.6351091 0 -237.4476091 0 -127.7601091 0 -193.0101091 0 -220.6351091 0 -164.5101091 0 -268.3226091 0 -333.6976091 0 -34.26010911 0 -154.8851091 0 -97.74528053 0 101.1056549 0 2.543154874 0 -43.26934513 0 -163.5818451 0 -162.8318451 0 46.54315487 0 26.66815487 0 -107.1443451 0 42.48065487 0 76.91815487 0 196.2931549 0 201.4329835 0 12.28391886 0 -0.278581137 0 42.90891886 0 87.59641886 0 84.34641886 0 57.72141886 0 173.8464189 0 -185.9660811 0 47.65891886 0 89.09641886 0 -68.52858114 0 272.6112475 0 146.4621829 0 162.8996829 0 10.08718285 0 279.7746829 0 212.5246829 0 248.8996829 0 -41.97531715 0 -5.787817149 0 52.83718285 0 274.2746829 0 414.6496829 0 310.7895114 0 362.6404468 0 26.07794684 0 403.2654468 0 327.9529468 0 193.7029468 0 317.0779468 0 202.2029468 0 321.3904468 0 178.0154468 0 16.45294684 0 -68.17205316 0 -157.0322246 0 -76.18128917 0 -81.74378917 0 -134.5562892 0 77.13121083 0 199.8812108 0 105.2562108 0 198.3812108 0 262.5687108 0 196.1937108 0 11.63121083 0 -145.9937892 0 -166.8539606 0 -202.0030252 0 43.43447482 0 -113.3780252 0 -113.6905252 0 -155.9405252 0 -210.5655252 0 -124.4405252 0 -64.25302518 0 -298.6280252 0 -154.1905252 0 23.18447482 0 -249.6756966 0 118.1752388 0 -180.3872612 0 -79.19976119 0 -81.51226119 0 -246.7622612 0 -105.3872612 0 -319.2622612 0 -72.07476119 0 -90.44976119 0 -80.01226119 0 119.3627388 0 -53.49743261 0 -114.6464972 0 -155.2089972 0 -50.02149721 0 -196.3339972 0 -14.58399721 0 -82.20899721 0 17.91600279 0 -162.8964972 0 -132.2714972 0 -16.83399721 0 81.54100279 0 275.6808314 0 -32.46823322 0 17.96926678 0 27.15676678 0 -123.1557332 0 108.5942668 0 67.96926678 0 34.09426678 0 -13.71823322 0 -113.0932332 0 54.34426678 0 149.7192668 0 153.8590954 0 -28.28996923 0 238.1475308 0 50.33503077 0 8.022530771 0 -61.22746923 0 -140.8524692 0 -28.72746923 0 9.460030771 0 -121.9149692 0 41.52253077 0 115.8975308 0 27.03735936 0 -91.11170524 0 3.325794759 0 -29.48670524 0 -73.79920524 0 50.95079476 0 -86.67420524 0 -9.54920524 0 -66.36170524 0 73.26329476 0 -216.2992052 0 -128.9242052 0 -142.7843767 0 27.06655875 0 60.50405875 0 35.69155875 0 16.37905875 0 -64.87094125 0 115.5040587 0 -30.37094125 0 87.81655875 0 205.4415587 0 -64.12094125 0 -322.7459413 0 -139.6061127 0 35.24482274 0 -4.317677263 0 17.86982274 0 2.557322737 0 129.3073227 0 -16.31767726 0 164.8073227 0 21.99482274 0 138.6198227 0 87.05732274 0 51.43232274 0 -80.42784867 0 -105.1918797 1 5.245620328 1 68.43312033 1 -0.879379672 1 -105.1293797 1 -82.75437967 1 -132.6293797 1 102.5581203 1 23.18312033 1 -180.3793797 1 -267.0043797 1 30.13544892 1 23.98638432 1 90.42388432 1 31.61138432 1 81.29888432 1 25.04888432 1 -13.57611568 1 33.54888432 1 140.7363843 1 132.3613843 1 94.79888432 1 4.173884316 1
 
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 time10 seconds
R Server'Herman Ole Andreas Wold' @ 193.190.124.10:1001


Multiple Linear Regression - Estimated Regression Equation
P-value[t] = + 1.21653950577152e-08 + 6.88756950871496e-10Law[t] -6.8333017401161e-09M1[t] -4.29667373082038e-09M2[t] + 1.47050293456406e-09M3[t] -9.13730976906158e-09M4[t] -5.57645836433235e-10M5[t] -7.72799154627015e-09M6[t] -7.64830459275601e-09M7[t] -1.13186308858503e-08M8[t] -5.48896305955923e-09M9[t] -1.17842930906774e-08M10[t] -1.07959395723505e-09M11[t] -7.96719688530047e-11t + e[t]


Multiple Linear Regression - Ordinary Least Squares
VariableParameterS.D.T-STAT
H0: parameter = 0		2-tail p-value1-tail p-value
(Intercept)1.21653950577152e-0844.029939010.5
Law6.88756950871496e-1041.037226010.5
M1-6.8333017401161e-0953.942919010.5
M2-4.29667373082038e-0953.941479010.5
M31.47050293456406e-0953.931287010.5
M4-9.13730976906158e-0953.922166010.5
M5-5.57645836433235e-1053.914117010.5
M6-7.72799154627015e-0953.907141010.5
M7-7.64830459275601e-0953.901237010.5
M8-1.13186308858503e-0853.896405010.5
M9-5.48896305955923e-0953.892648010.5
M10-1.17842930906774e-0853.889963010.5
M11-1.07959395723505e-0953.888353010.5
t-7.96719688530047e-110.240551010.5


Multiple Linear Regression - Regression Statistics
Multiple R4.14282620138605e-11
R-squared1.71630089348908e-21
Adjusted R-squared-0.0730337078651686
F-TEST (value)2.35001199262351e-20
F-TEST (DF numerator)13
F-TEST (DF denominator)178
p-value1
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation152.417759557116
Sum Squared Residuals4135148.87025712


Multiple Linear Regression - Actuals, Interpolation, and Residuals
Time or IndexActualsInterpolation
Forecast		Residuals
Prediction Error
1-183.92354455.25250243299524e-09-183.923544505252
2-177.07260917.70947394812538e-09-177.072609107709
3-228.63510911.33968285354058e-08-228.635109113397
4-237.44760912.70938471658155e-09-237.447609102709
5-127.76010911.12092948256759e-08-127.760109111209
6-193.01010913.95934307562129e-09-193.010109103959
7-220.63510913.95937149733072e-09-220.635109103959
8-164.51010912.09439576792647e-10-164.510109100209
9-268.32260915.95940718994825e-09-268.322609105959
10-333.6976091-4.1575276554795e-10-333.697609099584
11-34.260109111.02093622444954e-08-34.2601091202094
12-154.88510911.12093516690948e-08-154.885109111209
13-97.745280534.29636770604702e-09-97.7452805342964
14101.10565496.75331079946773e-09101.105654893247
152.5431548741.24408501278594e-082.54315486155915
16-43.269345131.75334236018898e-09-43.2693451317533
17-163.58184511.02534443158220e-08-163.581845110253
18-162.83184513.00332203551079e-09-162.831845103003
1946.543154873.00332203551079e-0946.5431548669967
2026.66815487-7.46670281159822e-1026.6681548707467
21-107.14434515.00334351727361e-09-107.144345105003
2242.48065487-1.37168854053016e-0942.4806548713717
2376.918154879.2533269935302e-0976.9181548607467
24196.29315491.02533590506937e-08196.293154889747
25201.43298353.34028982251766e-09201.432983496660
2612.283918865.79725423222044e-0912.2839188542027
27-0.2785811371.14847887866532e-08-0.278581148484789
2842.908918867.97307109223766e-1042.9089188592027
2987.596418869.29728116716433e-0987.5964188507027
3084.346418862.04724415198143e-0984.3464188579528
3157.721418862.04725125740879e-0957.7214188579527
32173.8464189-1.70268776855664e-09173.846418901703
33-185.96608114.04730826630839e-09-185.966081104047
3447.65891886-2.32772379149537e-0947.6589188623277
3589.096418868.297291742565e-0989.0964188517027
36-68.528581149.29719590203604e-09-68.5285811492972
37272.61124752.38418351727887e-09272.611247497616
38146.46218294.84118345411844e-09146.462182895159
39162.89968291.05286801499460e-08162.899682889471
4010.08718285-1.58797419658185e-1010.0871828501588
41279.77468298.3411464402161e-09279.774682891659
42212.52468291.0911946901615e-09212.524682898909
43248.89968291.09110942503321e-09248.899682898909
44-41.97531715-2.65878696836808e-09-41.9753171473412
45-5.7878171493.09120373742644e-09-5.7878171520912
4652.83718285-3.28380167502473e-0952.8371828532838
47274.27468297.34121385903563e-09274.274682892659
48414.64968298.34120328363497e-09414.649682891659
49310.78951141.42802036862122e-09310.789511398572
50362.64044683.88530452255509e-09362.640446796115
5126.077946849.5726626625492e-0926.0779468304273
52403.2654468-1.11492681753589e-09403.265446801115
53327.95294687.38509697839618e-09327.952946792615
54193.70294681.35173650051001e-10193.702946799865
55317.07794681.35003119794419e-10317.077946799865
56202.2029468-3.61484353561536e-09202.202946803615
57321.39044682.13498196899309e-09321.390446797865
58178.0154468-4.23986534769938e-09178.01544680424
5916.452946846.38513952821995e-0916.4529468336149
60-68.172053167.38506855668675e-09-68.1720531673851
61-157.03222464.72113015348441e-10-157.032224600472
62-76.181289172.92907031962386e-09-76.181289172929
63-81.743789178.61655280459672e-09-81.7437891786166
64-134.5562892-2.07086259251810e-09-134.556289197929
6577.131210836.42910435999511e-0977.1312108235709
66199.8812108-8.20904233478359e-10199.881210800821
67105.2562108-8.20904233478359e-10105.256210800821
68198.3812108-4.57092141914472e-09198.381210804571
69262.56871081.17893250717316e-09262.568710798821
70196.1937108-5.19585796610045e-09196.193710805196
7111.631210835.42908651368634e-0911.6312108245709
72-145.99378926.42901909486682e-09-145.993789206429
73-166.8539606-4.83964868180919e-10-166.853960599516
74-202.00302521.97292138182092e-09-202.003025201973
7543.434474827.66054597534094e-0943.4344748123395
76-113.3780252-3.02692626519274e-09-113.378025196973
77-113.69052525.47304068732046e-09-113.690525205473
78-155.9405252-1.77703896042658e-09-155.940525198223
79-210.5655252-1.77689685187943e-09-210.565525198223
80-124.4405252-5.52695667010994e-09-124.440525194473
81-64.253025182.23010943045665e-10-64.253025180223
82-298.6280252-6.15204953646753e-09-298.628025193848
83-154.19052524.47300863015698e-09-154.190525204473
8423.184474825.4729341059101e-0923.1844748145271
85-249.6756966-1.44015643854800e-09-249.67569659856
86118.17523881.01691455256514e-09118.175238798983
87-180.38726126.704397037538e-09-180.387261206704
88-79.19976119-3.98303257043153e-09-79.199761186017
89-81.512261194.51693438208167e-09-81.512261194517
90-246.7622612-2.73303157882765e-09-246.762261197267
91-105.3872612-2.73304578968236e-09-105.387261197267
92-319.2622612-6.48316245133174e-09-319.262261193517
93-72.07476119-7.3305272962898e-10-72.074761189267
94-90.44976119-7.10807057657803e-09-90.449761182892
95-80.012261193.51694495748234e-09-80.012261193517
96119.36273884.51687753866281e-09119.362738795483
97-53.49743261-2.39605668639342e-09-53.4974326076039
98-114.64649726.08082473263494e-11-114.646497200061
99-155.20899725.7483759974275e-09-155.208997205748
100-50.02149721-4.93908913767882e-09-50.0214972050609
101-196.33399723.56095597453532e-09-196.333997203561
102-14.58399721-3.68914676585064e-09-14.5839972063109
103-82.20899721-3.68915209492116e-09-82.2089972063109
10417.91600279-7.43911954259602e-0917.9160027974391
105-162.8964972-1.68910219144891e-09-162.896497198311
106-132.2714972-8.06412003839796e-09-132.271497191936
107-16.833997212.56089194294873e-09-16.8339972125609
10881.541002793.56081386598817e-0981.5410027864392
109275.6808314-3.35217009705957e-09275.680831403352
110-32.46823322-8.95191476502077e-10-32.4682332191048
11117.969266784.79233008832125e-0917.9692667752077
11227.15676678-5.89517767934922e-0927.1567667858952
113-123.15573322.60486388015124e-09-123.155733202605
114108.5942668-4.64515892417694e-09108.594266804645
11567.96926678-4.64517313503165e-0967.9692667846452
11634.09426678-8.3951761098433e-0934.0942667883952
117-13.71823322-2.64519073311931e-09-13.7182332173548
118-113.0932332-9.0201837110726e-09-113.093233190980
11954.344266781.60485313926984e-0954.3442667783951
120149.71926682.60476440416824e-09149.719266797395
121153.8590954-4.30816271546064e-09153.859095404308
122-28.28996923-1.85123738560833e-09-28.2899692281488
123238.14753083.83619180865935e-09238.147530796164
12450.33503077-6.85119516674604e-0950.3350307768512
1258.0225307711.64875046948509e-098.02253076935125
126-61.22746923-5.60127233484309e-09-61.2274692243987
127-140.8524692-5.60117996428744e-09-140.852469194399
128-28.72746923-9.35122912437691e-09-28.7274692206488
1299.460030771-3.60123664222556e-099.46003077460124
130-121.9149692-9.97624738374725e-09-121.914969190024
13141.522530776.4878946659519e-1041.5225307693512
132115.89753081.64871494234831e-09115.897530798351
13327.03735936-5.26424415170368e-0927.0373593652642
134-91.11170524-2.80729750556930e-09-91.1117052371927
1353.3257947592.88021873018351e-093.32579475611978
136-29.48670524-7.80728726113011e-09-29.4867052321927
137-73.799205246.92679691383091e-10-73.7992052406927
13850.95079476-6.55733600751773e-0950.9507947665573
139-86.67420524-6.55732890209038e-09-86.6742052334427
140-9.54920524-1.03072945734084e-08-9.5492052296927
141-66.36170524-4.55730742032756e-09-66.3617052354427
14273.26329476-1.09322968455672e-0873.2632947709323
143-216.2992052-3.07267100652098e-10-216.299205199693
144-128.92420526.92637058818946e-10-128.924205200693
145-142.7843767-6.22031848251936e-09-142.784376693780
14627.06655875-3.76337538909866e-0927.0665587537634
14760.504058751.92417104472042e-0960.5040587480758
14835.69155875-8.76336514465947e-0935.6915587587634
14916.37905875-2.63376875864196e-1016.3790587502634
150-64.87094125-7.51340678561974e-09-64.8709412424866
151115.5040587-7.51330730963673e-09115.504058707513
152-30.37094125-1.12633635751536e-08-30.3709412387366
15387.81655875-5.51337109300221e-0987.8165587555134
154205.4415587-1.18883178856777e-08205.441558711888
155-64.12094125-1.26337340589089e-09-64.1209412487366
156-322.7459413-2.63526089838706e-10-322.745941299737
157-139.6061127-7.17639636604872e-09-139.606112692824
15835.24482274-4.7194390617733e-0935.2448227447194
159-4.3176772639.68088720298965e-10-4.31767726396809
16017.86982274-9.7194323700478e-0917.8698227497194
1612.557322737-1.21943788400358e-092.55732273821944
162129.3073227-8.46941361487552e-09129.307322708469
163-16.31767726-8.4694349311576e-09-16.3176772515306
164164.8073227-1.22194023788325e-08164.807322712219
16521.99482274-6.46942410753581e-0921.9948227464694
166138.6198227-1.28444241909165e-08138.619822712844
16787.05732274-2.21943707856553e-0987.0573227422194
16851.43232274-1.21948318110299e-0951.4323227412195
169-80.42784867-8.13241740615922e-09-80.4278486618676
170-105.1918797-4.9867026064021e-09-105.191879695013
1715.2456203287.00747904147647e-105.24562032729925
17268.43312033-9.98674920538178e-0968.4331203399867
173-0.879379672-1.4867470587987e-09-0.879379670513253
174-105.1293797-8.73671979206847e-09-105.129379691263
175-82.75437967-8.7367482137779e-09-82.7543796612633
176-132.6293797-1.24867938211537e-08-132.629379687513
177102.5581203-6.7367409428698e-09102.558120306737
17823.18312033-1.31117801061009e-0823.1831203431118
179-180.3793797-2.48672904490377e-09-180.379379697513
180-267.0043797-1.48668277688557e-09-267.004379698513
18130.13544892-8.3997520050616e-0930.1354489283998
18223.98638432-5.94283733335033e-0923.9863843259428
18390.42388432-2.55283794103889e-1090.4238843202553
18431.61138432-1.09428128780564e-0831.6113843309428
18581.29888432-2.44280329297908e-0981.2988843224428
18625.04888432-9.6928545190167e-0925.0488843296929
187-13.57611568-9.69283497909146e-09-13.5761156703072
18833.54888432-1.34428148612642e-0833.5488843334428
189140.7363843-7.69270513956144e-09140.736384307693
190132.3613843-1.40678082516388e-08132.361384314068
19194.79888432-3.44282113928784e-0994.7988843234428
1924.173884316-2.44289033446421e-094.17388431844289


Goldfeld-Quandt test for Heteroskedasticity
p-valuesAlternative Hypothesis
breakpoint indexgreater2-sidedless
170.3220302286743520.6440604573487050.677969771325648
180.2335210890644340.4670421781288680.766478910935566
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230.05298521088744230.1059704217748850.947014789112558
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250.03611929193871180.07223858387742370.963880708061288
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290.02500352156547530.05000704313095060.974996478434525
300.01517277417425770.03034554834851540.984827225825742
310.01048625145758190.02097250291516370.989513748542418
320.006139053854505460.01227810770901090.993860946145495
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350.007661079757120540.01532215951424110.99233892024288
360.02407759818224590.04815519636449190.975922401817754
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470.006822710572932710.01364542114586540.993177289427067
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500.01653371531065540.03306743062131070.983466284689345
510.02939038049365330.05878076098730660.970609619506347
520.05664310797871710.1132862159574340.943356892021283
530.06467971961883490.1293594392376700.935320280381165
540.06142328328166580.1228465665633320.938576716718334
550.07444424138654210.1488884827730840.925555758613458
560.07616840888683780.1523368177736760.923831591113162
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770.9999854089290632.91821418733052e-051.45910709366526e-05
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800.99999665797996.68404019971216e-063.34202009985608e-06
810.9999952810591579.43788168510053e-064.71894084255026e-06
820.9999989772538842.04549223223336e-061.02274611611668e-06
830.9999990850055351.82998892942439e-069.14994464712195e-07
840.9999987655233912.46895321734940e-061.23447660867470e-06
850.9999994673938231.06521235310553e-065.32606176552766e-07
860.9999995786832988.42633403447027e-074.21316701723514e-07
870.9999996427861067.14427787509259e-073.57213893754629e-07
880.999999435762871.12847426120219e-065.64237130601095e-07
890.9999991947837941.61043241203341e-068.05216206016706e-07
900.9999996239060027.5218799554856e-073.7609399777428e-07
910.9999994640397821.07192043523218e-065.35960217616092e-07
920.9999999136772361.72645528787992e-078.63227643939959e-08
930.9999998541724842.91655031956371e-071.45827515978186e-07
940.9999997763282894.47343422620061e-072.23671711310030e-07
950.9999996365908167.26818367139513e-073.63409183569756e-07
960.999999706932795.86134421997582e-072.93067210998791e-07
970.9999994912858111.01742837721940e-065.08714188609702e-07
980.999999260080281.47983944134794e-067.3991972067397e-07
990.9999993825245741.23495085230344e-066.1747542615172e-07
1000.9999989743435152.05131297027360e-061.02565648513680e-06
1010.9999992037447381.59251052460845e-067.96255262304223e-07
1020.9999985989037032.80219259369341e-061.40109629684671e-06
1030.9999977726557014.45468859760985e-062.22734429880492e-06
1040.9999962326317457.53473650983175e-063.76736825491588e-06
1050.9999971276116275.74477674555739e-062.87238837277870e-06
1060.9999975174215944.96515681165057e-062.48257840582528e-06
1070.9999957038142168.59237156825406e-064.29618578412703e-06
1080.9999949403718671.01192562657260e-055.05962813286301e-06
1090.9999993059416441.38811671204135e-066.94058356020675e-07
1100.9999987588257752.48234844915784e-061.24117422457892e-06
1110.9999979106727544.17865449119598e-062.08932724559799e-06
1120.9999964024012057.19519759004054e-063.59759879502027e-06
1130.999995631727098.7365458203122e-064.3682729101561e-06
1140.9999949641256541.00717486927912e-055.03587434639562e-06
1150.9999937901985721.24196028560466e-056.2098014280233e-06
1160.9999900943247511.98113504970457e-059.90567524852283e-06
1170.999983601657923.27966841587607e-051.63983420793804e-05
1180.9999850725194362.98549611287282e-051.49274805643641e-05
1190.9999803172748433.9365450313025e-051.96827251565125e-05
1200.9999938155444961.23689110083710e-056.18445550418549e-06
1210.9999982285660083.54286798335589e-061.77143399167794e-06
1220.9999969061658516.18766829790909e-063.09383414895455e-06
1230.999999405207661.18958468174067e-065.94792340870335e-07
1240.999999119634381.76073124086417e-068.80365620432087e-07
1250.999998561347942.87730411880328e-061.43865205940164e-06
1260.9999973602112255.27957755055156e-062.63978877527578e-06
1270.9999960290415527.9419168959176e-063.9709584479588e-06
1280.999992948839711.41023205815387e-057.05116029076937e-06
1290.9999874501413042.50997173929061e-051.25498586964531e-05
1300.9999903301517461.93396965085089e-059.66984825425444e-06
1310.999991466215081.70675698403653e-058.53378492018264e-06
1320.9999996705869476.58826105612456e-073.29413052806228e-07
1330.9999999076940071.84611986462813e-079.23059932314063e-08
1340.9999998112876873.77424626627252e-071.88712313313626e-07
1350.9999996398243437.20351314905194e-073.60175657452597e-07
1360.9999992594027521.48119449654589e-067.40597248272943e-07
1370.9999985198656562.96026868710363e-061.48013434355181e-06
1380.999998728249742.54350052100532e-061.27175026050266e-06
1390.9999974785201015.0429597980809e-062.52147989904045e-06
1400.9999960837587437.8324825144108e-063.9162412572054e-06
1410.9999930195564321.39608871359909e-056.98044356799544e-06
1420.9999880654546842.38690906311963e-051.19345453155982e-05
1430.999986986462462.60270750792493e-051.30135375396246e-05
1440.999984427600123.11447997612417e-051.55723998806208e-05
1450.9999717042434855.65915130297727e-052.82957565148864e-05
1460.9999567824586428.64350827161438e-054.32175413580719e-05
1470.9999326787412940.0001346425174112666.73212587056331e-05
1480.999880892135040.0002382157299209530.000119107864960477
1490.9997878403267280.0004243193465446620.000212159673272331
1500.9996175144836960.0007649710326075030.000382485516303751
1510.999849347637690.0003013047246202760.000150652362310138
1520.9997124556531970.0005750886936060720.000287544346803036
1530.9995665141746420.0008669716507151170.000433485825357559
1540.9998324163472810.0003351673054375160.000167583652718758
1550.9996890386370530.0006219227258946850.000310961362947343
1560.9998140077318620.0003719845362750830.000185992268137541
1570.9996637509020650.000672498195869510.000336249097934755
1580.9993434560422940.001313087915412620.000656543957706311
1590.9990544363991190.001891127201762250.000945563600881126
1600.9985508548803470.0028982902393050.0014491451196525
1610.9980072674171350.003985465165729770.00199273258286489
1620.9973269090916550.005346181816690380.00267309090834519
1630.994901009307660.01019798138468050.00509899069234027
1640.9961929795162670.00761404096746680.0038070204837334
1650.996594747565430.00681050486913940.0034052524345697
1660.9931032326244170.01379353475116680.00689676737558341
1670.9887368045874710.02252639082505710.0112631954125285
1680.9979813145622880.004037370875424090.00201868543771204
1690.9949340535515120.01013189289697560.00506594644848782
1700.987866899394760.02426620121047960.0121331006052398
1710.973650040107280.05269991978543930.0263499598927197
1720.9797063900110620.04058721997787580.0202936099889379
1730.9576677756947730.08466444861045480.0423322243052274
1740.9022180598098420.1955638803803160.0977819401901579
1750.8323476539644250.335304692071150.167652346035575


Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity
Description# significant tests% significant testsOK/NOK
1% type I error level990.622641509433962NOK
5% type I error level1300.817610062893082NOK
10% type I error level1370.861635220125786NOK
 
Charts produced by software:
http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Nov/23/t1227439859b1p1u1d3y34prsa/10lr0g1227439763.png (open in new window)
http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Nov/23/t1227439859b1p1u1d3y34prsa/10lr0g1227439763.ps (open in new window)


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http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Nov/23/t1227439859b1p1u1d3y34prsa/1d1331227439763.ps (open in new window)


http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Nov/23/t1227439859b1p1u1d3y34prsa/2qajr1227439763.png (open in new window)
http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Nov/23/t1227439859b1p1u1d3y34prsa/2qajr1227439763.ps (open in new window)


http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Nov/23/t1227439859b1p1u1d3y34prsa/355c71227439763.png (open in new window)
http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Nov/23/t1227439859b1p1u1d3y34prsa/355c71227439763.ps (open in new window)


http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Nov/23/t1227439859b1p1u1d3y34prsa/49mhy1227439763.png (open in new window)
http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Nov/23/t1227439859b1p1u1d3y34prsa/49mhy1227439763.ps (open in new window)


http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Nov/23/t1227439859b1p1u1d3y34prsa/5qo7l1227439763.png (open in new window)
http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Nov/23/t1227439859b1p1u1d3y34prsa/5qo7l1227439763.ps (open in new window)


http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Nov/23/t1227439859b1p1u1d3y34prsa/64lbi1227439763.png (open in new window)
http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Nov/23/t1227439859b1p1u1d3y34prsa/64lbi1227439763.ps (open in new window)


http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Nov/23/t1227439859b1p1u1d3y34prsa/7rnba1227439763.png (open in new window)
http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Nov/23/t1227439859b1p1u1d3y34prsa/7rnba1227439763.ps (open in new window)


http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Nov/23/t1227439859b1p1u1d3y34prsa/8bb7b1227439763.png (open in new window)
http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Nov/23/t1227439859b1p1u1d3y34prsa/8bb7b1227439763.ps (open in new window)


http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Nov/23/t1227439859b1p1u1d3y34prsa/9nlgm1227439763.png (open in new window)
http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Nov/23/t1227439859b1p1u1d3y34prsa/9nlgm1227439763.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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