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multiple regression

*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: Wed, 29 Dec 2010 17:06:25 +0000
 
Cite this page as follows:
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL http://www.freestatistics.org/blog/date/2010/Dec/29/t1293642269l23luvup4fvrwu8.htm/, Retrieved Wed, 29 Dec 2010 18:04:38 +0100
 
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/2010/Dec/29/t1293642269l23luvup4fvrwu8.htm/},
    year = {2010},
}
@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 = {2010},
    note = {{ISBN} 3-900051-07-0},
    url = {http://www.R-project.org},
}
 
Original text written by user:
 
IsPrivate?
No (this computation is public)
 
User-defined keywords:
 
Dataseries X:
» Textbox « » Textfile « » CSV «
347553 0,032500 125,01 0,012257 353245 0,025000 120,96 0,014315 347966 0,025000 117,07 0,012208 364343 0,025000 112,45 0,009063 341713 0,025000 110,23 0,009054 361162 0,025000 107,34 0,009063 354400 0,025000 107,73 0,019270 345183 0,025000 103,71 0,018200 341807 0,017500 105,28 0,015106 348712 0,017500 106,92 0,013078 349011 0,017500 107,8 0,010081 416259 0,017500 109,7 0,011089 360289 0,017500 111,51 0,013118 367557 0,017500 106,21 0,012097 364611 0,017500 105,14 0,013065 378688 0,017500 103,53 0,007984 351763 0,017500 103,99 0,007976 377765 0,017500 102,72 0,004990 373212 0,017500 98,5 -0,001990 365819 0,017500 99,85 0,000000 364686 0,017500 98,81 0,001984 363333 0,017500 98,42 0,007944 362536 0,017500 97,96 0,009980 428803 0,017500 100,13 0,005982 375361 0,017500 99,75 0,004980 377205 0,017500 98,24 0,001992 381266 0,017500 90,79 -0,002976 390516 0,010000 83,67 -0,001980 366117 0,010000 85,1 -0,000989 393928 0,010000 84,53 0,001986 387784 0,010000 87,22 0,000997 385656 0,0100 etc...
 
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 time7 seconds
R Server'Gwilym Jenkins' @ www.wessa.org
R Framework
error message
Warning: there are blank lines in the 'Data X' field.
Please, use NA for missing data - blank lines are simply
 deleted and are NOT treated as missing values.


Multiple Linear Regression - Estimated Regression Equation
Banknotes[t] = + 952695.721801893 -17024358.4005245Loan_Interest[t] -2261.87936460689Exchange_Rate_USD[t] -583456.00996409Inflation[t] + e[t]


Multiple Linear Regression - Ordinary Least Squares
VariableParameterS.D.T-STAT
H0: parameter = 0		2-tail p-value1-tail p-value
(Intercept)952695.72180189378403.80854412.151100
Loan_Interest-17024358.40052451499128.74551-11.356200
Exchange_Rate_USD-2261.87936460689681.415855-3.31940.0010630.000531
Inflation-583456.00996409944730.073981-0.61760.5375110.268756


Multiple Linear Regression - Regression Statistics
Multiple R0.680344765580795
R-squared0.462869000053186
Adjusted R-squared0.455232066404654
F-TEST (value)60.6092734800841
F-TEST (DF numerator)3
F-TEST (DF denominator)211
p-value0
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation113207.900804473
Sum Squared Residuals2704182077761.17


Multiple Linear Regression - Actuals, Interpolation, and Residuals
Time or IndexActualsInterpolation
Forecast		Residuals
Prediction Error
1347553109495.114101206238057.885898794
2353245245137.66106329108107.33893671
3347966255165.71360460892800.2863953919
4364343267450.56542042996892.4345795712
5341713272477.18871394669235.8112860541
6361162279008.7689735782153.2310264298
7354400272171.3005276782228.69947233
8345183281888.35350405163294.6464959486
9341807407825.103800382-66018.1038003816
10348712405298.870430633-56586.8704306334
11349011405057.034251642-56046.0342516418
12416259400171.33980084516087.6601991552
13360289394893.505906689-34604.5059066892
14367557407477.175125279-39920.1751252791
15364611409332.600627763-44721.6006277632
16378688415938.766391408-37250.7663914079
17351763414902.969531768-63139.9695317684
18377765419517.755970572-41752.7559705719
19373212433135.409838762-59923.4098387624
20365819428920.795236715-63101.7952367145
21364686430115.573052137-65429.5730521369
22363333427520.308184948-64187.3081849476
23362536427372.85625638-64836.85625638
24428803424797.2351630194005.76483698057
25375361426241.372243554-50880.372243554
26377205431400.176641883-54195.1766418832
27381266451149.787365706-69883.7873657061
28390516594355.934259717-203839.934259717
29366117590543.241862455-224426.241862455
30393928590096.731470638-196168.731470638
31387784584589.3139737-196805.3139737
32385656569750.187508854-184094.187508854
33385320639700.051000059-254380.051000059
34389053643939.867852308-254886.867852308
35390595641078.950179457-250483.950179457
36462440639514.336137555-177074.336137555
37402532631067.642378648-228535.642378648
38409070630745.245675-221675.245675
39421329628734.537785544-207405.537785544
40428841623354.796554844-194513.796554844
41404864625505.915775261-220641.915775261
42432633621345.742168163-188712.742168163
43416886617980.788916747-201094.788916747
44414893622695.350803049-207802.350803049
45417914619332.669533663-201418.669533663
46417518610535.222582617-193017.222582617
47423137610752.658678929-187615.658678929
48506710606666.206933874-99956.2069338737
49436264597140.194072819-160876.194072819
50443712585846.414571311-142134.414571311
51452849587271.433594259-134422.433594259
52453009572131.85483815-119122.85483815
53437876586902.063079775-149026.063079775
54460041595967.426614031-135926.426614031
55450426595519.551477443-145093.551477443
56447873588151.589262432-140278.589262432
57444955580046.915102242-135091.915102242
58452043578775.831968221-126732.831968221
59480877571519.462985927-90642.4629859266
60546696563763.51966836-17067.5196683603
61483668563797.671591463-80129.6715914631
62489627571000.779165104-81373.7791651038
63490007563192.794620877-73185.7946208774
64496590567486.71417479-70896.7141747897
65480846559393.371209063-78547.3712090632
66497677549056.178642824-51379.1786428236
67492795549827.349515837-57032.3495158368
68488495542048.616390636-53553.6163906359
69486769564274.239672069-77505.2396720687
70494455592084.810053273-97629.8100532728
71498054590313.565025729-92259.565025729
72558648598313.998025335-39665.9980253348
73506424610440.184829691-104016.184829691
74512528604270.785821925-91742.7858219247
75512866598907.495001277-86041.495001277
76529324597142.365087353-67818.3650873532
77508431593626.230417554-85195.2304175536
78523026595807.070871232-72781.0708712321
79521355597033.355311193-75678.3553111926
80514103609370.784479713-95267.7844797131
81513885625391.970471777-111506.970471777
82522150631805.731742876-109655.731742876
83527384636898.987133096-109514.987133096
84654047641519.29255523312527.7074447673
85543115633676.362124865-90561.3621248651
86543200624236.876237067-81036.8762370673
87571201629614.415532229-58413.4155322286
88568892633509.177761697-64617.1777616966
89537223626995.649615135-89772.6496151353
90553186630693.11615512-77507.1161551204
91550954626929.197104456-75975.197104456
92543433625967.639618618-82534.6396186184
93557195631771.996364036-74576.996364036
94565522629247.6888461-63725.6888461001
95571691626386.043154461-54695.0431544608
96633972616614.54471333517357.4552866648
97575265604986.835378722-29721.8353787224
98572364632357.930056377-59993.9300563771
99586744640172.087371638-53428.0873716384
100600389634600.17823908-34211.1782390794
101578540638893.081383753-60353.0813837527
102610778638974.256285424-28196.2562854236
103596577632699.752107542-36122.7521075421
104590558639626.218076586-49068.2180765864
105597294671120.250246439-73826.2502464388
106602384665917.927707843-63533.9277078429
107614190664746.935598086-50556.9355980865
108690042654462.76748226235579.2325177384
109639497643618.380629375-4121.38062937472
110649304642844.744043826459.25595617935
111678762645810.99117074932951.0088292509
112691885645517.49528611446367.5047138858
113667973654747.1959499813225.8040500193
114682032660127.17003667821904.8299633216
115672651673223.486580998-572.486580998309
116671865671653.353555764211.646444236427
117671463667142.496803024320.50319698048
118675917660693.740845615223.2591544005
119680952663188.45901877417763.5409812257
120754718660847.73857653693870.2614234636
121694413669619.19788637724793.8021136226
122699390667062.75669261232327.2433073878
123710573668062.03278186342510.9672181371
124714217665300.78958901348916.2104109874
125702996671599.79891931331396.2010806874
126712370670496.66319049441873.3368095057
127708445668371.14598802440073.8540119756
128707083668630.35395881438452.646041186
129700632676284.22302808924347.7769719113
130706309687814.62262774518494.3773722553
131709523691576.83043586717946.1695641333
132769096693936.73487994175159.2651200587
133715100696573.31595185918526.6840481415
134713872694668.11710250419203.8828974964
135714032690568.31591571123463.6840842885
136732269695406.95646693636862.0435330642
137711137684446.07587725526690.9241227447
138715284688063.42935785227220.5706421485
139716888688894.52518590227993.4748140976
140716426687235.21988884629190.7801111541
141714726686842.01450096427883.9854990363
142718016686404.76935881431611.2306411861
143725932693732.56997439232199.4300256078
144779564699632.0650726879931.93492732
145732144701054.71524834231089.2847516575
146730816699029.49510737131786.5048926288
147746719697472.84751461649246.1524853839
148760065692253.12226321867811.8777367821
149734516693271.55143330141244.4485666991
150740167692869.01895374247297.9810462576
151740976684247.82378278156728.1762172191
152735764686982.94744592548781.0525540747
153734711686208.6573578748502.3426421307
154737916680583.9298121357332.0701878699
155739132673630.6949131265501.3050868804
156792705669648.818152143123056.181847857
157747488675120.26331145672367.7366885436
158746616669603.02802984577012.9719701546
159749781671496.04024724278284.9597527584
160760911671364.96011019989546.039889801
161739543682867.48981211956675.5101878808
162745626673698.1224430771927.8775569297
163746246621212.833329763125033.166670237
164744769617235.352235381127533.647764619
165741388616442.049159477124945.950840523
166744469613874.526403764130594.473596236
167745566617412.875997223128153.124002777
168798367617527.720333484180839.279666516
169752440611860.874415495140579.125584505
170756627553740.077087046202886.922912954
171758941560323.861382836198617.138617164
172771287556233.908901721215053.091098279
173749858551936.338108968197921.661891032
174758370548823.63048171209546.36951829
175755407549991.121855406205415.878144594
176752063562164.05108481189898.948915189
177756298566031.864798288190266.135201712
178755892561483.250316644194408.749683356
179758486569972.194336301188513.805663699
180812777566837.482292411245939.517707589
181762561577414.909334632185146.090665368
182763579576766.308186545186812.691813455
183764615590022.737575421174592.262424579
184773312588530.037287765184781.962712235
185755697581906.328350782173790.671649218
186762909571572.347762598191336.652237402
187760337570015.630123351190321.369876649
188759270565655.212625717193614.787374283
189754929571377.767418172183551.232581828
190766116630809.506292385135306.493707615
191765945642807.670332733123137.329667267
192814783692845.478575504121937.521424496
193768494697126.1332462171367.8667537903
194769222692979.34410409676242.6558959044
195768977681985.37753583686991.6224641644
196783341678274.794410111105066.205589889
197764061690114.32399244773946.6760075533
198767394693582.46103195973811.5389680409
199763910700980.05208477162929.947915229
200761677700172.50500414761504.494995853
201759173707749.8008755851423.19912442
202762486712182.91751846350303.0824815375
203762690710785.75124917951904.2487508207
204809542708862.908258989100679.091741011
205769041702962.14081139166078.859188609
206770889703812.52160877567076.4783912248
207773527703250.9999689570276.0000310493
208789890697354.3953319592535.6046680503
209768325699337.43115642168987.5688435787
210772712700040.4300717372671.5699282702
211772944708456.4417225964487.5582774106
212769637713529.91698068656107.0830193141
213768546714251.99893033554294.0010696653
214775013715275.67100002459737.3289999756
215776635714478.21368555862156.7863144416


Goldfeld-Quandt test for Heteroskedasticity
p-valuesAlternative Hypothesis
breakpoint indexgreater2-sidedless
70.001156714662267690.002313429324535380.998843285337732
80.0001183762598021330.0002367525196042660.999881623740198
91.40840800499684e-052.81681600999367e-050.99998591591995
101.05860664760653e-062.11721329521307e-060.999998941393352
117.42132766925973e-081.48426553385195e-070.999999925786723
122.08019070750409e-054.16038141500819e-050.999979198092925
133.79408043532642e-067.58816087065283e-060.999996205919565
146.58454840120356e-071.31690968024071e-060.99999934154516
151.07491513666429e-072.14983027332858e-070.999999892508486
161.9284979427035e-083.85699588540699e-080.99999998071502
174.46747239400329e-098.93494478800659e-090.999999995532528
187.32217447130169e-101.46443489426034e-090.999999999267783
191.09457521427899e-102.18915042855799e-100.999999999890542
201.69734279672647e-113.39468559345294e-110.999999999983027
212.41909194886914e-124.83818389773827e-120.99999999999758
223.23314235345985e-136.4662847069197e-130.999999999999677
234.215718946365e-148.43143789273001e-140.999999999999958
241.98756080400704e-123.97512160801407e-120.999999999998012
253.36322289219786e-136.72644578439573e-130.999999999999664
265.5164662215849e-141.10329324431698e-130.999999999999945
278.79375690290096e-151.75875138058019e-140.999999999999991
281.58792070398823e-153.17584140797645e-150.999999999999998
295.79571016567398e-161.1591420331348e-151
301.34911449331401e-162.69822898662801e-161
312.70051377423489e-175.40102754846979e-171
325.38967187657891e-181.07793437531578e-171
331.44630465949546e-182.89260931899092e-181
344.08721467269162e-198.17442934538324e-191
351.11187902662134e-192.22375805324268e-191
368.89024846356204e-181.77804969271241e-171
372.83333553605794e-185.66667107211587e-181
389.03862785215871e-191.80772557043174e-181
394.01372774398711e-198.02745548797422e-191
402.44169177149616e-194.88338354299232e-191
418.98990880923735e-201.79798176184747e-191
425.27879359181157e-201.05575871836231e-191
432.02542464633922e-204.05084929267844e-201
448.33989916694203e-211.66797983338841e-201
453.41869036153435e-216.8373807230687e-211
461.37602463763035e-212.75204927526069e-211
476.30335467380133e-221.26067093476027e-211
481.11538885585596e-182.23077771171193e-181
494.75489606468618e-199.50979212937237e-191
501.80610319720834e-193.61220639441668e-191
518.11355597181473e-201.62271119436295e-191
523.24524261161195e-206.4904852232239e-201
531.43890097328965e-202.87780194657929e-201
541.43234919001758e-202.86469838003516e-201
559.2446629706912e-211.84893259413824e-201
565.46771399257409e-211.09354279851482e-201
573.43241416904894e-216.86482833809787e-211
582.46694301515511e-214.93388603031021e-211
592.91928850172571e-215.83857700345142e-211
606.7490120704802e-191.34980241409604e-181
614.4923074132624e-198.9846148265248e-191
624.92716461882829e-199.85432923765658e-191
634.88890794787677e-199.77781589575353e-191
644.13447426791113e-198.26894853582225e-191
651.91529843929122e-193.83059687858243e-191
667.50784500270693e-201.50156900054139e-191
672.67285422645732e-205.34570845291463e-201
688.85741533170073e-211.77148306634015e-201
694.04409949728505e-218.0881989945701e-211
701.004868521998e-202.009737043996e-201
713.83231115686618e-207.66462231373236e-201
724.22156290800205e-178.4431258160041e-171
734.03691479794101e-168.07382959588202e-161
742.32595407021374e-154.65190814042749e-150.999999999999998
756.8137228661236e-151.36274457322472e-140.999999999999993
763.95716586206869e-147.91433172413738e-140.99999999999996
776.69866979815012e-141.33973395963002e-130.999999999999933
781.95900454496285e-133.9180090899257e-130.999999999999804
796.65747560660795e-131.33149512132159e-120.999999999999334
805.86768063494188e-121.17353612698838e-110.999999999994132
817.72486816261642e-111.54497363252328e-100.999999999922751
829.3724004207021e-101.87448008414042e-090.99999999906276
838.09016631986917e-091.61803326397383e-080.999999991909834
841.62515592938862e-053.25031185877724e-050.999983748440706
857.58417939629174e-050.0001516835879258350.999924158206037
860.000241687850280830.0004833757005616610.99975831214972
870.001131179335469610.002262358670939210.99886882066453
880.004068181761875580.008136363523751160.995931818238124
890.01143541042973140.02287082085946290.988564589570269
900.03463690627448420.06927381254896840.965363093725516
910.08886363394338790.1777272678867760.911136366056612
920.2171717849815530.4343435699631060.782828215018447
930.4060691007612030.8121382015224050.593930899238797
940.612586219136920.774827561726160.38741378086308
950.820933021167670.3581339576646590.179066978832329
960.9360229776511940.1279540446976110.0639770223488056
970.9827228469892780.03455430602144310.0172771530107215
980.9971906155145650.005618768970869330.00280938448543467
990.999183769662670.001632460674658950.000816230337329474
1000.9996901775381730.0006196449236530410.00030982246182652
1010.9999597611847568.04776304875783e-054.02388152437892e-05
1020.9999904520525861.90958948283424e-059.54794741417122e-06
1030.9999987556039782.4887920435007e-061.24439602175035e-06
1040.9999999640657277.18685452734227e-083.59342726367114e-08
1050.9999999993072571.38548561503816e-096.92742807519082e-10
1060.999999999991121.77585510956225e-118.87927554781123e-12
1070.9999999999998632.73077171124669e-131.36538585562335e-13
1080.9999999999999161.69011801196534e-138.4505900598267e-14
1090.9999999999999637.43536821461076e-143.71768410730538e-14
1100.9999999999999755.08123937863228e-142.54061968931614e-14
1110.9999999999999745.10492196588177e-142.55246098294088e-14
1120.9999999999999764.8385992617301e-142.41929963086505e-14
1130.999999999999991.99992360699611e-149.99961803498055e-15
1140.9999999999999976.68321817654467e-153.34160908827234e-15
11517.45499100908792e-163.72749550454396e-16
11618.80685948614233e-174.40342974307116e-17
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12015.31665543859097e-212.65832771929548e-21
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12517.4516867903e-243.72584339515e-24
12614.07913511083245e-242.03956755541623e-24
12712.00355353241414e-241.00177676620707e-24
12811.08291385645351e-245.41456928226756e-25
12912.5711976925677e-251.28559884628385e-25
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13219.0227881030398e-284.5113940515199e-28
13312.57086605265084e-281.28543302632542e-28
13416.27846784161761e-293.13923392080881e-29
13512.13489888879702e-291.06744944439851e-29
13611.92240252223203e-299.61201261116016e-30
13718.88152265267611e-304.44076132633806e-30
13813.55395546054912e-301.77697773027456e-30
13911.57322512987554e-307.86612564937772e-31
14017.0361968570965e-313.51809842854825e-31
14112.196836180772e-311.098418090386e-31
14216.73356054126683e-323.36678027063341e-32
14312.43190930595008e-321.21595465297504e-32
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14515.79628528001305e-332.89814264000652e-33
14614.69383791322202e-332.34691895661101e-33
14711.0047472469728e-325.02373623486402e-33
14812.16755699971721e-321.0837784998586e-32
14912.90969184330239e-321.4548459216512e-32
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15111.81947113058368e-319.09735565291838e-32
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15315.19397054102973e-312.59698527051487e-31
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15513.77661323723665e-301.88830661861833e-30
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15719.2777994710535e-314.63889973552675e-31
15813.88492690362132e-301.94246345181066e-30
15911.68885525935239e-298.44427629676196e-30
16015.320782324996e-292.660391162498e-29
16111.38772801963412e-286.93864009817061e-29
16214.6435076564871e-282.32175382824355e-28
16311.1544497942422e-275.77224897121099e-28
16412.18993432592597e-271.09496716296298e-27
16512.93538997807206e-271.46769498903603e-27
16614.09825651909349e-272.04912825954674e-27
16713.55000444925382e-271.77500222462691e-27
16811.37977060585974e-276.89885302929872e-28
16913.76269094099137e-271.88134547049568e-27
17011.4571453593777e-267.28572679688852e-27
17115.73245234319575e-262.86622617159788e-26
17211.47100939082504e-257.35504695412518e-26
17315.41101603287011e-252.70550801643505e-25
17412.52626829726673e-241.26313414863337e-24
17511.13073808351959e-235.65369041759793e-24
17614.61754388008215e-232.30877194004108e-23
17712.0981887551325e-221.04909437756625e-22
17818.30757897245316e-224.15378948622658e-22
17913.37388196991793e-211.68694098495897e-21
18019.89400356304722e-244.94700178152361e-24
18115.4280859658195e-232.71404298290975e-23
18212.93489101950486e-221.46744550975243e-22
18311.596933187193e-217.98466593596502e-22
18412.89981087397788e-211.44990543698894e-21
18511.97314595924037e-209.86572979620184e-21
18611.18197534046638e-195.9098767023319e-20
18718.0665913970733e-194.03329569853665e-19
18815.40223044059402e-182.70111522029701e-18
18913.64196616420125e-171.82098308210062e-17
19012.79713112165446e-161.39856556082723e-16
1910.9999999999999992.19856343693077e-151.09928171846538e-15
19213.31490062394433e-161.65745031197216e-16
1930.9999999999999992.72010906947575e-151.36005453473788e-15
1940.9999999999999892.24973109566673e-141.12486554783337e-14
1950.9999999999999131.74344134368563e-138.71720671842813e-14
1960.9999999999992761.44715959540582e-127.23579797702911e-13
1970.9999999999947971.04060420895857e-115.20302104479283e-12
1980.9999999999553668.92684653033057e-114.46342326516529e-11
1990.9999999996333867.33227937383966e-103.66613968691983e-10
2000.9999999975113624.97727635000438e-092.48863817500219e-09
2010.9999999854960962.90078082947871e-081.45039041473936e-08
2020.9999999190304971.6193900551732e-078.09695027586602e-08
2030.999999806617313.86765379182889e-071.93382689591444e-07
2040.9999999841355573.17288858334399e-081.586444291672e-08
2050.999999756436844.87126318980227e-072.43563159490114e-07
2060.9999962144248197.5711503623028e-063.7855751811514e-06
2070.999940667922090.0001186641558213225.9332077910661e-05
2080.9999775606684424.48786631150407e-052.24393315575204e-05


Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity
Description# significant tests% significant testsOK/NOK
1% type I error level1930.955445544554455NOK
5% type I error level1950.965346534653465NOK
10% type I error level1960.97029702970297NOK
 
Charts produced by software:
http://www.freestatistics.org/blog/date/2010/Dec/29/t1293642269l23luvup4fvrwu8/107buc1293642378.png (open in new window)
http://www.freestatistics.org/blog/date/2010/Dec/29/t1293642269l23luvup4fvrwu8/107buc1293642378.ps (open in new window)


http://www.freestatistics.org/blog/date/2010/Dec/29/t1293642269l23luvup4fvrwu8/1v78b1293642378.png (open in new window)
http://www.freestatistics.org/blog/date/2010/Dec/29/t1293642269l23luvup4fvrwu8/1v78b1293642378.ps (open in new window)


http://www.freestatistics.org/blog/date/2010/Dec/29/t1293642269l23luvup4fvrwu8/2v78b1293642378.png (open in new window)
http://www.freestatistics.org/blog/date/2010/Dec/29/t1293642269l23luvup4fvrwu8/2v78b1293642378.ps (open in new window)


http://www.freestatistics.org/blog/date/2010/Dec/29/t1293642269l23luvup4fvrwu8/35g7w1293642378.png (open in new window)
http://www.freestatistics.org/blog/date/2010/Dec/29/t1293642269l23luvup4fvrwu8/35g7w1293642378.ps (open in new window)


http://www.freestatistics.org/blog/date/2010/Dec/29/t1293642269l23luvup4fvrwu8/45g7w1293642378.png (open in new window)
http://www.freestatistics.org/blog/date/2010/Dec/29/t1293642269l23luvup4fvrwu8/45g7w1293642378.ps (open in new window)


http://www.freestatistics.org/blog/date/2010/Dec/29/t1293642269l23luvup4fvrwu8/55g7w1293642378.png (open in new window)
http://www.freestatistics.org/blog/date/2010/Dec/29/t1293642269l23luvup4fvrwu8/55g7w1293642378.ps (open in new window)


http://www.freestatistics.org/blog/date/2010/Dec/29/t1293642269l23luvup4fvrwu8/6g76h1293642378.png (open in new window)
http://www.freestatistics.org/blog/date/2010/Dec/29/t1293642269l23luvup4fvrwu8/6g76h1293642378.ps (open in new window)


http://www.freestatistics.org/blog/date/2010/Dec/29/t1293642269l23luvup4fvrwu8/7w2v81293642378.png (open in new window)
http://www.freestatistics.org/blog/date/2010/Dec/29/t1293642269l23luvup4fvrwu8/7w2v81293642378.ps (open in new window)


http://www.freestatistics.org/blog/date/2010/Dec/29/t1293642269l23luvup4fvrwu8/8w2v81293642378.png (open in new window)
http://www.freestatistics.org/blog/date/2010/Dec/29/t1293642269l23luvup4fvrwu8/8w2v81293642378.ps (open in new window)


http://www.freestatistics.org/blog/date/2010/Dec/29/t1293642269l23luvup4fvrwu8/9w2v81293642378.png (open in new window)
http://www.freestatistics.org/blog/date/2010/Dec/29/t1293642269l23luvup4fvrwu8/9w2v81293642378.ps (open in new window)


 
Parameters (Session):
par1 = 1 ; par2 = Do not include Seasonal Dummies ; par3 = No Linear Trend ;
 
Parameters (R input):
par1 = 1 ; par2 = Do not include Seasonal Dummies ; par3 = No 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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