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Q2

*Unverified author*
R Software Module: rwasp_multipleregression.wasp (opens new window with default values)
Title produced by software: Multiple Regression
Date of computation: Thu, 27 Nov 2008 18:01:26 -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/28/t122783421747x7frfevyh7zzd.htm/, Retrieved Fri, 28 Nov 2008 01:03:37 +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/28/t122783421747x7frfevyh7zzd.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)
 
Feedback Forum:
2008-11-27 13:41:43 [a2386b643d711541400692649981f2dc] [reply] 
test

Post a new message
 
Original text written by user:
 
IsPrivate?
No (this computation is public)
 
User-defined keywords:
 
Dataseries X:
» Textbox « » Textfile « » CSV «
1687 0 -183,9235445 1508 0 -177,0726091 1507 0 -228,6351091 1385 0 -237,4476091 1632 0 -127,7601091 1511 0 -193,0101091 1559 0 -220,6351091 1630 0 -164,5101091 1579 0 -268,3226091 1653 0 -333,6976091 2152 0 -34,26010911 2148 0 -154,8851091 1752 0 -97,74528053 1765 0 101,1056549 1717 0 2,543154874 1558 0 -43,26934513 1575 0 -163,5818451 1520 0 -162,8318451 1805 0 46,54315487 1800 0 26,66815487 1719 0 -107,1443451 2008 0 42,48065487 2242 0 76,91815487 2478 0 196,2931549 2030 0 201,4329835 1655 0 12,28391886 1693 0 -0,278581137 1623 0 42,90891886 1805 0 87,59641886 1746 0 84,34641886 1795 0 57,72141886 1926 0 173,8464189 1619 0 -185,9660811 1992 0 47,65891886 2233 0 89,09641886 2192 0 -68,52858114 2080 0 272,6112475 1768 0 146,4621829 1835 0 162,8996829 1569 0 10,08718285 1976 0 279,7746829 1853 0 212,5246829 1965 0 248,8996829 1689 0 -41,97531715 1778 0 -5,787817149 1976 0 52,83718285 2397 0 274,2746829 2654 0 414,6496829 2097 0 310,7895114 1963 0 362,6404468 1677 0 26,07794684 1941 0 403,2654468 2003 0 327,9529468 1813 0 193,7029468 2012 0 317,0779468 1912 0 202,2029468 2084 0 321,3904468 2080 0 178,0154468 2118 0 16,45294684 2150 0 -68,17205316 1608 0 -157,0322246 1503 0 -76,18128917 1548 0 -81,74378917 1382 0 -134,5562892 1731 0 77,13121083 1798 0 199,8812108 1779 0 105,2562108 1887 0 198,3812108 2004 0 262,5687108 2077 0 196,1937108 2092 0 11,63121083 2051 0 -145,9937892 1577 0 -166,8539606 1356 0 -202,0030252 1652 0 43,43447482 1382 0 -113,3780252 1519 0 -113,6905252 1421 0 -155,9405252 1442 0 -210,5655252 1543 0 -124,4405252 1656 0 -64,25302518 1561 0 -298,6280252 1905 0 -154,1905252 2199 0 23,18447482 1473 0 -249,6756966 1655 0 118,1752388 1407 0 -180,3872612 1395 0 -79,19976119 1530 0 -81,51226119 1309 0 -246,7622612 1526 0 -105,3872612 1327 0 -319,2622612 1627 0 -72,07476119 1748 0 -90,44976119 1958 0 -80,01226119 2274 0 119,3627388 1648 0 -53,49743261 1401 0 -114,6464972 1411 0 -155,2089972 1403 0 -50,02149721 1394 0 -196,3339972 1520 0 -14,58399721 1528 0 -82,20899721 1643 0 17,91600279 1515 0 -162,8964972 1685 0 -132,2714972 2000 0 -16,83399721 2215 0 81,54100279 1956 0 275,6808314 1462 0 -32,46823322 1563 0 17,96926678 1459 0 27,15676678 1446 0 -123,1557332 1622 0 108,5942668 1657 0 67,96926678 1638 0 34,09426678 1643 0 -13,71823322 1683 0 -113,0932332 2050 0 54,34426678 2262 0 149,7192668 1813 0 153,8590954 1445 0 -28,28996923 1762 0 238,1475308 1461 0 50,33503077 1556 0 8,022530771 1431 0 -61,22746923 1427 0 -140,8524692 1554 0 -28,72746923 1645 0 9,460030771 1653 0 -121,9149692 2016 0 41,52253077 2207 0 115,8975308 1665 0 27,03735936 1361 0 -91,11170524 1506 0 3,325794759 1360 0 -29,48670524 1453 0 -73,79920524 1522 0 50,95079476 1460 0 -86,67420524 1552 0 -9,54920524 1548 0 -66,36170524 1827 0 73,26329476 1737 0 -216,2992052 1941 0 -128,9242052 1474 0 -142,7843767 1458 0 27,06655875 1542 0 60,50405875 1404 0 35,69155875 1522 0 16,37905875 1385 0 -64,87094125 1641 0 115,5040587 1510 0 -30,37094125 1681 0 87,81655875 1938 0 205,4415587 1868 0 -64,12094125 1726 0 -322,7459413 1456 0 -139,6061127 1445 0 35,24482274 1456 0 -4,317677263 1365 0 17,86982274 1487 0 2,557322737 1558 0 129,3073227 1488 0 -16,31767726 1684 0 164,8073227 1594 0 21,99482274 1850 0 138,6198227 1998 0 87,05732274 2079 0 51,43232274 1494 0 -80,42784867 1057 1 -105,1918797 1218 1 5,245620328 1168 1 68,43312033 1236 1 -0,879379672 1076 1 -105,1293797 1174 1 -82,75437967 1139 1 -132,6293797 1427 1 102,5581203 1487 1 23,18312033 1483 1 -180,3793797 1513 1 -267,0043797 1357 1 30,13544892 1165 1 23,98638432 1282 1 90,42388432 1110 1 31,61138432 1297 1 81,29888432 1185 1 25,04888432 1222 1 -13,57611568 1284 1 33,54888432 1444 1 140,7363843 1575 1 132,3613843 1737 1 94,79888432 1763 1 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 time8 seconds
R Server'Sir Ronald Aylmer Fisher' @ 193.190.124.24
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
Cons[t] = + 2324.06337309061 -226.385033603347Inc[t] + 1.00000000000397Price[t] -451.374973249478M1[t] -635.461053319472M2[t] -583.133697992862M3[t] -694.556342649877M4[t] -555.47898732608M5[t] -609.464131986533M6[t] -532.074276654236M7[t] -515.434421318189M8[t] -460.857065991641M9[t] -319.717210652969M10[t] -118.389855331297M11[t] -1.76485533229718t + e[t]


Multiple Linear Regression - Ordinary Least Squares
VariableParameterS.D.T-STAT
H0: parameter = 0		2-tail p-value1-tail p-value
(Intercept)2324.063373090610391993752573.56300
Inc-226.3850336033470-40968397489.961700
Price1.00000000000397099080745599.400700
M1-451.3749732494780-62141580921.796400
M2-635.4610533194720-87487368071.247100
M3-583.1336979928620-80298349345.831500
M4-694.5563426498770-95657585277.17300
M5-555.478987326080-76514615361.614200
M6-609.4641319865330-83961679974.973200
M7-532.0742766542360-73308241116.19200
M8-515.4344213181890-71021997300.748300
M9-460.8570659916410-63506180850.223100
M10-319.7172106529690-44059279702.850100
M11-118.3898553312970-16315442153.802100
t-1.764855332297180-54485436388.454500


Multiple Linear Regression - Regression Statistics
Multiple R1
R-squared1
Adjusted R-squared1
F-TEST (value)2.71658123083033e+21
F-TEST (DF numerator)14
F-TEST (DF denominator)177
p-value0
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation2.05237307523673e-08
Sum Squared Residuals7.45565637472327e-14


Multiple Linear Regression - Actuals, Interpolation, and Residuals
Time or IndexActualsInterpolation
Forecast		Residuals
Prediction Error
116871687.00000000809-8.09466233742612e-09
215081508.00000000584-5.83672302286647e-09
315071506.999999999945.54353707539376e-11
413851385.00000001060-1.05964211598314e-08
516321632.00000000253-2.53260473223269e-09
615111511.00000000952-9.52327192249162e-09
715591559.00000000941-9.41417004823992e-09
816301630.00000001339-1.33865384877148e-08
915791579.00000000722-7.2239640656975e-09
1016531653.00000001334-1.33392586399936e-08
1121522151.999999993906.09609561726636e-09
1221482148.00000000242-2.42475577019582e-09
1317521751.999999990889.12362036742162e-09
1417651765.00000001937-1.93749806906656e-08
1517171716.999999987301.27038276209283e-08
1615581557.999999993806.19812893690176e-09
1715751575.00000001482-1.48239883312839e-08
1815201520.00000002208-2.20769605557911e-08
1918051804.999999992917.09159628874473e-09
2018001799.999999996583.42047753899862e-09
2117191719.00000002030-2.02981678493176e-08
2220082007.999999997272.73271044185949e-09
2322422241.999999986781.32211427103247e-08
2424782478.00000001625-1.62530602616941e-08
2520302030.0000000345-3.4498530019966e-08
2616551654.999999991468.54384477578644e-09
2716931692.999999988721.12812772140773e-08
2816231622.999999996583.42216026118904e-09
2918051804.999999988261.17447738234229e-08
3017461745.999999995494.50762107651805e-09
3117951794.999999995394.6134640980979e-09
3219261926.00000003960-3.95976708543584e-08
3316191619.00000003242-3.24188796478388e-08
3419921991.999999999722.78330331271626e-10
3522332232.999999989261.07387994836616e-08
3621922191.999999987631.23648134311047e-08
3720802080.00000004722-4.72149109583496e-08
3817681768.00000004442-4.44228019432756e-08
3918351835.0000000388-3.88006169964304e-08
4015691568.999999998881.11877062353349e-09
4119761976.00000004145-4.14521883661812e-08
4218531853.00000004844-4.84351266452844e-08
4319651965.00000004858-4.85794990005347e-08
4416891689.00000000117-1.17458082219511e-09
4517781777.999999996573.43179310164736e-09
4619761976.00000000218-2.17600242830424e-09
4723972397.00000004243-4.24302813057513e-08
4826542654.00000004199-4.1987589276188e-08
4920972096.99999995984.01996795873908e-08
5019631962.999999957724.22849363240074e-08
5116771676.999999990699.30901768509177e-09
5219411940.999999962883.71236017589809e-08
5320032002.999999954084.59226681823917e-08
5418131812.999999960793.92057253101091e-08
5520122011.999999961283.87159069529794e-08
5619121911.999999964583.5422119879629e-08
5720842083.99999995934.06987706059973e-08
5820802079.999999965113.48931176320159e-08
5921182117.999999993846.15963482585196e-09
6021502149.999999992507.49569164811917e-09
6116081607.999999970382.96235402814871e-08
6215031502.999999998411.59370936413413e-09
6315481547.999999992707.30330630143498e-09
6413821381.999999973172.68254735954740e-08
6517311730.999999995524.48487430293789e-09
6617981797.999999973252.67475172651107e-08
6717791778.999999972882.71232582289066e-08
6818871886.999999977002.30035021307751e-08
6920042003.99999997152.84984609135775e-08
7020772076.999999977612.23870794758279e-08
7120922091.999999996263.74496581191342e-09
7220512050.999999964633.53708228377979e-08
7315771576.999999982771.72286655834564e-08
7413561355.999999980341.96595352968932e-08
7516521651.999999995634.37237675761424e-09
7613821381.999999985691.43076026827758e-08
7715191518.999999977192.28088511484011e-08
7814211420.999999984271.57265713464459e-08
7914421441.999999984061.59434716242434e-08
8015431542.999999988151.18514906285199e-08
8116561656.00000000264-2.63743127612705e-09
8215611560.999999988081.19181646036450e-08
8319051904.999999978032.19696202524785e-08
8421992198.999999997732.26532298329701e-09
8514731472.999999994885.12377882481993e-09
8616551654.999999994055.95424918809887e-09
8714071406.999999987171.28274649830031e-08
8813951395.00000000826-8.26198345287567e-09
8915301529.999999999752.47282173868373e-10
9013091308.999999996353.65350688474578e-09
9115261525.999999996913.09212312502133e-09
9213271326.999999999811.91390262382428e-10
9316271627.00000000504-5.04009698508406e-09
9417481748.00000001134-1.13423036838369e-08
9519581958.00000000076-7.5867117573887e-10
9622742273.999999990559.44969327054e-09
9716481647.999999998091.91094934839675e-09
9814011401.00000000555-5.55500313370994e-09
9914111410.999999999712.93593083814679e-10
10014031403.00000000081-8.11653928989127e-10
10113941394.00000000173-1.73060759510710e-09
10215201519.999999999702.97690458438329e-10
10315281527.999999999435.66358796766865e-10
10416431643.00000000358-3.58139559156053e-09
10515151515.00000000711-7.11343152204831e-09
10616851685.00000001361-1.36100591957914e-08
10720001999.999999993446.55655519611814e-09
10822152214.999999992837.1659353604642e-09
10919561956.00000002183-2.18300096796505e-08
11014621461.999999998321.68486022056954e-09
11115631562.999999992837.17202884349938e-09
11214591459.00000000355-3.55186189622869e-09
11314461446.00000001446-1.44550390728575e-08
11416221622.00000002263-2.26252693284799e-08
11516571657.00000000246-2.46393420331570e-09
11616381638.00000000608-6.07943357267753e-09
11716431643.00000000014-1.39675341088314e-10
11816831683.00000002612-2.61200199208287e-08
11920502049.999999996163.84012225239023e-09
12022622262.00000001554-1.55385939436452e-08
12118131813.00000003378-3.37800490886401e-08
12214451445.00000000077-7.65504954082656e-10
12317621762.00000002614-2.61360653902929e-08
12414611461.00000000608-6.07770177169053e-09
12515561555.999999998411.5903317131173e-09
12614311431.00000000438-4.3847528245859e-09
12714271427.00000003407-3.40684481694932e-08
12815541554.00000000826-8.26383691434723e-09
12916451645.00000000367-3.665419847865e-09
13016531653.00000003852-3.85187600164273e-08
13120162015.999999998541.45727752674211e-09
13222072207.00000002784-2.78380455126278e-08
13316651665.00000000571-5.7102330655916e-09
13413611361.00000000295-2.94989473368423e-09
13515061505.999999996643.36269176642351e-09
13613601360.00000000819-8.19468739814986e-09
13714531452.999999999524.81517691848854e-10
13815221522.00000000726-7.26392580952587e-09
13914601460.00000000672-6.71743458272675e-09
14015521552.00000001077-1.07738883429402e-08
14115481548.00000000480-4.79809677720584e-09
14218271827.00000001173-1.17276250342147e-08
14317371737.00000003995-3.99527835454640e-08
14419411941.0000000393-3.92997509888455e-08
14514741473.999999957474.25302709394121e-08
14614581458.00000000585-5.85291511132981e-09
14715421542.00000000030-2.98226691651927e-10
14814041404.00000001089-1.08872419114997e-08
14915221522.00000000231-2.31035572659452e-09
15013851385.00000000924-9.23784131142284e-09
15116411640.999999959954.00459062245221e-08
15215101510.00000001312-1.31248267300459e-08
15316811681.00000000784-7.84421439661115e-09
15419381937.999999964693.5313683209073e-08
15518681868.00000000299-2.99072843532721e-09
15617261725.999999950964.90360715324301e-08
15714561455.999999969923.00839536726539e-08
15814451445.00000000832-8.31916109299814e-09
15914561455.999999999475.25458088982008e-10
16013651365.00000001325-1.32502706775981e-08
16114871487.00000000169-1.68940994600398e-09
16215581557.999999972442.75572497284067e-08
16314881488.00000001186-1.186441992304e-08
16416841683.999999976332.36662949519726e-08
16515941594.00000001002-1.00166979658726e-08
16618501849.999999976852.31453154274353e-08
16719981998.00000000602-6.02491851770193e-09
16820792079.00000000488-4.883585609956e-09
16914941494.00000001258-1.25849422133831e-08
17010571056.999999976852.31513023437012e-08
17112181217.99999999964.00246563087357e-10
17211681168.00000001254-1.25381522317927e-08
17312361236.00000000176-1.76299537810104e-09
17410761075.999999980601.94010217734595e-08
17511741174.00000001069-1.06878570900814e-08
17611391138.999999984241.57602684258114e-08
17714271426.999999979422.05762401740005e-08
17814871487.00000001548-1.54835637229191e-08
17914831482.999999974052.59497722624189e-08
18015131512.999999972712.72938285889219e-08
18113571357.00000001211-1.21111212420314e-08
18211651165.00000000980-9.79545283057834e-09
18312821282.00000000437-4.37181520033531e-09
18411101110.00000001483-1.48257634301992e-08
18512971297.00000000652-6.52310988762609e-09
18611851185.00000001355-1.35497554456525e-08
18712221222.00000001340-1.33963223218506e-08
18812841284.00000001733-1.73333725022492e-08
18914441443.999999992017.99081087953359e-09
19015751574.999999998351.64919152118771e-09
19117371737.00000000758-7.57660295918251e-09
19217631763.00000000222-2.21679828952258e-09


Goldfeld-Quandt test for Heteroskedasticity
p-valuesAlternative Hypothesis
breakpoint indexgreater2-sidedless
180.254416347004210.508832694008420.74558365299579
190.1393680701620680.2787361403241370.860631929837932
200.07771399313019310.1554279862603860.922286006869807
210.06010792861889140.1202158572377830.939892071381109
220.02814297142945610.05628594285891220.971857028570544
230.01341643076788350.02683286153576700.986583569232117
240.01784441841660240.03568883683320490.982155581583398
250.07591480213281670.1518296042656330.924085197867183
260.07292324259364940.1458464851872990.92707675740635
270.04452423105585520.08904846211171050.955475768944145
280.02636860703166750.05273721406333510.973631392968332
290.02245331056981350.0449066211396270.977546689430187
300.01791796107768930.03583592215537860.98208203892231
310.01024981088995750.02049962177991510.989750189110042
320.0357173083611520.0714346167223040.964282691638848
330.04097814713233760.08195629426467510.959021852867662
340.02715752343700970.05431504687401930.97284247656299
350.01726998730484680.03453997460969360.982730012695153
360.01463092645419510.02926185290839020.985369073545805
370.04303350603811430.08606701207622860.956966493961886
380.1022754864183760.2045509728367530.897724513581624
390.2046465252502380.4092930505004750.795353474749762
400.1665348169657170.3330696339314340.833465183034283
410.2263103190039340.4526206380078670.773689680996066
420.3186158056588780.6372316113177570.681384194341122
430.4883176050741270.9766352101482540.511682394925873
440.4689638671206990.9379277342413980.531036132879301
450.5303811781910190.9392376436179610.469618821808981
460.4868838818011590.9737677636023180.513116118198841
470.6928602213541850.614279557291630.307139778645815
480.7988456588253410.4023086823493170.201154341174659
490.9721773956308940.05564520873821260.0278226043691063
500.9964274119090370.007145176181925990.00357258809096299
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610.9999607731222557.845375549047e-053.9226877745235e-05
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630.9999264403460460.0001471193079078847.3559653953942e-05
640.9999127853044650.0001744293910697448.72146955348722e-05
650.9998738702738580.0002522594522841460.000126129726142073
660.9998574040989570.00028519180208650.00014259590104325
670.9998369968010380.0003260063979246420.000163003198962321
680.9998019084733830.0003961830532346940.000198091526617347
690.9998236492513330.000352701497334060.00017635074866703
700.9998204971590670.0003590056818656010.000179502840932800
710.999752768387350.0004944632252999410.000247231612649970
720.9997949919239930.0004100161520132350.000205008076006617
730.9997216920266070.0005566159467864270.000278307973393213
740.99962752368970.0007449526206007930.000372476310300396
750.9995136850378280.0009726299243448380.000486314962172419
760.9994919564496030.001016087100794330.000508043550397166
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780.9992757830409170.001448433918166800.000724216959083402
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800.9989079891526430.002184021694713150.00109201084735658
810.9987175613875580.002564877224884250.00128243861244213
820.9984693974345140.003061205130971730.00153060256548586
830.9983999077642530.003200184471492970.00160009223574648
840.9979206636239790.004158672752042630.00207933637602131
850.9973495948777680.005300810244464140.00265040512223207
860.9967992933803240.006401413239352930.00320070661967647
870.9960744494846270.007851101030746560.00392555051537328
880.996472390457010.007055219085981740.00352760954299087
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900.9945375847025070.01092483059498680.00546241529749339
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930.9902161605357560.01956767892848740.00978383946424371
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980.9793935000200880.04121299995982430.0206064999799122
990.9745902971170220.05081940576595620.0254097028829781
1000.972554308797650.05489138240469940.0274456912023497
1010.9666900909637630.0666198180724740.033309909036237
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1050.9358151416453780.1283697167092430.0641848583546215
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1080.9196273047700090.1607453904599830.0803726952299914
1090.9194719871552530.1610560256894940.0805280128447468
1100.9055458816283860.1889082367432290.0944541183716143
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1120.8937783820611420.2124432358777170.106221617938858
1130.8814212404653260.2371575190693480.118578759534674
1140.8787537597551030.2424924804897940.121246240244897
1150.8676692092772180.2646615814455650.132330790722782
1160.847783290471480.3044334190570390.152216709528519
1170.8245694972366760.3508610055266480.175430502763324
1180.8306032425607020.3387935148785950.169396757439298
1190.8258892918766340.3482214162467330.174110708123366
1200.80571093385740.3885781322851980.194289066142599
1210.829460691132640.3410786177347210.170539308867361
1220.8020216061845190.3959567876309630.197978393815481
1230.7985656348953130.4028687302093730.201434365104687
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1290.6684338048119960.6631323903760080.331566195188004
1300.77485311013880.45029377972240.2251468898612
1310.7567955548398730.4864088903202540.243204445160127
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1390.4402303946920370.8804607893840750.559769605307963
1400.4010194905552840.8020389811105670.598980509444716
1410.3573779605553020.7147559211106030.642622039444698
1420.3529399618947360.7058799237894720.647060038105264
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1500.8672616114340730.2654767771318550.132738388565927
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1580.9859353235676540.02812935286469290.0140646764323464
1590.9771709659068240.04565806818635250.0228290340931762
1600.964915615965040.0701687680699210.0350843840349605
1610.9459923389670060.1080153220659880.054007661032994
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1630.9279207631106770.1441584737786450.0720792368893226
1640.9614944018315490.0770111963369030.0385055981684515
1650.9855857627148650.02882847457027100.0144142372851355
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1670.9945067414089810.01098651718203770.00549325859101885
1680.989569526467720.02086094706456060.0104304735322803
1690.977348427836810.04530314432638010.0226515721631900
1700.9702962706798020.05940745864039660.0297037293201983
1710.9404311266912840.1191377466174310.0595688733087157
1720.8895548660140480.2208902679719040.110445133985952
1730.7943535697687260.4112928604625480.205646430231274
1740.7348071712759030.5303856574481950.265192828724097


Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity
Description# significant tests% significant testsOK/NOK
1% type I error level400.254777070063694NOK
5% type I error level660.420382165605096NOK
10% type I error level860.547770700636943NOK
 
Charts produced by software:
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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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