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*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, 22 Dec 2010 10:37:56 +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/22/t1293014206lqhd0q0qp4auhau.htm/, Retrieved Wed, 22 Dec 2010 11:36:58 +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/22/t1293014206lqhd0q0qp4auhau.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 «
162556 162556 1081 1081 213118 213118 230380558 6282929 29790 29790 309 309 81767 81767 25266003 4324047 87550 87550 458 458 153198 153198 70164684 4108272 84738 0 588 0 -26007 0 -15292116 -1212617 54660 54660 299 299 126942 126942 37955658 1485329 42634 42634 156 156 157214 157214 24525384 1779876 40949 0 481 0 129352 0 62218312 1367203 42312 42312 323 323 234817 234817 75845891 2519076 37704 37704 452 452 60448 60448 27322496 912684 16275 16275 109 109 47818 47818 5212162 1443586 25830 0 115 0 245546 0 28237790 1220017 12679 0 110 0 48020 0 5282200 984885 18014 18014 239 239 -1710 -1710 -408690 1457425 43556 0 247 0 32648 0 8064056 -572920 24524 24524 497 497 95350 95350 47388950 929144 6532 0 103 0 151352 0 15589256 1151176 7123 0 109 0 288170 0 31410530 790090 20813 20813 502 502 114337 114337 57397174 774497 37597 37597 248 248 37884 37884 9395232 990576 17821 0 373 0 122844 0 45820812 454195 12988 12988 119 119 82340 82340 9798460 876607 22330 22330 84 84 79801 79801 6703284 711969 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 time29 seconds
R Server'Gwilym Jenkins' @ 72.249.127.135
R Framework
error message
The field 'Names of X columns' contains a hard return which cannot be interpreted.
Please, resubmit your request without hard returns in the 'Names of X columns'.


Multiple Linear Regression - Estimated Regression Equation
Wealth [t] = + 182460.443928356 -5.6906670339827Costs[t] + 38.7325798343116GrCosts[t] -530.762801621119Trades[t] -89.522048236311GrTrades[t] + 2.47987676375574Dividends[t] -0.849109032245004GrDiv[t] + 0.00599727936229474TrDiv[t] + e[t]


Multiple Linear Regression - Ordinary Least Squares
VariableParameterS.D.T-STAT
H0: parameter = 0		2-tail p-value1-tail p-value
(Intercept)182460.44392835630978.4180385.889900
Costs-5.69066703398272.417972-2.35350.0190550.009528
GrCosts38.73257983431163.74448710.343900
Trades-530.762801621119275.377981-1.92740.0545990.0273
GrTrades-89.522048236311340.354163-0.2630.7926580.396329
Dividends2.479876763755740.4425425.603700
GrDiv-0.8491090322450040.328938-2.58140.0101770.005088
TrDiv0.005997279362294740.0020922.86680.0043540.002177


Multiple Linear Regression - Regression Statistics
Multiple R0.886728582419853
R-squared0.786287578880322
Adjusted R-squared0.782750966710492
F-TEST (value)222.327906234145
F-TEST (DF numerator)7
F-TEST (DF denominator)423
p-value0
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation208540.915702847
Sum Squared Residuals18395979619883.0


Multiple Linear Regression - Actuals, Interpolation, and Residuals
Time or IndexActualsInterpolation
Forecast		Residuals
Prediction Error
162829296612296.22177421-329367.221774209
243240471259981.271106123064065.72889388
341082723461817.01460959646454.985390412
4-1212617-768049.07323812-444567.92676188
514853292237709.82926611-752380.829266114
617798761897870.0151371-117994.015137101
71367203388054.029633765979148.970366235
825190762217978.83505122301097.164948778
99126841410341.26123793-497657.261237931
101443586761845.369100168681740.630899832
111220017752706.527291124467310.472708876
12984885202687.079669227782197.920330773
131457425624189.741074094833235.258925906
14-572920-67175.2481959467-505744.751804053
159291441124197.21809984-195053.218099836
161151176559447.869525694591728.130474306
17790090987076.487607827-196986.487607827
187744971089462.75761515-314965.757615145
199905761389032.4324358-398456.432435799
20454195462510.733049060-8315.73304905951
21876607730836.42719886145770.572801140
227119691038520.79190677-326551.791906767
23702380564296.883349036138083.116650964
24264449428283.457693807-163834.457693806
25450033502837.118654765-52804.1186547647
26541063241255.558799028299807.441200972
275888641121231.98107937-532367.981079371
28-37216150659.129602705-187875.129602705
29783310200975.318711178582334.681288822
30467359140398.9273287326960.0726713
31688779433186.426864783255592.573135217
32608419747397.346293914-138978.346293914
33696348526557.164522314169790.835477686
34597793497943.87893709199849.1210629093
35821730946057.188634366-124327.188634366
36377934343393.62424857134540.3757514291
37651939343394.666904818308544.333095182
38697458546591.915187055150866.084812945
39700368615208.99165789885159.0083421021
40225986349646.596709925-123660.596709925
41348695651478.870643875-302783.870643875
42373683346482.45836401427200.5416359857
43501709396547.536499809105161.463500191
44413743453080.303597258-39337.3035972582
45379825320438.0225910159386.9774089898
46336260468926.225377646-132666.225377646
47636765584352.2703529952412.7296470103
48481231718144.52067442-236913.520674419
49469107473752.801683216-4645.80168321616
50211928356538.746809350-144610.746809350
51563925466171.48262460997753.517375391
52511939567530.388739285-55591.388739285
53521016790109.291373168-269093.291373168
54543856499945.67027404143910.3297259587
55329304642153.004737749-312849.004737749
56423262305233.727813834118028.272186166
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58455881369121.68491208986759.3150879113
59367772428919.752298388-61147.752298388
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61493408517652.434854365-24244.4348543649
62232942316945.255131933-84003.2551319327
63416002438216.314803723-22214.3148037235
64337430548063.585890834-210633.585890834
65361517299623.90870479861893.0912952016
66360962345510.74934331915451.2506566812
67235561374382.871814060-138821.871814060
68408247413107.01539268-4860.0153926799
69450296523532.644877644-73236.6448776444
70418799478139.603996129-59340.603996129
71247405301171.956624166-53766.9566241663
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73326638443127.444999367-116489.444999367
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75386225472408.597906965-86183.5979069649
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84297476270817.18680249626658.8131975037
85416776435560.397442762-18784.3974427616
86357257458372.055187335-101115.055187335
87458343386482.1430640571860.85693595
88388386438493.47314242-50107.4731424198
89358934441849.116987032-82915.116987032
90407560436495.986245258-28935.9862452576
91392558410226.852260711-17668.8522607113
92373177410049.793667675-36872.7936676755
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95358649251016.478759975107632.521240025
96376641370516.780368656124.21963134984
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99436230496094.644649335-59864.6446493347
100329118345571.114765784-16453.1147657844
101317365342844.889446085-25479.8894460846
102286849401705.688927882-114856.688927882
103376685441905.495453132-65220.4954531318
104407198464022.766764836-56824.7667648360
105377772342060.38338557335711.6166144266
106271483353341.063069087-81858.0630690873
107153661369812.99603111-216151.99603111
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110264512358689.112617849-94177.1126178494
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201325560281480.66058569344079.3394143066
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305353417325169.48599192828247.5140080721
306325590331565.715485029-5975.71548502871
307325560281480.66058569344079.3394143066
308328576290688.71161941137887.2883805887
309326126311420.43022620614705.5697737941
310325560281480.66058569344079.3394143066
311325560281480.66058569344079.3394143066
312369376395957.379630842-26581.3796308419
313325560281480.66058569344079.3394143066
314332013286736.58652530645276.4134746942
315325871332457.715528667-6586.71552866691
316342165343460.620142037-1295.62014203656
317324967330870.191880217-5903.19188021737
318314832329266.137815753-14434.1378157527
319325557332030.706503680-6473.70650368036
320325560333038.56102361-7478.56102360978
321325560333038.56102361-7478.56102360978
322325560333038.56102361-7478.56102360978
323325560333038.56102361-7478.56102360978
324325560281480.66058569344079.3394143066
325325560333038.56102361-7478.56102360978
326322649332585.134094022-9936.13409402187
327325560281480.66058569344079.3394143066
328325560281480.66058569344079.3394143066
329325560333038.56102361-7478.56102360978
330325560333038.56102361-7478.56102360978
331325560333038.56102361-7478.56102360978
332325560333038.56102361-7478.56102360978
333325560333038.56102361-7478.56102360978
334324598330803.353656881-6205.35365688097
335325567332717.097458348-7150.09745834803
336325560333038.56102361-7478.56102360978
337324005331928.341835114-7923.34183511383
338325560333038.56102361-7478.56102360978
339325748333161.509513572-7413.50951357248
340323385327639.292044779-4254.29204477902
341315409334589.039325114-19180.0393251136
342325560333038.56102361-7478.56102360978
343325560333038.56102361-7478.56102360978
344325560333038.56102361-7478.56102360978
345325560333038.56102361-7478.56102360978
346325560333038.56102361-7478.56102360978
347312275327331.315229343-15056.3152293432
348325560333038.56102361-7478.56102360978
349325560333038.56102361-7478.56102360978
350325560333038.56102361-7478.56102360978
351320576323490.095258626-2914.09525862597
352325246332057.140235326-6811.1402353258
353332961324828.0188591348132.98114086573
354323010335288.671905273-12278.6719052729
355325560333038.56102361-7478.56102360978
356325560333038.56102361-7478.56102360978
357345253371868.681581674-26615.6815816744
358325560333038.56102361-7478.56102360978
359325560333038.56102361-7478.56102360978
360325560333038.56102361-7478.56102360978
361325559332371.446093368-6812.44609336789
362325560333038.56102361-7478.56102360978
363325560333038.56102361-7478.56102360978
364319634284079.60980842235554.3901915784
365319951327419.30915346-7468.30915346025
366325560333038.56102361-7478.56102360978
367325560333038.56102361-7478.56102360978
368325560333038.56102361-7478.56102360978
369325560333038.56102361-7478.56102360978
370325560333038.56102361-7478.56102360978
371325560333038.56102361-7478.56102360978
372318519321270.960148667-2751.96014866701
373343222370596.371293345-27374.3712933454
374317234342073.860537738-24839.8605377381
375325560333038.56102361-7478.56102360978
376325560333038.56102361-7478.56102360978
377314025316434.046652972-2409.04665297192
378320249327028.617646179-6779.617646179
379325560333038.56102361-7478.56102360978
380325560333038.56102361-7478.56102360978
381325560333038.56102361-7478.56102360978
382349365356127.305620641-6762.30562064087
383289197259507.82994135529689.1700586451
384325560333038.56102361-7478.56102360978
385329245335029.110817511-5784.11081751147
386240869331477.006900867-90608.0069008672
387327182328629.139443817-1447.13944381705
388322876321144.7158641291731.28413587112
389323117331324.695311142-8207.6953111419
390306351321605.488380488-15254.4883804876
391335137334167.586842876969.413157123832
392308271325618.539145254-17347.5391452541
393301731328912.737412711-27181.7374127112
394382409346310.82980220636098.1701977942
395279230430568.284783427-151338.284783427
396298731321883.549247523-23152.5492475234
397243650276454.505681773-32804.5056817725
398532682440269.87142935392412.1285706471
399319771336510.360849701-16739.3608497010
400171493218736.937607471-47243.9376074706
401347262350500.84664854-3238.84664853989
402343945336016.9529123937928.04708760707
403311874324361.081327964-12487.0813279645
404302211340868.587589591-38657.5875895906
405316708337456.025051779-20748.0250517795
406333463349658.198684162-16195.1986841616
407344282345603.873922054-1321.87392205442
408319635321020.737503065-1385.73750306536
409301186322603.328468378-21417.3284683782
410300381351537.576013773-51156.576013773
411318765341478.867843827-22713.8678438271
412286146489351.179200866-203205.179200866
413306844309695.983252357-2851.98325235735
414307705408931.217465746-101226.217465746
415312448371257.593214747-58809.5932147474
416299715358945.025385119-59230.0253851186
417373399230269.613517485143129.386482515
418299446317340.729932673-17894.7299326732
419325586343847.055869754-18261.0558697541
420291221341766.122847501-50545.1228475008
421261173349492.134789147-88319.1347891467
422255027340165.279139763-85138.2791397633
423-78375490122.028562986-568497.028562986
424-58143278680.36851964-336823.36851964
425227033301604.640484821-74571.6404848211
426235098418669.335934659-183571.335934659
42721267280100.403163127-258833.403163127
428238675461748.617488291-223073.617488291
429197687324397.276278963-126710.276278963
430418341281829.083681384136511.916318616
431-29770681190.0305754425-378896.030575442


Goldfeld-Quandt test for Heteroskedasticity
p-valuesAlternative Hypothesis
breakpoint indexgreater2-sidedless
1115.08394136191042e-922.54197068095521e-92
1211.53214508183024e-997.66072540915121e-100
1313.65740444750403e-1131.82870222375202e-113
1411.04640036554998e-1205.23200182774992e-121
1511.23517441039347e-1256.17587205196734e-126
1611.94130559635344e-1369.70652798176718e-137
1715.81708574242861e-1392.90854287121430e-139
1813.30468495323336e-1401.65234247661668e-140
1918.37289008308297e-1464.18644504154149e-146
2019.5040936069431e-1494.75204680347155e-149
2111.41036451440825e-1537.05182257204127e-154
2213.38517803052837e-1571.69258901526418e-157
2317.7202634289005e-1583.86013171445025e-158
2417.91884378218446e-1593.95942189109223e-159
2511.20970582399157e-1586.04852911995785e-159
2611.49768390416793e-1607.48841952083965e-161
2711.83326661744947e-1639.16633308724733e-164
2814.02244190116406e-1662.01122095058203e-166
2916.83268133382341e-1793.41634066691171e-179
3019.68634159525702e-1814.84317079762851e-181
3113.97140707831915e-1841.98570353915958e-184
3217.28100565802655e-1863.64050282901328e-186
3315.05188506107250e-1922.52594253053625e-192
3411.40053647515494e-1937.0026823757747e-194
3511.08406978961258e-1925.42034894806291e-193
3611.73369909596349e-1928.66849547981743e-193
3711.39951014075523e-1996.99755070377615e-200
3811.00507662909093e-2045.02538314545463e-205
3913.00097143741025e-2041.50048571870512e-204
4017.0830069941228e-2053.5415034970614e-205
4116.74649518600588e-2073.37324759300294e-207
4212.62227844329336e-2071.31113922164668e-207
4311.98182234605058e-2079.9091117302529e-208
4411.05147637818140e-2065.25738189090699e-207
4511.73424781250499e-2068.67123906252496e-207
4615.39612863817527e-2062.69806431908764e-206
4715.80157798736883e-2052.90078899368441e-205
4811.49198592775506e-2047.45992963877531e-205
4915.66582494267438e-2042.83291247133719e-204
5011.0618585607886e-2045.309292803943e-205
5118.9951765889645e-2064.49758829448225e-206
5216.19627875738608e-2053.09813937869304e-205
5312.54825753169678e-2041.27412876584839e-204
5412.99004106448643e-2031.49502053224322e-203
5512.60590089383921e-2071.30295044691960e-207
5615.21864039180576e-2082.60932019590288e-208
5711.04779828347759e-2125.23899141738793e-213
5819.51708566285217e-2144.75854283142609e-214
5914.82255278334875e-2132.41127639167437e-213
6011.52030545432483e-2137.60152727162416e-214
6113.26069268022895e-2151.63034634011447e-215
6215.51383107192765e-2152.75691553596382e-215
6312.20151082375449e-2141.10075541187725e-214
6414.30703788016079e-2142.15351894008039e-214
6517.45048250281062e-2143.72524125140531e-214
6619.47174722200555e-2144.73587361100278e-214
6716.2533241962136e-2153.1266620981068e-215
6815.98692461810832e-2142.99346230905416e-214
6911.91875677575813e-2139.59378387879065e-214
7017.63727111301774e-2133.81863555650887e-213
7113.69391378859169e-2121.84695689429584e-212
7211.32698494878050e-2146.63492474390249e-215
7312.49770692537592e-2141.24885346268796e-214
7411.91933945949328e-2139.5966972974664e-214
7511.29424168842658e-2126.47120844213292e-213
7616.22058365781995e-2123.11029182890997e-212
7711.55914078877348e-2117.79570394386742e-212
7812.29519250264517e-2111.14759625132258e-211
7912.45794986373658e-2101.22897493186829e-210
8011.45330799316557e-2117.26653996582787e-212
8111.01886595352085e-2105.09432976760424e-211
8218.26285377361961e-2114.13142688680980e-211
8313.81498028805752e-2111.90749014402876e-211
8413.5831026427251e-2101.79155132136255e-210
8513.21171879354759e-2091.60585939677379e-209
8614.85108655970443e-2102.42554327985221e-210
8714.50802718329163e-2102.25401359164582e-210
8814.32829371807625e-2092.16414685903812e-209
8911.25580794908058e-2086.27903974540288e-209
9011.18666953477424e-2075.93334767387118e-208
9111.21498835162035e-2066.07494175810175e-207
9215.95314339259609e-2062.97657169629804e-206
9318.56665658334322e-2074.28332829167161e-207
9414.52664120131445e-2062.26332060065722e-206
9516.8930182626099e-2073.44650913130495e-207
9611.95383897454220e-2079.76919487271098e-208
9718.2398352999743e-2074.11991764998715e-207
9818.14780610508176e-2064.07390305254088e-206
9916.9180801074457e-2053.45904005372285e-205
10017.24315315797623e-2043.62157657898812e-204
10117.09651927465742e-2033.54825963732871e-203
10216.96507111862366e-2033.48253555931183e-203
10313.88043982857987e-2021.94021991428994e-202
10413.49285313048032e-2011.74642656524016e-201
10511.41848487111267e-2007.09242435556333e-201
10613.1325982180579e-2001.56629910902895e-200
10713.79325746460594e-2011.89662873230297e-201
10819.6109823456077e-2044.80549117280385e-204
10918.63721179728476e-2034.31860589864238e-203
11013.54931577411001e-2021.77465788705500e-202
11111.78994963815902e-2028.94974819079509e-203
11211.78353484042478e-2038.9176742021239e-204
11317.22776652890255e-2053.61388326445128e-205
11414.40917519870053e-2042.20458759935027e-204
11511.39708574302574e-2036.98542871512872e-204
11613.90064640367045e-2031.95032320183522e-203
11714.06727662913458e-2022.03363831456729e-202
11812.2683028098963e-2031.13415140494815e-203
11913.59109423540181e-2041.79554711770090e-204
12013.43972308046694e-2031.71986154023347e-203
12119.86735510485847e-2054.93367755242923e-205
12217.35684785132238e-2043.67842392566119e-204
12313.35925952486751e-2031.67962976243376e-203
12411.60175586331958e-2048.0087793165979e-205
12511.66098979400005e-2038.30494897000024e-204
12611.79600116493436e-2038.9800058246718e-204
12711.99030945092425e-2029.95154725462125e-203
12812.19984165908637e-2011.09992082954318e-201
12912.42476744432795e-2001.21238372216397e-200
13012.6476732861498e-1991.3238366430749e-199
13112.88195353737527e-1981.44097676868764e-198
13211.41885418199597e-1987.09427090997987e-199
13311.54103320788880e-1977.70516603944402e-198
13411.66057096065881e-1968.30285480329405e-197
13511.7860006353844e-1958.930003176922e-196
13611.84405702984807e-1949.22028514924036e-195
13711.97030779902124e-1939.85153899510619e-194
13812.08787279585852e-1921.04393639792926e-192
13912.20149509703835e-1911.10074754851918e-191
14012.30977864489818e-1901.15488932244909e-190
14112.40878354216859e-1891.20439177108430e-189
14212.5020453937354e-1881.2510226968677e-188
14312.15014308231356e-1871.07507154115678e-187
14412.21508134556178e-1861.10754067278089e-186
14511.81229118759045e-1859.06145593795224e-186
14611.80339120340691e-1849.01695601703453e-185
14711.82940089367416e-1839.14700446837079e-184
14811.84653142087122e-1829.23265710435609e-183
14911.85454827196496e-1819.27274135982482e-182
15011.85380236085226e-1809.2690118042613e-181
15111.84154408287019e-1799.20772041435095e-180
15211.28697417361344e-1786.4348708680672e-179
15311.26832604029382e-1776.3416302014691e-178
15411.14908844799997e-1765.74544223999984e-177
15511.12182621444056e-1755.6091310722028e-176
15611.08957491101526e-1745.44787455507629e-175
15711.05301240315635e-1735.26506201578176e-174
15811.01321373267333e-1725.06606866336664e-173
15918.23121625803006e-1724.11560812901503e-172
16017.8427693958215e-1713.92138469791075e-171
16117.43581943384109e-1703.71790971692054e-170
16217.01526503148632e-1693.50763251574316e-169
16316.58593082442893e-1683.29296541221446e-168
16415.80365942101376e-1672.90182971050688e-167
16515.40159764365887e-1662.70079882182943e-166
16614.99741322621935e-1652.49870661310968e-165
16714.60083805177421e-1642.30041902588710e-164
16811.25031301986506e-1646.25156509932529e-165
16911.15593888113180e-1635.77969440565898e-164
17011.06349267406024e-1625.31746337030119e-163
17119.73687366339644e-1624.86843683169822e-162
17218.85086172493491e-1614.42543086246746e-161
17318.02512938248992e-1604.01256469124496e-160
17417.19725522458023e-1593.59862761229012e-159
17516.46292296672105e-1583.23146148336052e-158
17615.77950929180372e-1572.88975464590186e-157
17715.13975106315919e-1562.56987553157959e-156
17814.49297565696952e-1552.24648782848476e-155
17913.95637673586605e-1541.97818836793303e-154
18013.46710856461412e-1531.73355428230706e-153
18118.05121679608323e-1534.02560839804161e-153
18216.01383855043677e-1523.00691927521839e-152
18314.06023392899598e-1512.03011696449799e-151
18412.58300785973248e-1501.29150392986624e-150
18512.19711474647973e-1491.09855737323987e-149
18611.79001836811388e-1488.95009184056941e-149
18719.32707916332608e-1484.66353958166304e-148
18817.91373537354252e-1473.95686768677126e-147
18915.66483968275183e-1462.83241984137592e-146
19014.78385418763035e-1452.39192709381517e-145
19113.84709332139976e-1441.92354666069988e-144
19213.21873401919376e-1431.60936700959688e-143
19312.63603214839338e-1421.31801607419669e-142
19412.18481646370926e-1411.09240823185463e-141
19511.80271838265538e-1409.01359191327688e-141
19611.46412636550572e-1397.32063182752862e-140
19717.81516103389757e-1393.90758051694879e-139
19816.30153834423008e-1383.15076917211504e-138
19915.05966390798824e-1372.52983195399412e-137
20012.92594661752071e-1361.46297330876036e-136
20112.3323260190265e-1351.16616300951325e-135
20211.85120800569878e-1349.25604002849389e-135
20311.46303221321523e-1337.31516106607617e-134
20411.14456044738380e-1325.72280223691902e-133
20517.57874593252716e-1323.78937296626358e-132
20615.9151860035464e-1312.9575930017732e-131
20714.58307659477178e-1302.29153829738589e-130
20813.54566757333531e-1291.77283378666766e-129
20914.79203057136556e-1292.39601528568278e-129
21013.70473021384567e-1281.85236510692284e-128
21112.86545997409748e-1271.43272998704874e-127
21212.20598203406429e-1261.10299101703214e-126
21311.65172603271139e-1258.25863016355695e-126
21411.22864927944801e-1246.14324639724006e-125
21519.22326242580827e-1244.61163121290414e-124
21616.9707739625857e-1233.48538698129285e-123
21715.2462998133848e-1222.6231499066924e-122
21813.82616832597167e-1211.91308416298584e-121
21912.85159689294575e-1201.42579844647287e-120
22011.40034612539293e-1197.00173062696466e-120
22118.75414925662466e-1194.37707462831233e-119
22216.45205295276505e-1183.22602647638253e-118
22314.73368648804449e-1172.36684324402225e-117
22413.45613914801006e-1161.72806957400503e-116
22512.51168559647767e-1151.25584279823883e-115
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35911.88500696948923e-219.42503484744615e-22
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3720.9999999999999975.78453884423206e-152.89226942211603e-15
3730.9999999999999921.69710408885765e-148.48552044428826e-15
3740.9999999999999754.94177032177756e-142.47088516088878e-14
3750.9999999999999291.42176940753715e-137.10884703768573e-14
3760.9999999999997984.04357480234684e-132.02178740117342e-13
3770.999999999999431.14043952142018e-125.70219760710092e-13
3780.9999999999984283.14487103188104e-121.57243551594052e-12
3790.9999999999956858.63034427788839e-124.31517213894419e-12
3800.9999999999883042.33911213489193e-111.16955606744596e-11
3810.99999999996876.25978346458318e-113.12989173229159e-11
3820.9999999999180461.63908544432858e-108.19542722164288e-11
3830.9999999998029163.94167984853247e-101.97083992426623e-10
3840.999999999491221.01755844655987e-095.08779223279933e-10
3850.999999998700922.59816021318899e-091.29908010659450e-09
3860.9999999972570645.48587171502496e-092.74293585751248e-09
3870.9999999932188131.35623748924512e-086.7811874462256e-09
3880.9999999840545493.18909022182876e-081.59454511091438e-08
3890.9999999613667737.72664537911535e-083.86332268955768e-08
3900.9999999074009831.85198033279203e-079.25990166396016e-08
3910.999999786160354.27679298036193e-072.13839649018097e-07
3920.9999995030742729.93851455242344e-074.96925727621172e-07
3930.9999988609886542.27802269163924e-061.13901134581962e-06
3940.9999978367823924.32643521648201e-062.16321760824101e-06
3950.9999954886288679.02274226542304e-064.51137113271152e-06
3960.9999900958729941.98082540124548e-059.90412700622738e-06
3970.9999804954937163.90090125680493e-051.95045062840246e-05
3980.999960663507097.86729858186002e-053.93364929093001e-05
3990.9999182904191720.0001634191616562668.17095808281332e-05
4000.999877008047940.0002459839041176260.000122991952058813
4010.999758444014810.000483111970378090.000241555985189045
4020.999548149339890.0009037013202222050.000451850660111103
4030.9991385823965230.001722835206954610.000861417603477305
4040.9983439938757170.003312012248566010.00165600612428300
4050.9969256247172690.006148750565462630.00307437528273132
4060.9944487437807820.01110251243843670.00555125621921833
4070.9903315547147830.01933689057043450.00966844528521727
4080.9842337004607990.03153259907840250.0157662995392013
4090.9737508523132540.0524982953734930.0262491476867465
4100.956589919741390.08682016051721820.0434100802586091
4110.9305377796986150.1389244406027690.0694622203013846
4120.8941316333114750.211736733377050.105868366688525
4130.8456750759788210.3086498480423580.154324924021179
4140.7804252108097330.4391495783805330.219574789190267
4150.6944754669734750.6110490660530490.305524533026525
4160.5901293842419210.8197412315161570.409870615758079
4170.8756992932878020.2486014134243960.124300706712198
4180.7858569765425020.4282860469149960.214143023457498
4190.6622700632913190.6754598734173620.337729936708681
4200.4985274233528070.9970548467056140.501472576647193


Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity
Description# significant tests% significant testsOK/NOK
1% type I error level3950.963414634146341NOK
5% type I error level3980.970731707317073NOK
10% type I error level4000.97560975609756NOK
 
Charts produced by software:
http://www.freestatistics.org/blog/date/2010/Dec/22/t1293014206lqhd0q0qp4auhau/107trg1293014244.png (open in new window)
http://www.freestatistics.org/blog/date/2010/Dec/22/t1293014206lqhd0q0qp4auhau/107trg1293014244.ps (open in new window)


http://www.freestatistics.org/blog/date/2010/Dec/22/t1293014206lqhd0q0qp4auhau/10ac41293014244.png (open in new window)
http://www.freestatistics.org/blog/date/2010/Dec/22/t1293014206lqhd0q0qp4auhau/10ac41293014244.ps (open in new window)


http://www.freestatistics.org/blog/date/2010/Dec/22/t1293014206lqhd0q0qp4auhau/20ac41293014244.png (open in new window)
http://www.freestatistics.org/blog/date/2010/Dec/22/t1293014206lqhd0q0qp4auhau/20ac41293014244.ps (open in new window)


http://www.freestatistics.org/blog/date/2010/Dec/22/t1293014206lqhd0q0qp4auhau/30ac41293014244.png (open in new window)
http://www.freestatistics.org/blog/date/2010/Dec/22/t1293014206lqhd0q0qp4auhau/30ac41293014244.ps (open in new window)


http://www.freestatistics.org/blog/date/2010/Dec/22/t1293014206lqhd0q0qp4auhau/4t2tp1293014244.png (open in new window)
http://www.freestatistics.org/blog/date/2010/Dec/22/t1293014206lqhd0q0qp4auhau/4t2tp1293014244.ps (open in new window)


http://www.freestatistics.org/blog/date/2010/Dec/22/t1293014206lqhd0q0qp4auhau/5t2tp1293014244.png (open in new window)
http://www.freestatistics.org/blog/date/2010/Dec/22/t1293014206lqhd0q0qp4auhau/5t2tp1293014244.ps (open in new window)


http://www.freestatistics.org/blog/date/2010/Dec/22/t1293014206lqhd0q0qp4auhau/64taa1293014244.png (open in new window)
http://www.freestatistics.org/blog/date/2010/Dec/22/t1293014206lqhd0q0qp4auhau/64taa1293014244.ps (open in new window)


http://www.freestatistics.org/blog/date/2010/Dec/22/t1293014206lqhd0q0qp4auhau/7wk9v1293014244.png (open in new window)
http://www.freestatistics.org/blog/date/2010/Dec/22/t1293014206lqhd0q0qp4auhau/7wk9v1293014244.ps (open in new window)


http://www.freestatistics.org/blog/date/2010/Dec/22/t1293014206lqhd0q0qp4auhau/8wk9v1293014244.png (open in new window)
http://www.freestatistics.org/blog/date/2010/Dec/22/t1293014206lqhd0q0qp4auhau/8wk9v1293014244.ps (open in new window)


http://www.freestatistics.org/blog/date/2010/Dec/22/t1293014206lqhd0q0qp4auhau/9wk9v1293014244.png (open in new window)
http://www.freestatistics.org/blog/date/2010/Dec/22/t1293014206lqhd0q0qp4auhau/9wk9v1293014244.ps (open in new window)


 
Parameters (Session):
par1 = 8 ; par2 = Do not include Seasonal Dummies ; par3 = No Linear Trend ;
 
Parameters (R input):
par1 = 8 ; 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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Software written by Ed van Stee & Patrick Wessa


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