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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, 24 Nov 2010 09:22:15 +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/Nov/24/t1290590490vv0zjp3p541qmp2.htm/, Retrieved Wed, 24 Nov 2010 10:21:30 +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/Nov/24/t1290590490vv0zjp3p541qmp2.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 «
1 162556 162556 1081 1081 213118 213118 230380558 6282929 1 29790 29790 309 309 81767 81767 25266003 4324047 1 87550 87550 458 458 153198 153198 70164684 4108272 0 84738 0 588 0 -26007 -0 -15292116 -1212617 1 54660 54660 299 299 126942 126942 37955658 1485329 1 42634 42634 156 156 157214 157214 24525384 1779876 0 40949 0 481 0 129352 0 62218312 1367203 1 42312 42312 323 323 234817 234817 75845891 2519076 1 37704 37704 452 452 60448 60448 27322496 912684 1 16275 16275 109 109 47818 47818 5212162 1443586 0 25830 0 115 0 245546 0 28237790 1220017 0 12679 0 110 0 48020 0 5282200 984885 1 18014 18014 239 239 -1710 -1710 -408690 1457425 0 43556 0 247 0 32648 0 8064056 -572920 1 24524 24524 497 497 95350 95350 47388950 929144 0 6532 0 103 0 151352 0 15589256 1151176 0 7123 0 109 0 288170 0 31410530 790090 1 20813 20813 502 502 114337 114337 57397174 774497 1 37597 37597 248 248 37884 37884 9395232 990576 0 17821 0 373 0 122844 0 45820812 454195 1 12988 12988 119 119 82340 82340 9798460 876607 1 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 time20 seconds
R Server'Sir Ronald Aylmer Fisher' @ 193.190.124.24


Multiple Linear Regression - Estimated Regression Equation
Wealth[t] = + 163762.659664875 + 70658.1155063091Group[t] -5.43448960658277Costs[t] + 38.5712533454338GrCosts[t] -581.876599718096Trades[t] -70.3635153411706GrTrades[t] + 2.7041924766397Dividends[t] -1.64332857766759GrDiv[t] + 0.00640665268048797TrDiv[t] + e[t]


Multiple Linear Regression - Ordinary Least Squares
VariableParameterS.D.T-STAT
H0: parameter = 0		2-tail p-value1-tail p-value
(Intercept)163762.65966487534306.115394.77362e-061e-06
Group70658.115506309155872.9697311.26460.2067050.103353
Costs-5.434489606582772.424738-2.24130.0255280.012764
GrCosts38.57125334543383.74401110.302100
Trades-581.876599718096278.135559-2.09210.037030.018515
GrTrades-70.3635153411706340.450565-0.20670.8363610.418181
Dividends2.70419247663970.4764765.675400
GrDiv-1.643328577667590.70885-2.31830.020910.010455
TrDiv0.006406652680487970.0021153.02850.0026080.001304


Multiple Linear Regression - Regression Statistics
Multiple R0.887183427060639
R-squared0.78709443325106
Adjusted R-squared0.783058308762928
F-TEST (value)195.012427284032
F-TEST (DF numerator)8
F-TEST (DF denominator)422
p-value0
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation208393.352152515
Sum Squared Residuals18326527051414.8


Multiple Linear Regression - Actuals, Interpolation, and Residuals
Time or IndexActualsInterpolation
Forecast		Residuals
Prediction Error
162829296617986.38898894-335057.388988939
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71367203409746.920889049957456.07911095
825190762160857.12436939358218.875630611
99126841428169.62637512-515485.626375123
101443586786748.334049011656837.665950989
111220017801387.34302279418629.65697721
12984885194548.883491134790336.116508866
131457425671028.637512452786396.362487548
14-572920-76715.407804476-496204.592195524
159291441127661.34822831-198517.348228313
161151176577491.172247298573684.827752702
177900901042131.74304122-252041.743041225
187744971085691.45538445-311194.455384448
199905761418889.88915133-428313.889151335
20454195475626.497313377-21431.4973133769
21876607737311.352384347139295.647615653
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24264449438816.248050248-174367.248050248
25450033516428.701998247-66395.7019982471
26541063239332.658276364301730.341723636
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28-37216136882.171915981-174098.171915981
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30467359125493.879557454341865.120442546
31688779435897.254403975252881.745596025
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308328576306111.16826735622464.8317326437
309326126304455.25740983521670.7425901649
310325560298836.43111677126723.5688832287
311325560298836.43111677126723.5688832287
312369376395631.799027960-26255.7990279595
313325560298836.43111677126723.5688832287
314332013302121.04791242429891.9520875763
315325871327285.387364365-1414.38736436472
316342165339262.1118299962902.88817000388
317324967325610.299967406-643.29996740623
318314832323940.093829692-9108.09382969188
319325557326795.861830686-1238.86183068567
320325560327961.226846438-2401.22684643810
321325560327961.226846438-2401.22684643810
322325560327961.226846438-2401.22684643810
323325560327961.226846438-2401.22684643810
324325560298836.43111677126723.5688832287
325325560327961.226846438-2401.22684643810
326322649327461.372788740-4812.37278873955
327325560298836.43111677126723.5688832287
328325560298836.43111677126723.5688832287
329325560327961.226846438-2401.22684643810
330325560327961.226846438-2401.22684643810
331325560327961.226846438-2401.22684643810
332325560327961.226846438-2401.22684643810
333325560327961.226846438-2401.22684643810
334324598325542.139622057-944.139622057467
335325567327589.082099388-2022.08209938783
336325560327961.226846438-2401.22684643810
337324005326734.533649900-2729.53364990049
338325560327961.226846438-2401.22684643810
339325748328104.130914468-2356.13091446845
340323385322026.2209531251358.77904687524
341315409329714.029579793-14305.0295797929
342325560327961.226846438-2401.22684643810
343325560327961.226846438-2401.22684643810
344325560327961.226846438-2401.22684643810
345325560327961.226846438-2401.22684643810
346325560327961.226846438-2401.22684643810
347312275321763.63759636-9488.63759635994
348325560327961.226846438-2401.22684643810
349325560327961.226846438-2401.22684643810
350325560327961.226846438-2401.22684643810
351320576317636.9357304992939.06426950119
352325246326824.887617846-1578.88761784611
353332961319328.09931246113632.9006875386
354323010330496.214228423-7486.21422842266
355325560327961.226846438-2401.22684643810
356325560327961.226846438-2401.22684643810
357345253369993.269236206-24740.2692362064
358325560327961.226846438-2401.22684643810
359325560327961.226846438-2401.22684643810
360325560327961.226846438-2401.22684643810
361325559327189.793399171-1630.79339917080
362325560327961.226846438-2401.22684643810
363325560327961.226846438-2401.22684643810
364319634300919.15271489618714.8472851036
365319951321850.99534181-1899.99534180995
366325560327961.226846438-2401.22684643810
367325560327961.226846438-2401.22684643810
368325560327961.226846438-2401.22684643810
369325560327961.226846438-2401.22684643810
370325560327961.226846438-2401.22684643810
371325560327961.226846438-2401.22684643810
372318519315032.1189340913486.88106590942
373343222368971.552698681-25749.5526986815
374317234337936.217436147-20702.2174361466
375325560327961.226846438-2401.22684643810
376325560327961.226846438-2401.22684643810
377314025309694.0834047374330.91659526334
378320249321752.975470355-1503.97547035535
379325560327961.226846438-2401.22684643810
380325560327961.226846438-2401.22684643810
381325560327961.226846438-2401.22684643810
382349365352774.333904560-3409.33390456039
383289197247529.52813394241667.4718660582
384325560327961.226846438-2401.22684643810
385329245330008.766134447-763.766134447301
386240869327692.084865358-86823.0848653576
387327182323187.6731103293994.32688967066
388322876315615.8397819167260.1602180843
389323117326114.41084392-2997.41084392022
390306351315760.528720342-9409.52872034206
391335137329383.9233998915753.07660010923
392308271320128.942582978-11857.9425829783
393301731323863.200748874-22132.2007488743
394382409342871.74529173239537.2547082676
395279230435225.440393795-155995.440393795
396298731316088.950882269-17357.9508822689
397243650269623.918822756-25973.9188227557
398532682425392.688515589107289.311484411
399319771332050.434908833-12279.4349088329
400171493255706.965330241-84213.9653302406
401347262347758.618678768-496.618678768005
402343945331702.38282228212242.6171777180
403311874318882.004587077-7008.00458707719
404302211353361.140268918-51150.1402689176
405316708333153.04506781-16445.0450678101
406333463346832.734856854-13369.7348568538
407344282341947.3760461662334.62395383377
408319635315498.3539625164136.64603748366
409301186316800.211685507-15614.2116855071
410300381348655.99259033-48274.99259033
411318765337412.912669407-18647.9126694065
412286146505718.2447746-219572.2447746
413306844328955.503534256-22111.5035342559
414307705418293.42234755-110588.422347550
415312448370594.691650172-58146.6916501723
416299715356916.327220088-57201.3272200876
417373399217891.968187152155507.031812848
418299446333802.480163722-34356.4801637224
419325586340406.259750724-14820.2597507241
420291221337952.179929952-46731.1799299523
421261173346659.261904158-85486.2619041581
422255027337068.928186231-82041.9281862308
423-78375548811.380661323-627186.380661323
424-58143273443.223768383-331586.223768383
425227033295178.588228295-68145.5882282945
426235098432423.484599008-197325.484599008
42721267273019.723444757-251752.723444757
428238675490416.395546613-251741.395546613
429197687325013.890677954-127326.890677954
430418341282658.353957259135682.646042741
431-29770666052.3687006833-363758.368700683


Goldfeld-Quandt test for Heteroskedasticity
p-valuesAlternative Hypothesis
breakpoint indexgreater2-sidedless
1217.85125144720938e-1003.92562572360469e-100
1312.19116517333217e-1131.09558258666609e-113
1416.07267516206369e-1213.03633758103185e-121
1512.67178632099303e-1251.33589316049652e-125
1612.73136778968596e-1351.36568389484298e-135
1711.14830021211010e-1375.74150106055051e-138
1817.99386110463218e-1393.99693055231609e-139
1917.65985333469227e-1463.82992666734614e-146
2016.11807142156165e-1483.05903571078083e-148
2118.79125566583466e-1544.39562783291733e-154
2213.52518892530796e-1581.76259446265398e-158
2314.27448833238106e-1592.13724416619053e-159
2411.19964662455829e-1595.99823312279143e-160
2516.36435992143235e-1593.18217996071618e-159
2619.9998427651967e-1614.99992138259835e-161
2714.20970941321153e-1642.10485470660576e-164
2812.85663066585754e-1661.42831533292877e-166
2915.11218417759924e-1792.55609208879962e-179
3011.07118669593966e-1805.3559334796983e-181
3112.74932112566167e-1841.37466056283084e-184
3214.37017157819649e-1862.18508578909824e-186
3312.25660186008592e-1921.12830093004296e-192
3417.310422497883e-1943.6552112489415e-194
3517.13416144816881e-1933.56708072408441e-193
3611.27111558953126e-1926.35557794765631e-193
3717.61055695187331e-2003.80527847593666e-200
3818.52837358099755e-2054.26418679049878e-205
3914.02955341978635e-2042.01477670989317e-204
4012.04437016275046e-2041.02218508137523e-204
4112.06984162687483e-2061.03492081343742e-206
4211.00183257392765e-2065.00916286963824e-207
4317.1680542567473e-2073.58402712837365e-207
4414.67226007713934e-2062.33613003856967e-206
4511.13409014422652e-2055.67045072113258e-206
4611.98661265545849e-2059.93306327729245e-206
4712.01134950342912e-2041.00567475171456e-204
4815.77415752424975e-2042.88707876212487e-204
4912.33356562205959e-2031.16678281102979e-203
5018.27217991632305e-2044.13608995816153e-204
5117.63610975983228e-2053.81805487991614e-205
5215.3398987417748e-2042.6699493708874e-204
5312.07057805184281e-2031.03528902592141e-203
5412.47486310336157e-2021.23743155168079e-202
5512.85466231838554e-2071.42733115919277e-207
5617.6526910263813e-2083.82634551319065e-208
5712.35934080821546e-2121.17967040410773e-212
5812.01184810440423e-2131.00592405220212e-213
5911.52736643435564e-2127.63683217177818e-213
6013.52383033536460e-2131.76191516768230e-213
6111.20682872815659e-2146.03414364078296e-215
6212.84029187757288e-2141.42014593878644e-214
6311.11881667938861e-2135.59408339694305e-214
6411.51161765005045e-2137.55808825025225e-214
6513.17299464324306e-2131.58649732162153e-213
6613.76895980068761e-2131.88447990034380e-213
6713.64620185440556e-2141.82310092720278e-214
6813.45276386658486e-2131.72638193329243e-213
6911.53277099414184e-2127.66385497070922e-213
7016.26177398638633e-2123.13088699319317e-212
7111.36661126907383e-2116.83305634536914e-212
7216.44672755853211e-2143.22336377926606e-214
7311.52309042955462e-2137.61545214777312e-214
7411.36373216539032e-2126.8186608269516e-213
7511.05558580234839e-2115.27792901174194e-212
7613.96379466447609e-2111.98189733223805e-211
7711.17811918786767e-2105.89059593933835e-211
7812.05610482731136e-2101.02805241365568e-210
7912.27508841638406e-2091.13754420819203e-209
8011.16866457567227e-2105.84332287836133e-211
8118.8053354189484e-2104.4026677094742e-210
8217.3427514787423e-2103.67137573937115e-210
8313.76869312310473e-2101.88434656155237e-210
8413.73964465788107e-2091.86982232894054e-209
8513.58954716426106e-2081.79477358213053e-208
8614.1225086922304e-2092.0612543461152e-209
8713.91414737357389e-2091.95707368678695e-209
8814.0080489282504e-2082.0040244641252e-208
8911.19947959471071e-2075.99739797355355e-208
9011.20572038969398e-2066.02860194846988e-207
9111.28818912812913e-2056.44094564064564e-206
9215.51273318952035e-2052.75636659476017e-205
9317.56175029017044e-2063.78087514508522e-206
9414.11316568925684e-2052.05658284462842e-205
9515.67390431509792e-2062.83695215754896e-206
9611.46472483589059e-2067.32362417945295e-207
9716.77166980119121e-2063.38583490059561e-206
9816.78379133999101e-2053.39189566999551e-205
9915.97019220765457e-2042.98509610382729e-204
10015.68351384823571e-2032.84175692411785e-203
10115.1578295402038e-2022.5789147701019e-202
10215.34900976452674e-2022.67450488226337e-202
10312.87803257759788e-2011.43901628879894e-201
10412.50584632287278e-2001.25292316143639e-200
10511.05263527084093e-1995.26317635420464e-200
10612.38930946096676e-1991.19465473048338e-199
10712.07970825976844e-2001.03985412988422e-200
10812.84537557212071e-2031.42268778606035e-203
10912.35301246867954e-2021.17650623433977e-202
11019.21168581785473e-2024.60584290892736e-202
11114.99394243840713e-2022.49697121920357e-202
11212.91897417563603e-2031.45948708781802e-203
11316.75718923425862e-2053.37859461712931e-205
11414.22017606653879e-2042.11008803326940e-204
11511.43460859274665e-2037.17304296373324e-204
11613.4134379526014e-2031.7067189763007e-203
11713.32929052758505e-2021.66464526379252e-202
11814.45141316344687e-2032.22570658172343e-203
11918.23962766037429e-2044.11981383018714e-204
12017.87643574203732e-2033.93821787101866e-203
12114.38568590705008e-2042.19284295352504e-204
12213.35439168231527e-2031.67719584115763e-203
12311.35131368604808e-2026.75656843024042e-203
12413.49335382573473e-2041.74667691286737e-204
12513.42062008707606e-2031.71031004353803e-203
12614.38603588795401e-2032.19301794397701e-203
12714.94179171352976e-2022.47089585676488e-202
12815.54605234050769e-2012.77302617025385e-201
12916.15879780720296e-2003.07939890360148e-200
13016.82741330209294e-1993.41370665104647e-199
13117.53691136932179e-1983.76845568466090e-198
13213.19494047554963e-1981.59747023777482e-198
13313.52127037769803e-1971.76063518884901e-197
13413.85147141256603e-1961.92573570628302e-196
13514.20002857673364e-1952.10001428836682e-195
13614.35762755823189e-1942.17881377911594e-194
13714.71147717900429e-1932.35573858950215e-193
13815.05661443378769e-1922.52830721689385e-192
13915.39825121708729e-1912.69912560854364e-191
14015.73241584984387e-1902.86620792492194e-190
14116.01317404387181e-1893.00658702193590e-189
14216.31782698274428e-1883.15891349137214e-188
14315.25087649445653e-1872.62543824722827e-187
14415.4664023744088e-1862.7332011872044e-186
14514.52711126768347e-1852.26355563384173e-185
14614.46085178760299e-1842.23042589380150e-184
14714.57193754726988e-1832.28596877363494e-183
14814.66129863820546e-1822.33064931910273e-182
14914.72752517306983e-1812.36376258653492e-181
15014.7700231542396e-1802.3850115771198e-180
15114.76034463843369e-1792.38017231921684e-179
15213.28928771595800e-1781.64464385797900e-178
15313.27113208573676e-1771.63556604286838e-177
15413.03913457327119e-1761.51956728663560e-176
15512.99229348215425e-1751.49614674107712e-175
15612.93074685382129e-1741.46537342691065e-174
15712.85570516110599e-1731.42785258055300e-173
15812.76740274618534e-1721.38370137309267e-172
15912.23251393143572e-1711.11625696571786e-171
16012.14356301517168e-1701.07178150758584e-170
16112.047658994016e-1691.023829497008e-169
16211.94608777217690e-1689.73043886088448e-169
16311.84015634290039e-1679.20078171450196e-168
16411.61991970146757e-1668.09959850733785e-167
16511.51531488799680e-1657.57657443998398e-166
16611.41146204645263e-1647.05731023226313e-165
16711.30809944190603e-1636.54049720953014e-164
16811.99980218631491e-1649.99901093157454e-165
16911.86496761606856e-1639.3248380803428e-164
17011.73052975588383e-1628.65264877941916e-163
17111.59776836754952e-1617.98884183774758e-162
17211.46550011728701e-1607.32750058643505e-161
17311.3396467753167e-1596.6982338765835e-160
17411.20892761805529e-1586.04463809027643e-159
17511.09418328654973e-1575.47091643274867e-158
17619.8560667502091e-1574.92803337510455e-157
17718.83244440826989e-1564.41622220413494e-156
17817.89241545623706e-1553.94620772811853e-155
17917.00265408486395e-1543.50132704243198e-154
18016.18261515365466e-1533.09130757682733e-153
18111.69917517707377e-1528.49587588536885e-153
18211.27345928498102e-1516.36729642490511e-152
18318.11126551691675e-1514.05563275845838e-151
18415.20897839996945e-1502.60448919998472e-150
18514.53061878002764e-1492.26530939001382e-149
18613.77816243667856e-1481.88908121833928e-148
18712.040726865831e-1471.0203634329155e-147
18811.74100379012615e-1468.70501895063073e-147
18911.22897122509530e-1456.14485612547652e-146
19011.04467612838592e-1445.22338064192959e-145
19118.32004125861331e-1444.16002062930666e-144
19217.0055869981287e-1433.50279349906435e-143
19315.75209490776214e-1422.87604745388107e-142
19414.79690941135141e-1412.39845470567571e-141
19513.98073940901288e-1401.99036970450644e-140
19613.29084419776701e-1391.64542209888350e-139
19712.39033987736106e-1381.19516993868053e-138
19811.95826625974194e-1379.79133129870968e-138
19911.59648196300461e-1367.98240981502304e-137
20019.86781252627668e-1364.93390626313834e-136
20117.97368774186378e-1353.98684387093189e-135
20216.41172806814164e-1343.20586403407082e-134
20315.1305999472883e-1332.56529997364415e-133
20414.08969696492586e-1322.04484848246293e-132
20512.91922395790976e-1311.45961197895488e-131
20612.30192949455416e-1301.15096474727708e-130
20711.79601094231981e-1298.98005471159903e-130
20811.40268226536127e-1287.01341132680636e-129
20912.33848453203932e-1281.16924226601966e-128
21011.82480656293133e-1279.12403281465663e-128
21111.41511495686373e-1267.07557478431863e-127
21211.09215420455163e-1255.46077102275815e-126
21318.12247738540908e-1254.06123869270454e-125
21416.07273791263065e-1243.03636895631533e-124
21514.56764620581275e-1232.28382310290638e-123
21613.45929229865641e-1221.72964614932820e-122
21712.60723367724666e-1211.30361683862333e-121
21811.89720018034737e-1209.48600090173684e-121
21911.41646296650019e-1197.08231483250094e-120
22016.63075819483809e-1193.31537909741905e-119
22114.21042787523831e-1182.10521393761915e-118
22213.10826990148276e-1171.55413495074138e-117
22312.28371786204695e-1161.14185893102347e-116
22411.66977068450079e-1158.34885342250396e-116
22511.21480467324468e-1146.0740233662234e-115
22618.65982257631623e-1144.32991128815811e-114
22716.24128469524267e-1133.12064234762134e-113
22814.47656549558165e-1122.23828274779083e-112
22913.07009339368719e-1111.53504669684359e-111
23012.18145762205030e-1101.09072881102515e-110
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34817.55342271012003e-273.77671135506002e-27
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35019.9274561962875e-264.96372809814375e-26
35113.53121578164861e-251.76560789082431e-25
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35515.00831675656683e-232.50415837828342e-23
35611.71890613691995e-228.59453068459975e-23
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35811.74390048028400e-218.71950240142002e-22
35915.8347528499151e-212.91737642495755e-21
36011.93416001716541e-209.67080008582707e-21
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37011.83090433204441e-159.15452166022205e-16
3710.9999999999999975.43251596100976e-152.71625798050488e-15
3720.9999999999999921.60812523934868e-148.0406261967434e-15
3730.9999999999999774.62954406035348e-142.31477203017674e-14
3740.9999999999999331.33675748144439e-136.68378740722195e-14
3750.999999999999813.79781372798376e-131.89890686399188e-13
3760.9999999999994671.06625649751938e-125.3312824875969e-13
3770.9999999999985142.97278764205520e-121.48639382102760e-12
3780.9999999999959588.08402300437208e-124.04201150218604e-12
3790.999999999989062.18789235167555e-111.09394617583777e-11
3800.9999999999707715.84577279263208e-112.92288639631604e-11
3810.9999999999229241.5415172383979e-107.7075861919895e-11
3820.9999999998063223.87356260509940e-101.93678130254970e-10
3830.9999999995369749.2605118416374e-104.6302559208187e-10
3840.9999999988232.35399995295035e-091.17699997647518e-09
3850.999999997024465.95108113549e-092.975540567745e-09
3860.9999999939317011.21365978744696e-086.06829893723481e-09
3870.9999999852550142.94899719248486e-081.47449859624243e-08
3880.9999999663648556.7270290072212e-083.3635145036106e-08
3890.9999999198179461.60364107725635e-078.01820538628177e-08
3900.999999810378853.79242301391817e-071.89621150695908e-07
3910.9999995684978968.63004207179112e-074.31502103589556e-07
3920.999999013079931.97384014185768e-069.86920070928838e-07
3930.9999977651082634.46978347445359e-062.23489173722680e-06
3940.9999957759502348.44809953264923e-064.22404976632462e-06
3950.9999913853336671.72293326668780e-058.61466633343901e-06
3960.9999813884747263.72230505475205e-051.86115252737602e-05
3970.9999656382456196.87235087629668e-053.43617543814834e-05
3980.9999298574672820.0001402850654358287.01425327179138e-05
3990.9998565279479240.0002869441041516040.000143472052075802
4000.9997498440988160.0005003118023677510.000250155901183875
4010.99951690817690.0009661836461993120.000483091823099656
4020.999117652077450.001764695845100330.000882347922550163
4030.9983704203909150.00325915921816940.0016295796090847
4040.9969592072887650.006081585422469680.00304079271123484
4050.9945000467027530.01099990659449460.00549995329724729
4060.9902794922131720.01944101557365530.00972050778682764
4070.9834526300813790.03309473983724240.0165473699186212
4080.9740392243267580.05192155134648450.0259607756732422
4090.9583871333611510.08322573327769740.0416128666388487
4100.9330290911174620.1339418177650760.066970908882538
4110.8963088769511430.2073822460977140.103691123048857
4120.8463392087650150.3073215824699690.153660791234985
4130.7773995649010640.4452008701978710.222600435098936
4140.689603338931710.6207933221365790.310396661068289
4150.5858268021391020.8283463957217970.414173197860898
4160.4683596983699310.9367193967398630.531640301630069
4170.7841718480925340.4316563038149310.215828151907466
4180.6533324118379090.6933351763241830.346667588162091
4190.4907133769657860.9814267539315720.509286623034214


Meta Analysis of Goldfeld-Quandt test for Heteroskedasticity
Description# significant tests% significant testsOK/NOK
1% type I error level3930.963235294117647NOK
5% type I error level3960.970588235294118NOK
10% type I error level3980.975490196078431NOK
 
Charts produced by software:
http://www.freestatistics.org/blog/date/2010/Nov/24/t1290590490vv0zjp3p541qmp2/10140s1290590509.png (open in new window)
http://www.freestatistics.org/blog/date/2010/Nov/24/t1290590490vv0zjp3p541qmp2/10140s1290590509.ps (open in new window)


http://www.freestatistics.org/blog/date/2010/Nov/24/t1290590490vv0zjp3p541qmp2/1nu2j1290590509.png (open in new window)
http://www.freestatistics.org/blog/date/2010/Nov/24/t1290590490vv0zjp3p541qmp2/1nu2j1290590509.ps (open in new window)


http://www.freestatistics.org/blog/date/2010/Nov/24/t1290590490vv0zjp3p541qmp2/2nu2j1290590509.png (open in new window)
http://www.freestatistics.org/blog/date/2010/Nov/24/t1290590490vv0zjp3p541qmp2/2nu2j1290590509.ps (open in new window)


http://www.freestatistics.org/blog/date/2010/Nov/24/t1290590490vv0zjp3p541qmp2/3nu2j1290590509.png (open in new window)
http://www.freestatistics.org/blog/date/2010/Nov/24/t1290590490vv0zjp3p541qmp2/3nu2j1290590509.ps (open in new window)


http://www.freestatistics.org/blog/date/2010/Nov/24/t1290590490vv0zjp3p541qmp2/4y31m1290590509.png (open in new window)
http://www.freestatistics.org/blog/date/2010/Nov/24/t1290590490vv0zjp3p541qmp2/4y31m1290590509.ps (open in new window)


http://www.freestatistics.org/blog/date/2010/Nov/24/t1290590490vv0zjp3p541qmp2/5y31m1290590509.png (open in new window)
http://www.freestatistics.org/blog/date/2010/Nov/24/t1290590490vv0zjp3p541qmp2/5y31m1290590509.ps (open in new window)


http://www.freestatistics.org/blog/date/2010/Nov/24/t1290590490vv0zjp3p541qmp2/6y31m1290590509.png (open in new window)
http://www.freestatistics.org/blog/date/2010/Nov/24/t1290590490vv0zjp3p541qmp2/6y31m1290590509.ps (open in new window)


http://www.freestatistics.org/blog/date/2010/Nov/24/t1290590490vv0zjp3p541qmp2/7qc071290590509.png (open in new window)
http://www.freestatistics.org/blog/date/2010/Nov/24/t1290590490vv0zjp3p541qmp2/7qc071290590509.ps (open in new window)


http://www.freestatistics.org/blog/date/2010/Nov/24/t1290590490vv0zjp3p541qmp2/8140s1290590509.png (open in new window)
http://www.freestatistics.org/blog/date/2010/Nov/24/t1290590490vv0zjp3p541qmp2/8140s1290590509.ps (open in new window)


http://www.freestatistics.org/blog/date/2010/Nov/24/t1290590490vv0zjp3p541qmp2/9140s1290590509.png (open in new window)
http://www.freestatistics.org/blog/date/2010/Nov/24/t1290590490vv0zjp3p541qmp2/9140s1290590509.ps (open in new window)


 
Parameters (Session):
par1 = 9 ; par2 = Do not include Seasonal Dummies ; par3 = No Linear Trend ;
 
Parameters (R input):
par1 = 9 ; 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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